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1 OBSERVATIONS AND MODELING OF PROCESSES IN ARTIFIC I ALLY INITIATED ( TRIGGERED ) LIGHTNING By CHRISTOPHER JOHN BIAGI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE RE QUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2011
2 2011 Christopher John Biagi
3 To my mother and father
4 ACKNOWLEDGMENTS First and foremost, I would like to thank my advisor, Dr. Martin Uman, for providing me wit h the best academic guidance at every step of my Ph.D. studies. His generous support made this work possible and I will always be grateful for his mentorship I would also like to thank Dr. Vladimir Rakov for so often lending his encyclopedic knowledge to me. I am grateful for the considerable experimental assistanc e of Dr. Douglas Jordan, and the help of Dr. Robert Moore I am indebted and grateful to Dr. Jay Gopalakrishnan for contributing his expert ise in numerical modeling. I thank Dr. William Bea sley for his assistance and Michael Stapleton for helping me with electronics design. I would like to acknowledge and give thanks to J ulia Jorda n for being an excellent assistant Many other people have contributed in various ways to this work that I would like to acknowledge and thank, including Terry Ngin, Dimitris Tsalikis, Dr. Amitabh Nag, Paul Anderson, George Schnetzer, Rob Olsen III and Shreeharsh Mallick. I would like to express special gratitude to Dr. Joseph Howard and Jonathan Hill, not only for their considerable contributions to this work, but for helping me transition to the field of electrical engineering, and for being great friends Finally, I would like to say that i t has been a great honor and privilege to work with all of the talented people in the Lightning Research Group at the University of Florida
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...............................................................................................................4 LIST OF TABLES ...........................................................................................................................8 LIST OF FIGURES .......................................................................................................................10 ABSTRACT ...................................................................................................................................14 CHAPTER 1 INTRODUCTION ..................................................................................................................16 2 LITERATURE REVIEW .......................................................................................................20 2.1 The Lightning Discharge ...............................................................................................20 2.2 Photography of Lightning .............................................................................................27 2.2 Rocket Triggered Lightning .........................................................................................30 2.2.1 Classical Triggered Lightning ..........................................................................31 184.108.40.206 Precursors ...........................................................................................33 220.127.116.11 The sustained upward positive leader .................................................35 2.2.2 Altitude Triggered Lightning ............................................................................37 2.3 Corona Space Charge Layer at Ground ........................................................................41 2.4 The Stepping Mechanisms of Long Negative Laboratory Discharges and Their Relationship to Lightning ..............................................................................................45 3 EXPERIMENT DESCRIPTION ............................................................................................58 3.1 Experiment Control .......................................................................................................61 3.1.1 PICs ...................................................................................................................62 3.1.2 Fiber Optic Links ..............................................................................................63 3.1.3 Control Computers ............................................................................................65 3.1.4 Rocket Launching Apparatus ............................................................................66 3.2 Waveform Digitization and Storage .............................................................................68 3.2.1 Yokogawa DL716 .............................................................................................68 3.2.2 Yokogawa DL750 .............................................................................................69 3.2.3 LeCroy LT344 Waverunner ..............................................................................70 3.2.4 LeCroy LT734 Waverunner 2 ...........................................................................70 3.2.5 Lecroy 44Xi ......................................................................................................70 3.2.6 MSE DSO Network ..........................................................................................71 3.2.7 Positive Lightnin g Experiment DSO Network .................................................71 3.3 Electric Field Mills ........................................................................................................73 3.4 Broadband Electric Field and dE/dt ..............................................................................74 3.4.1 The Flat Plate Antenna .....................................................................................74 3.4.2 Electric Field Sensor .........................................................................................80
6 3.4.3 dE/dt Sensor ......................................................................................................83 3.5 Channel Base Currents ..................................................................................................84 3.6 High Speed Video Cameras ..........................................................................................87 3.6.1 Photron SA1.1 ...................................................................................................87 3.6.2 Phantom V7.1 ....................................................................................................90 4 DATA ...................................................................................................................................118 4.1 Summary of Colle cted Data ........................................................................................118 4.2 Data Processing ...........................................................................................................118 4.2.1 Waveform Data ...............................................................................................119 4.2.2 Image Data ......................................................................................................120 5 OBSERVATIONS OF LIGHTNING LEADERS WITH HIGHSPEED VIDEO AND CORRELATED CHANNEL BASE CURRENT, REMOTE ELEC TRIC FIELDS, AND X RAY EMISSION ..............................................................................................................127 5.1 Observations of a Stepped Upward Positive Leader Initiating Triggered Lightning .128 5.2 Observations of Leader Stepping Mechanisms ...........................................................132 5.2.1 Dart Stepped Leaders in Classical Triggered Lightning .................................132 5.2.2 Downward Negative Stepped Leader in Altitude Triggered Lightning ..........135 5.3 Upward Positive Connecting Leaders .........................................................................139 5.4 Discussion ...................................................................................................................142 6 TRANSIENT CURRENT PULSES IN ROCKET EXTENDED WIRES USED TO TRIGGER LIGHTNING ......................................................................................................171 6.1 Data and Observations ................................................................................................172 6.1.1 Luminosity Associated with Precursor Current Pulses ...................................172 6.1.2 Precursor Current and Electric Field Signatures .............................................172 6.1.3 Precursor Rates ................................................................................................174 6.1.4 Negative Polarity Precursors ..........................................................................175 6.2 Analysis .......................................................................................................................176 6.2.1 Propagation Speed ...........................................................................................176 6.2.2 Precursor Charge and Current .........................................................................177 6.3 Modeling .....................................................................................................................178 6.3.1 Model Input .....................................................................................................178 6.3.2 Model Description ...........................................................................................179 6.3.3 Model Predictions ...........................................................................................185 6.4 Discussion ...................................................................................................................189 7 DETERMINATION OF THE ELECTRIC FIELD INTENSITY AND SPACE CHARGE DENSITY VERSUS HEIGHT PRIOR TO TRIGGERED LIGHTNING ..........210 7.1 The Wire Shielding Effect ..........................................................................................212 7.2 Data .............................................................................................................................213 7.2.1 Rocket Height and Wire Extension Rate ........................................................213 7.2.2 GroundLevel Quasi Static Electric Field Measurements ..............................214
7 7.2.3 Precursor Current in the Wire and Corresponding Charge Transfer ...............217 7.3 Modeling .....................................................................................................................219 7.3.1 Model Description ...........................................................................................219 7.3.2 Model Pr edictions ...........................................................................................221 7.3.3 Model Fit .........................................................................................................222 7.3.4 Model Predicted Line Charge Density ............................................................223 7.4 Discussion ...................................................................................................................224 8 SUMMARY OF RESULTS AND RECOMMENDATIONS FOR FUTURE RESEARCH .........................................................................................................................242 8.1 Summary .....................................................................................................................242 8.2 Recommendations for Future Research ......................................................................249 LIST OF REFERENCES .............................................................................................................251 BIOGRAPHI CAL SKETCH .......................................................................................................268
8 LIST OF TABLES Table page 31 Sensor locations at the ICLRT. ..........................................................................................92 32 M akes, models, and salient specifications of the DSO used at the ICLRT. ......................94 33 PLE DSO channel assignment. ..........................................................................................94 34 Electric field sensor configuration. ....................................................................................95 35 2008 channel base current measurements configurations. ................................................95 36 2009 channel base current measurement s. ........................................................................96 37 OU Photron configurations in 2008. ..................................................................................96 38 UF Photron configurations in 2008....................................................................................97 39 UF Photron configurations in 2009....................................................................................97 310 Photron framing rates, specified and actual. ......................................................................98 311 Ph antom configurations 2009 ............................................................................................99 41 Summary of triggering in 2008 and 2009. .......................................................................122 42 Summary of data acquired in 2008. .................................................................................122 43 Summary of data acquired in 2009. .................................................................................123 44 Summary of the triggered lightning flash from 2010. .....................................................123 45 Summary of return stroke ti mes and peak currents in 2008. ...........................................124 46 Summary of return stroke times and peak currents in 2009.. ..........................................125 51 Salient information for the stepped upward positive leader of UF0930. ........................149 52 Lengths and distances for the space stems and space leaders observed in event UF0925......................................................................................................................................150 53 Lengths and distances for the space stems and space leaders observed in event UF09 13......................................................................................................................................150 54 Upward positi ve connecting leader lengths. ....................................................................151
9 61 Precursor information, triggeringwire transmission line parameters corresponding to the model predicted precursor signatures that best match the measured precursor signatures, and the amplitude scaling factor of the input current pulse. ..........................195 71 Salient values of the quasi static ground level electric fields and the upward positive leader (UPL) initiation height. .........................................................................................230 72 The number of precursors, the height at which they first occurred, and the total ground level field change they produced. ........................................................................230 73 The initial stage (IS) duration, the time interval between the end of the IS and the first return stroke, and the duration of the return stroke stage.. .......................................231 74 Sa lient statistics of precursor charge and electric field change (sample size of 96). .......231 75 Model parameters the corresponding space charge density at ground, and the electric field and the e lectric potential at the triggering height. ...................................................231
10 LIST OF FIGURES Figure page 21 The four types of cloud to ground lightning, defined by the charge transfer to ground and direction of the leader. .................................................................................................53 22 The sequence of events in a natural, downward negative cloudto ground lightning flash. ...................................................................................................................................54 23 The sequence of events in a classical triggered lightning. .................................................55 24 Sequence of events in altitude triggered lightning. ............................................................56 25 Schematics illustrating the stepped development of the negative leader. ..........................57 31 The launch tower with the current interceptor installed. .................................................100 32 The layout of stations and buildings at the ICLRT. .........................................................101 33 The 2001 PIC controller. ..................................................................................................102 34 T he 2006 PIC controller. ..................................................................................................103 35 Schematic of the typical 2001 PIC installation.. ..............................................................103 36 Schematic of a typical 2006 PIC install ation. ..................................................................104 37 The launch tube apparatus. ..............................................................................................105 38 The bottom of the launch tubes showing a loaded rocket installation. ............................106 39 A Campbell Scientific field mill installation (LC field mill). ..........................................107 310 A field deployed flat plate antenna sensor. ......................................................................108 311 The frequency domain Norton equivalent circuit for the flat plate antenna. ..................108 312 Schematic of an electric field sensor configurat ion. ........................................................109 313 Picture of an RC box. .......................................................................................................109 314 Circuitry of the amplifier used in the electric field and II VLS current s ensors. ..........110 315 Amplifier circuit board mounted inside a Pomona box. ..................................................111 316 Flat plate antenna covered with a plastic dome. ..............................................................112 317 Schematic of the dE/dt measurement configuration. .......................................................112
11 318 Inside the 2008 shunt box. ...............................................................................................113 319 Current schematic for the 2008 current setup. .................................................................114 320 The 2009 tower current measurement configuration. ......................................................115 321 Schematic of the 2009 tower current configuration. ........................................................116 322 The high speed video cameras setup in the office trailer. ...............................................117 323 The Phantom V7.2 and the Photron SA1.1. .....................................................................117 51 High speed video images of the channel during the initial stage of UF09 30. ................152 52 The sequence of 60 Photron images containing the UPL for UF09 30, along with the synchronized wire base current. ......................................................................................153 53 The wirebase current associated with the ten upward positive leader steps in UF0930 that were imaged with highspeed video. ...................................................................154 54 High speed video images, and correlated electric field and current pulses for the dart stepped leader preced ing return stroke 8 of UF08 18. .....................................................155 55 Ten high speed video frames depicting the leader for the fifth stroke of UF0925 developing from 150 m height to ground during a time of 41.7 s. ................................156 56 Expanded and contrast enhanced reproductions of the bottom of the downwardextending leader channel seen in the first nine frames in Figure 5 5.. ............................157 57 The x ray emission, dE/dt, and tower current that were recorded during the time when the 10 images shown in Figures 55 and 56 were recorded. .................................158 58 An image of t he lower 200 m of channel for UF0913 recorded by the HD camera. .....159 59 A sequence of 64 images recorded at 108 kfps (9.3 s per image) showing the first downward negative stepped leader in U F09 13. ..............................................................160 510 The leader tip seen in Images 7 through 11 from Figure 5 9 enlarged by a factor of 4. .160 511 The leader tip s een in images 33 through 37 from Figure 59 enlarged by a factor of 4........................................................................................................................................161 512 The tip of a leader branch seen in images 56 through 59 from Figure 59 enlarged by a factor of 4. .....................................................................................................................161 513 The dE/dt record from dE 5 during the time when the downward negative stepped leader in UF09 13 was imaged. .......................................................................................162 514 High speed vide o images of the leader precedi ng return stroke 1 of UF0808. ..............163
12 515 High speed video images of the leader precedi ng return stroke 2 of UF0808. ..............164 516 High speed video images of the leader precedi ng return stroke 2 of UF0811. ..............165 517 High speed video images of the leader preceding return stroke 3 of UF0811. ..............166 518 High speed video images of the leader preceding return strokes 1 through 8 of UF0818......................................................................................................................................167 519 High speed video images of the leader preceding return stroke 9 of UF0913. ..............168 520 High speed video images of the leader precedi ng return stroke 2 of UF0917. ..............169 521 High speed video images of the leader prec eding stroke seven of UF09 27. .................170 61 Current signature of a precursor in which the first current pulse, and subsequent current pulses resulting from reflections from the wire base and wire top, are clearly separated in time and easily distinguishable. ...................................................................196 62 Current and electric field signatures produced by a precursor tha t exhibited an initial low level, steady current, and corresponding electric field ramp. ...................................197 63 The wirebase current, and respective electric field measured by E2 at 156 m for three precurso r signatures from event UF0911. .............................................................198 64 The wirebase current, and respective electric field measured by E2 at 156 m for three precursor signatures for wire launch UF0911 on a 2 s time scale. ........................199 65 The wirebase current, and respective electric field measured by E2 at 156 m for UF09 12 on a 1.3s time scale. ........................................................................................200 66 An expanded view of the wire base current and electric field of the precursors in UF09 11 viewed at 300 ms full scale. .............................................................................201 67 Wire base current and electric field signatures of negativepol arity precursors during wire launch UF0901. ......................................................................................................202 68 A scatter plot showing the measured current propagation speeds (the ratio of wire top height to one half of the average peak to peak times) versus wire top heights for 271 precursors. .................................................................................................................203 69 A scatter plot of the current peak ratios.. .........................................................................204 610 A scatter plot of the charge transferred to ground during the initial precursor current pulse versus the total charge transferred to ground by the end of the precursor current signature. ..........................................................................................................................205 611 The incident curre nt pulses that are used as inputs to the distributedcircuit model shown in Figure 612. ......................................................................................................206
13 612 The distributed circuit used to model the current propagation on the triggering wire, ground l ead, and ground rod. ...........................................................................................207 613 Measurement and modeling results for three precursors for two model grounding configurations.. ................................................................................................................208 614 The model predictions for precursor 3 with varied values of GTW and RTW. ..................209 71 Schematic illustrations of the ambient electric field before and after the extension of a triggering wire ..............................................................................................................232 72 The model wire trajectory. ...............................................................................................233 73 The groundlevel electric field changes and wire top heights versus time for Launch es 1 through 6. ......................................................................................................234 74 Field change versus wire top heights for Launches 1 through 6. ....................................235 75 An example of a precursor that pr oduced a static electric field change. .........................236 76 The vertical profiles of space charge density, electric field magnitude, and electric potential for the nine combinations of d and E values and E0 = 6 kV m1. ....................237 77 The model predicted groundlevel field changes for no space charge and the nine cases of exponentially decaying space charge density for E0 = 6 kV m1.. ......................238 78 The model predictions that best fit the measured electric field changes for Launches 1 through 6. ......................................................................................................................239 79 Examples of the m odel predicted height profiles of the radial electric field 5 m from the wire and equivalent approximate line charge density. ...............................................240 710 Triggering height versus initial groundlevel electric fi eld magnitude. ..........................241
14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy OBSERVATIONS AND M ODELING OF PROCESSES IN ARTIFIC I ALLY INITIATED (TRIGGERED) LIGHTNING By Christopher John Biagi August 2011 Chair: Martin A. Uman Cochair: Vladimir A. Rakov Major: Electrical and Computer Engineering From 2008 to 2010, data were obtained for 38 artificia lly initiated lightning flashes. Images from highspeed framing cameras and synchronized remote electric field s and current s are employed to study lightning leader initiation and propagation: (1) Optical images and wire base current s recorded during the de velopment of a stepped upward positive leader from the tip of an extend ing triggering wire are examined and compared with positive po larity long laboratory discharges (2) The space stem and space leader, processes known to play a significant role in the step wise propagation of long, negati ve polarity long laboratory discharges, have been observed for the first time in association with steps in two downward negative dart stepped leaders in classical triggered lightning flashes and in a downward negative stepped leader in an altitude triggered flash. These observations confirm a previous hypothesis that the lightning leader and the long laboratory leader develop in a similar manner, albeit on different scales of length, time, and voltage. (3) Prior to th e attachment phase, h igh speed framing cameras imaged a total of 15 upward positive connecting leaders and their associated downward negative leaders within tens of meters of each other T he ir development and eventual attachment are examined.
15 In addition to the primarily optical measurements noted above, i nferences are made of t he vertical profiles of space charge density and electric field intensity above ground as well as the line charge density that forms along the extend ing triggering wire in response to the ambient electric field. These inferences are made by comparing modeling and measurements of the ground level electric field changes caused by the vertical extension of six grounded lightning triggering wires that initiated lightning T he sustaine d upward positive leader inception heights and the groundlevel electric field intensity at the wire launch time were linearly correlated with a correlation coefficient of 0.85. The transient current, electric field, and optical signatures produced by the sudden electrical breakdown processes (precursors) that occur at the top of the upwardextending lightning triggering wires are examined. The lightning triggering wire and its grounding system are modeled as uniform transmission lines with model predict ions that are consistent with the measured wire base precursor current signatures.
16 CHAPTER 1 INTRODUCTION The work presented in this dissertation represents the culmination of four years of research by the author on artificially initiated ( triggered ) lig htning at the University of Florida/Florida Institute of Technology International Center for Lightning Research and Testing (ICLRT) at Camp Blanding in northcentral Florida Th e purpose of the research was threefold: (1) T o use high speed video images and synchronized current and remote electric field waveform s to build upon the existing knowledge pertaining to the initiation and propagation mechanisms of lightning leaders. An an cillary goal was to demonstrate the utility of modern digital high speed video cameras, a research tool that is facilitating a new era of lightning research that will help unravel some of the long standing mysteries of lightning physics. (2) T o examine the electrical environment into which the grounded, lightningtriggering wir es are launched. This examination involved comparing measurements and modeling of the groundlevel electric field change during the vertical extension of the wire in order to infer vertical profiles of ambient electric field, space charge density, and the charge density that forms along the wire in response to the ambient electric field. (3) T o characterize the sudden electrical breakdown processes (precursors) that occur at the top of the grounded lightning triggering wires through analysis of t he curren t, electric field, and optical signatures they produce. Part of this characterization involved modeling the propagation of the current pulses on the triggering wire to determine the wires transmission line characteristics. Chapter 5 presents new observ ations and discoveries pertaining to lightning leaders, incl uding their propagation and initiation, and attachment mechanisms made from the highspeed video images and synchronized waveform data The most important contributions in Chapter 5 are summarized as follows: (1) The lower 12 m of an upward positive leader developing in a
17 stepped manner from the tip of a triggering wire was imaged at 300 kfps (3.3 s per frame) with synchronized current pulses detected at the wire base, and t he currents and charg es associ ated with positive leader steps were measured. (2) I ndividual steps in two downward negative dart stepped leaders in separate classically triggered lightning flashes, and in a downward negative stepped leader in virgin air in an altitude triggere d lightning flash were resolved temporally and spatially in high speed video images The highspeed video images show that the negative leader step in lightning develops via similar mechanisms as do negative leaders steps in laboratory sparks, namely thr ough the formation of space stems and space leaders in the streamer zone below the previously formed leader tip. (3) Upward positive connecting leaders and their corresponding downward negative leaders just prior to the attachment phase in triggered lightning were observed in highspeed video images The lengths of upward positive connecting leaders in triggered lightning have been measured, and it was observed that attachment heights can vary from stroke to stroke in a flash. C hannel base current and remote electric field observations indicate that the observed upward positive connecting leaders did not develop stepwise. In one image, the streamer zone of a downward negative dart stepped leader appears to be in contact with the upward positive connecting leader. Chapter 6 presents new observations of precursors and an examination of the propagation of transient current pulses on a triggering wire, and the transmissionline characteristics of the wire itself The most important new contributions in Cha pter 6 are as follows: (1) Luminous l eader channels associated with the precursors to the sustained upward positive leader were resolved for the first time, some of which reached 8 m in length. (2) Measurement s of the wire base precursor current signatur es have shown that transient current pulses propagate on the vertically extend ing triggering wire with a speed that is 10 to 20% slower than that of light, and
18 with a speed that decreases with increasing wire length s (3) P recursors were observed to somet imes occur rapidly ( every few hundreds of microseconds) with a rate that is inversely related t o their peak current amplitudes throughout the wire extension. (4) N egative polarity electrical breakdown was detected at the tip of triggering wires launched i n electric fields consistent with predominately positive charge was overhead. (5) The triggering wire and its grounding system were modeled as uniform transmission lines, and the model predictions of the wire base precursor current signatures were consist ent with the measured wire base precursor current signatures. The model was used to infer the distributed circuit characteristics of the triggering wire and the grounding system T he current reflection coefficient at the connection of the triggering wire to ground was found to be about 0.9, and the attenuation constant for a current pulse propagating on the wire was found to be about 8.2 x 104 Neper m1. In Chapter 7, inferences are made of the vertical profiles of electric field and space charge density and the line charge density contained in the corona sheath along a triggering wire is examined. The most important new contributions found in Chapter 7 are as follows: (1) F inite element modeling yielded ground level electric field changes that were co nsistent with measurements during several wire launches with groundlevel charge densities between 1.5 and 7 nC m3, space charge exponential height decay constants ranging from 67 to 200 m, and uniform electric field intensities far above the space charge layer ranging from 20 to 60 kV m1. (2) F inite element modeling predicted that the radial electric field along the wire increased with height and wa s of sufficient strength to produce a corona sheath having a radius of up to 5 m. The predicted radial el ectric field would require the charge per unit length contained by the corona sheath to increase steadily from less than 1 C m1 to about 60 C m1 at wire heights from 1 m to 285 m. (3) A strong inverse correlation was found between the triggering height and
19 the groundlevel electric field magnitude at the time that the wire was launched for six wire launches. In addition to the new contributions to lightning research presented in Chapters 5, 6 and 7, a review o f relevant literature is given in Chapter 2 and the experimental setup and equipment are described in Chapter 3. Chapter 4 summarizes the data, and describes how it was processed. Finally, a summar y of the results presented in this work and suggestions for future research are given in Chapter 8.
20 CHAPTER 2 LITERATURE REVIEW 2.1 The Lightning Discharge The term lightning is applied to transient, highcurrent electric discharges in the atmosphere with a length on the order of kilometers [ Uman 1987]. Thunderstorms are the primary source of lightning, although lightning is known to originate from volcanic plumes [e.g., Thomas et al ., 2007] and nuclear explosions as well [e.g., Uman et al., 1972]. All references to lightning herein refer to the type involved with thunderclouds. The vast majority of lightning, as much as 75%, occurs within clouds (intracloud) or between clouds (intercloud) [e.g., Williams et al., 1989; Rakov and Uman, 2003]. Cloudto ground (CG) lightning is the most deleterious type to humans; it kills an estimated 100 people and causes several hundred million dollars worth property damage per annum in the Uni ted States alone [ Rakov and Uman, 2003]. Given its impact on humans, it is understandable that the CG lightning discharge (also called CG flash) is by far the most studied form of lightning. There are four types of CG flashes, illustrated in Figure 2 1, a nd these can be characterized by the direction of the initial leader and the overall charge transferred to ground [ Berger et al. 1975; Rakov and Uman, 2003]: (1) downward negative, (2) upward negative, (3) downward positive, and (4) upward positive. Note that for the upward negative type, the initial upward leader is of positive polarity, and for the upward positive type, the initial upward l eader is of negative polarity. Nearly all lightning is the downward type, and upward lightning of either polarity is believed to only begin from the tips of tall structures or mountain tops where the electric field can be enhanced by the local topography. It is estimated that 90% of all CG flashes are of the downward negative type, with the remaining 10% being the do wnward positive type [e.g., Rakov and Uman, 2003].
21 The downward negative CG lightning apparently begins with a distinct process known as preliminary breakdown or initial breakdown that leads to the development of a downwardmoving stepped leader. Evidenc e for initial breakdown consists of observations of cloud luminosity lasting for a hundred or more milliseconds prior to a stepped leader emerging from the cloud, and relatively long electric field changes exceeding 100 ms in duration [ Rakov and Uman 2003]. The initial breakdown is likely the development of a channel between the negative and lower positive charge regions of a cloud [ Clarence and Malan, 1957], or multiple discharges with significant horizontal extent originating from the main negative char ge region [ Krehbiel et al ., 1979; Rhodes and Krehbiel 1989]. The stepped leader inception is associated with a train of bipolar electric field pulse s having an initial half cycle polarity that is the same as that of the following return stroke field chan ge [ Kitagawa and Brook 1960; Weidman and Krider 1979; Beasley et al. 1982; Rakov et al., 1996; Nag and Rakov 2009]. The train of bipolar pulses typically lasts for about 1 millisecond, and precedes the first return strokes by several tens of milliseco nds. The electric field pulses have durations of 20 to 40 s and occur on time intervals between 70 and 130 s [ Rakov et al., 1996]. The sequence of events in a typical downward negative CG lightning flash after a stepped leader has emerged from the clo ud is illustrated in Figure 22. A leader is defined as a self propagating electrical discharge that creates a channel with electrical conductivity of the order of 104 S m1 [ Rakov and Uman 2003]. The first downward negative leader in a CG flash is cal led a stepped leader because it develops intermittently, extending in length seemingly through a sequence of steps. The i ntermittent progression of downward propagating, negatively charged stepped and dart stepped leaders was first reported by Schonland [ 1935], motivating further studies of the development of stepped leaders. Stepped leader speeds have been found to
22 typically be in the range from about 105 to 106 m s1 [e.g., Schonland, 1956; Berger and Vogelsanger 1966; Orville and Idone 1982; Chen et al., 1999; Proctor et al., 1988; Shao et al., 1995]. Lengths of stepped leaders have been observed ranging from a few meters up to 200 m, and interstep intervals are typically between 5 and 100 s [ e.g., Schonland, 1956; Berger and Vogelsanger, 1966; Krid er et al. 1977; Chen et al., 1999]. The total charge deposited by a stepped leader just before ground contact is around 5 C, the line charge density ranges from 104 to 103 C m1, and the average current is tens to hundreds of amperes [e.g., Rakov and U man 2003]. Electric field waveforms have indicated that peak stepped leader currents are on average about 1 kA, but can reach levels as high as 8 kA [e.g., Krider et al. 1977; Krehbiel 1981; Th omson et al., 1985]. Howard et al.  using transmiss ion line modeling to reproduce measured electric field waveforms from leader steps, inferred peak currents for leader steps ranging from 5 to 7 kA, and a step charge of about 300 mC. Howard et al.  also demonstrated that leader step currents likely have a slow front that is similar to the slow front in return stroke currents. When the downwardmoving negative stepped leader reaches a height of several tens of meters, the electric field at ground is significantly enhanced due to the potential differen ce between the leader and ground, on the order of tens of megavolts, and probably on the order of the cloud potential [ Bazelyan et al., 1978]. In response to the enhanced electric field, one or more upward positive leaders develop from local ground object s or the ground itself, beginning the attachment process. It is thought that the relatively low conductivity streamers at the tips of the downward negative and upward leader meet to form a common streamer zone in which the two leaders accelerate towards e ach other [ Rakov and Uman, 2003]. The breakthrough phase occurs when the two leaders meet, which can be viewed as a switch closing operation that
23 launches return stroke waves in both directions [e.g., Wagner and Hileman, 1958; Uman et al., 1973; Weidman and Krider 1978; Willett et al. 1988; Willett et al. 1989; Leteinturier et al. 1990; Rakov and Uman, 2003; Jerauld et al., 2007]. The upward leader that connects to the downward leader is called an upward connecting leader. Yoko yam a et al.  repor ted time resolved optical observations, using t he ALPS optical imaging system, of upward connecting leaders ranging from 25 to 150 m in length from an 80m tall communications tower in Japan, and estimated that their speeds ranged from 0.8 x 105 to 2.7 x 105 m s1. Wang et al. [1999a], also using the ALPS system, estimated a propagation speed of 2 x 107 m s1 for one upward positive connecting leader in a triggered lightning stroke. Several researchers have reported observing in streak photography a return stroke beginning while the downward leader was some 20 to 50 m above ground, and inferred that an upward connecting leader too faint to be imaged intercepted the downward leader [ Golde, 1947; Berger and Vogelsanger 1966; Wagner, 1967; Orville and Idone 1982] Observations of loops and upward branches in lightning channels a few tens of meters above ground [e.g., Golde 1967; Orville, 1968; Hagenguth, 1947] or unconnected upward discharges in the vicinity of a the ground strike point of lightning chann els [e.g., Krider and Ladd, 1975; Rakov and Uman, 2003] indicate that upward connecting leaders play a significant role in the attachment process Upward connecting leaders a few tens of meters in length have been inferred in several triggered lightning strokes, which are similar to subsequent strokes in natural lightning [ Idone et al ., 1984; Idone 1990]. Using the ALPS optical imaging system, Wang et al. [1999a] observed in triggered lightning strokes in Florida one upward connecting leader that was 7 to 11 m in length, and inferred the existence of another one that was 4 to 7 m in length. The observed upward connecting leader lasted several hundred nanoseconds and had a luminosity that was an
24 order of magnitude lower than that of its associated downwa rd dart leader. Connecting leaders are not always observed for subsequent strokes, and they are typically shorter in length than those for first strokes. From streak photography in Florida and New Mexico, Orville and Idone  observed 21 dart leaders and 3 dart stepped leaders that showed no indication of upward connecting leaders. New observations of upward positive leaders in triggered lightning are presented in Chapter 5 of this work When the downwardmoving leader meets with an upward connecting leader, the return stroke phase begins. Initially, there is an upwardpropagating return stroke wave and a downwardpropagating return stroke wave. The downwardpropagating return stroke wave quickly reaches ground, and a reflected, upward propagating w ave is produced. Since the reflected wave propagates up in a returnstroke conditioned channel, it likely travels faster than and catches up to the initial upward propagating return stroke wave [ Rakov 1998]. The bi directional return stroke waves are sh ort lived, and a single upward moving wave quickly forms [ Rakov and Uman, 2003]. Of all the process es comprising a lightning flash, return strokes cause the most damage, produce the brightest luminosity and a distinct electromagnetic signature [ Rakov and Uman 2003]. Thus, the return stroke has been observed and studied extensively. Return strokes in negative cloudto ground lightning typically: have a peak current of 30 kA, transfer a charge of 5 C, propagate at speeds ranging from 1 x 108 to 2 x 108 m s1, and have a peak channel temperature on the order of 30,000 K [ Rakov and Uman, 2003, Table 1.1]. Return strokes are one of three ways charge is transferred by lightning from the cloud to the earth, the other two being continuing current and M components.
25 In about 80% of downward negative lightning, subsequent leader/return stroke sequences follow the first return stroke. Kitagawa et al  observed in New Mexico a CG flash containing 26 return strokes. However, CG flashes typically have 3 to 5 leader/return stroke sequences, and 1.7 ground contact points [ Rakov et al., 1994; Rakov and Uman, 2003]. About half of CG flashes in New Mexico and Florida have more than one ground contact point [ Kitagawa et al., 1962; Rakov and Uman, 1990]. Biagi et a l.  based on 16.7ms time resolution video observations, reported that 444 of 2338 (19%) and 126 of 338 (37%) of subsequent strokes in Southern Arizona and Texas/Oklahoma, respectively, struck ground at new locations. Saraiva et al.,  reporte d that 49% of 344 flashes observed in Arizona and near Sao Paulo, Brazil had more than one ground contact point. Subsequent return strokes that follow channels to ground that have been pre conditioned by previous strokes are preceded by dart leaders or dar t stepped leaders. The dart leader appears to develop continuously, that is, without stepping. Optical measurements show that dart leaders propagate faster than stepped leaders, with speeds typically on the order of 106 to 107 m s1 in natural lightning [e.g., Schonland et al., 1935; McEachron, 1939; Orville and Idone 1982; Jordan et al., 1992; Mach and Rust 1997] and in triggered lightning [e.g., Hubert and Mouget 1981; Idone et al., 1984; Jordan et al., 1992; Mach and Rust 1997]. Dart leader speeds have been observed to increase or decrease near ground [e.g., Schonland et al., 1935; Orville and Idone 1982; Jordan et al., 1992; Wang et al., 1999b]. Jordan et al.  observed in Florida that dart leader speeds and the following return stroke peak cur rents are positively correlated. These observations led Rakov  to infer that the dart leader propagation characteristics are determined primarily by the leader current wave magnitude, as opposed to the channel conditions ahead of the wavefront
26 The occurrence of dart stepped leaders preceding subsequent strokes is apparently related to the cumulative conditioning (or the lack of it) of the lightning channel, as first hypothesized by Rakov et al. (1994). Rakov and Uman  gave a histogram sho wing the percentage of dart stepped leaders occurring after an interstroke interval of 100 ms or less as a function of stroke order for 76 negative CG flashes near Tampa, Florida. The histogram shows that second strokes are initiated by dart stepped leade rs more often than all other stroke orders combined. The geometric mean of the interstroke interval preceding the 13 second strokes initiated by dart stepped leaders was 54 ms. Davis  observed in dE/dt measurements in Florida that dart stepped lead ers that initiated second strokes occurred after a typical interstroke interval of 61 ms. Davis  found that dart stepped leaders initiating strokes of higher order were preceded by a typical interstroke interval of 140 ms. The six dart stepped lead ers discussed by Schonland  preceded second strokes. Dart stepped leader develop with speeds on the order of 106 m s1 and, like the dart leader, the dart stepped leader apparently may increase or decrease its speed as it approaches ground [ Orville and Idone 1982; Davis 1999; Wang et al., 1999b]. Davis  reported a clear tendency for the downward dart stepped leader speed to decrease with decreasing altitude, from a mean of 1.6 x 107 m s1 at heights between 3 and 6 km, to 3.5 x 106 m s1 below heights of 1 km. Schonland  reported that leader step lengths in natural dart stepped leaders near ground were on average 10 m and the interstep time interval was typically 10 s. Orville and Idone  analyzed four dart stepped leaders in detail, and reported step lengths from a few meters to several tens of meters, interstep time intervals from several to tens of microseconds. In one stroke analyzed by Orville and Idone  the interstep time interval increased and the propagation spe ed decreased with decreasing height, and in another the opposite was observed. Idone and Orville  reported for two dart stepped
27 leaders in triggered lightning dart stepped leader that step length s ranged from 5 to 10 m, and interstep time intervals ranged from 2 to 8 s. Krider et al. , from electric field pulses 200 s before the returnstroke onset, found that the mean i nterstep time interval for dartstepped leaders in Florida and Arizona was 6.5 and 7.8 s, respectively. These times are s horter than the mean interstep time interval for stepped leaders reported in the same study, 16 and 25 s for Florida and Arizona, respectively. Davis  reported that interstep time intervals increased with decreasing altitude, from 1.6 s near the l eader origin to 4.1 s near ground. Wang et al. [1999b] reported that luminosity waves that began at the leader tip and traveled up the leader channel were associated with dart stepped leader steps. Rakov et al.  estimated for a dart stepped leader in triggered lightning that the charge and current associated with each step is a few millicoulombs and a few kiloamperes, respectively. New observations of a dart stepped leader in triggered lightning are presented in Chapter 5 of this work 2.2 Photogr aphy of Lightning T he first quantitative measurements of lightning were made with photography in the late nineteenth century. Kayser  in a still photograph of a single flash, spatially resolved return strokes in a flash that were separated by a st rong wind. Hoffert  and Weber  were the first researchers to attain photographs of lightning with crude temporal resolution by moving cameras photographing lightning. Hoffert  managed to observe that the first return stroke was branched that there was continuing luminosity between return strokes, and was able to estimate interstroke interval times. The se features, and their causes, are still studied today. Walter [1902, 1903, 1910, 1912, and 1918] using time resolved photography, was apparently the first to photograph the leader preceding a first return stroke. Larsen , using a moving camera in the United States, measured interstroke time intervals and imaged what
28 appeared to be 40 return strokes in a single flash, although many of these were likely M components. The invention of the two lens streak camera by Boys [ Boys, 1926; Boys 1928; Boys 1929] led to significant advances in lightning research made by B. F. J. Schonland, D. J. Malan, and their co workers in the 1930s in S outh Africa. A detailed review of these findings is given in Uman , but some are worth mentioning here. Schonland and Coll e ns  provided the first evidence in streak photography of return strokes moving from the ground to the cloud, with a mean speed of 3.8 x 107 m s1. They also reported a mean dart leader speed of 1.1 x 107 m s1. Schonland et al.  reported the first observations of the stepped leader preceding the first stroke in a flash, and the existence of dart stepped leaders. T hey measured an effective stepped leader speed of 1.5 x 105 m s1. Schonland  reported that step lengths varied from 10 to 200 m. M components were studied by Malan and Coll e ns  and Malan and Schonland . Schonland  reported a cum ulative frequency distribution of the number of return strokes per flash in 1,800 cloudto ground flashes showing that 50% of them consisted of four or more return strokes Other researchers have performed similar studies of natural lightning using streak photography [e.g., Hagenguth, 1947; Workman et al., 1960; Kitagawa et al., 1962, Brook et al. 1962; Orville and Idone 1982; Jordan et al., 1992, 1995, 1997]. Streak photography has been used to study lightning to tall buildings and towers that are known to be struck multiple times each year. McEachron [1939, 1941], and Hagenguth and Anderson  studied light ning to the Empire State Building in New York City, NY, using photographic observations with simultaneous oscilloscopic measurements of lightning currents. McEachron  reported the discovery of the upwardstepped leader, and continuing currents and corresponding luminosities lasting 0.5 s or longer. A majority of the flashes to the Empire
29 State Building were found to be the upward type, beg inning with a stepped leader that develop ed from the building to the cloud, with the tower currents increased steadily to smooth continuous current s. Dart leader/return stroke sequences sometimes occurred during the continuous current in different channel s (branches) Berger and Vogelsanger  studied lightning striking instrumented towers on Monte San Salvatore using streak photography. They observed that stepped leaders of both polarities can travel upwards from towers/buildings, or downward from t he clouds, and that there are distinct differences between negative and positive polarity steps. In some streak photographs of upwardnegative stepped leaders, Berger and Vogelsanger  reported observing corona like discharge up to 3 m in length exte nding from the leader tip. Streak photography has helped to elucidate the sequence of events that occur in rocket and wire triggered lightning [e.g., Fieux et al. 1978; Horii 1982; Hubert et al., 1984; Laroche et al., 1988; Idone 1992; Lalande et al., 1998; Rakov et al. 2003; Olsen et al., 2006]. Fieux et al.  using streak photography, were the first to resolve the upward positive leader, the wire destruction, the initial stage current, and return strokes in triggered lightning in France. Sever al other studies of triggered lightning with streak photography have examined upward connecting discharges [ Idone 1990], the relationship between luminosity and channel base current [ Idone and Orville 1985], channel tortuosity [ Idone and Orville 1988; I done 1995], and dart leader speeds [ Jordan et al., 1992]. Another photographic instrument that has been used to study lightning is the highspeed framing camera, which are often called high speed video cameras because the images can be displayed as a video sequence. Kito et al.  used a highspeed framing camera operating at 1,000 frames per second (1 kfps) to study triggered lightning during the winter season in Japan. Evans and Walker  photographed lightning an area of about 8 m x 11 m at a tower top on
30 Mount Bigelow near Tucson, AZ from a distance of about 110 m using a high speed framing camera operating with a 2 s exposure time (with 77 s between frames). Their images provided data on lightning channel radius, luminosity verses tim e, and changes in channel geometry during and between return strokes. In the past decade or so digital highspeed video cameras have played an important role in observations of lightning related transient luminous events above cloud tops [e.g., Stanley e t al. 1999; Cummer and Stanley 1999; Moudry et al., 2002; Cummer et al. 2006; Marshall and Inan, 2005; Stenback Nielsen and McHarg, 2008], and researchers have been making new observations of cloudto ground lightning [e.g., Ballarotti et al., 2005; Qie and Kong, 2007; Saba et al., 2008; Zhang et al., 2009; Kong et al., 2009; Warner et al. 2011] 2.2 Rocket Triggered Lightning The method of triggering lightning by quickly extending a thin wire using a rocket was first advanced by Newman . Brook et al.  demonstrated that rapidly introducing a thin wire into the electric field of a laboratory spark gap could trigger a discharge, whereas having the same wire stationary in the gap did not produce a spark. The first triggered lightning discharges were produced by Newman et al. in 1960 by using rockets to quickly extend thin wires into the air from a boat off the west coast of Florida [ Newman 1965; Newman et al., 1967; Newman and Robb, 1967]. The first triggered lightning over land was done i n 1973 at Saint Privat dAllier in France [ Fieux et al. 1975; Fieux et al. 1978]. These ground breaking experiments led to similar triggered lightning programs, as summarized in Table 7.1 in Rakov and Uman [2003, pg. 266] in Japan [ e.g., Horii 1982; Kito e t al. 1985; Nakamura et al. 1991; Nakamura et al., 1992], at Langmuir Laboratory in New Mexico [e.g., Hubert et al ., 1984; Idone et al. 1984], at the Kennedy Space Center in Florida [e.g., Eybert Berard et al., 1986; Willet, 1992], at various sites in China [e.g., Liu et al. 1994; Liu and Zhang, 1998 ], at Camp Blanding,
31 Florida [e.g., Uman et al. 1997; Rakov et al. 1998], and at Cachoeira Paulista Brazil [e.g., Saba et al. 2000; Saba et al., 2005]. Triggered lightning is relatively easy to study si nce researchers can essentially control the time and place in which it occurs. Further, direct channel base current measurements can be made for triggered lightning [e.g., Hubert et al., 1984; Horii and Ikeda, 1985; Leteinturier et al. 1991; Fis her et al ., 1993; Depasse 1994; Uman et al., 2002; Kodali et al., 2005; Wang et al., 2005; Schoene et al., 2009; Schoene et al., 2010] in contrast to the current measurements for natural lightning that have been made on tall towers [e.g., Berger et al. 1975] or inferred from the radiated fields. The tower currents can be influenced, or contaminated by the transient process that occur in the tower due to transmission line effects [e.g., Gorin and Shkilev 1984; Zundl 1994; Rakov 2001] Triggered lightning al so provides the means to study lightnings effect on structures, such as buildings and power transmission lines [ e.g., Nakamura et al., 1991; Rakov et al. 2002; DeCarlo et al. 2008] Triggered lightning can be us ed to validate models with current being a parameter [e.g., Rakov and Uman, 1998] and to validate location systems like the U.S. National Lightning Detection Network (NDLN) [ Jerauld et al., 2005; Nag et al., 2011] In the following, the classical and altitude types of rocket and wire triggered l ightning are described In the classical type, the triggering wire is attached to ground. In the altitude type, the triggering wire is extended so that its bottom end is up to several hundred meters above ground. Literature regarding triggered lightning experiments and observations will be reviewed with emphasis placed on reports of the leader process. 2.2.1 Classical Triggered Lightning The sequence of events in classical triggered lightning is depicted in Figure 23. The triggering process begins with the launching of a rocket trailing a grounded, thin metallic wire
32 into a thunderstorm environment w hen at ground intensified electric fields are observed The rocket quickly accelerates to a maximum speed of about 160 to 200 m s1. After extending for a time of 1 to 3 s, with the wire tip reaching a height between about 100 and 300 m, the electric field at the wire tip is sufficiently enhanced to launch a sustained upward positive leader (UPL) from the triggering wire tip that develops upward with a spee d between 104 to 106 m s1 [ e.g., Fieux et al. 1978; Kito et al. 1985; Laroche et al., 1988; Idone 1992; Biagi et al. 2009; Yoshida et al. 2010] The upward positive leader establishes a conductive channel between the cloud and ground, and leads to t he initial continuous current (ICC) phase. The triggering wire explodes from Joule heating several milliseconds to tens of milliseconds after the upward positive leader inception, effectively disconnecting the upward positive leader from ground. The wire explosion is typically associated with the so called initial current variation (ICV) [ e.g., Wang et al., 1999c; Rakov et al., 2003; Olsen et al. 2006] The ICV is preceded by a rise in current of several hundred amperes over a time of milliseconds, foll owed a rapid drop in current over a few hundred microseconds, sometimes to zero or near zero The resultant current cut off (or nearly cut off) is followed by a leader/ return stroke like process that re establishes the current flow. Following the wire ex plosion and its replacement by a plasma channel the initial continuous current flows for some hundreds of milliseconds, with a geometric mean current of about 100 A [ Wang et al. 1999c; Miki et al. 2005]. Yoshida et al.  reported maximum initial stage current of 18 kA for a flash triggered in an intense thunderstorm. O ften i mpulsive current features (ICC pulses) that resemble the M component mode of charge transfer occur during the ICC [ Wang et al., 1999a ; Rakov et al. 2003; Miki et al. 2005; Yoshida et al. 2010]. After the ICC, there is typically an interval lasting some tens of milliseconds with no channel base current. Then, one or more downwardleader/upward return stroke sequences may
33 occur that are guided to ground by the channel that has been established by the initial stage current These leader/return stroke sequences are similar to subsequent strokes in natural lightning [ e.g., Rakov and Uman, 2003] In some cases the downward negative leaders are dart stepped (some cases are presented in Chapter 5 of this work ). Dart stepped leaders in triggered lightning can exhibit some similarities to stepped leaders in natural lightning, including discrete dE/dt pulse bursts and x ray emission [e.g., Howard et al., 2010] 18.104.22.168 Precursors In rocket and wire triggered lightning, transient current pulses in the triggering wires are observed at ground before the development of a sustained upward positive leader from the wire tip. The current pulses are caused by electrical breakdown at the tip of wire where the electric field is significantly enhanced The triggering wire behaves like a transmission line with the precursor pulse round trip propagation time on the wire being greater than the pulse width. Current pulse reflections are produced at the ground and at the wire tip. As a result, t he current signature from a single precursor observed at ground is a sequence of pulses of alternating polarity and decreasing amplitude. Horii  identified pre discharge current pulses that were recorded at a 5 kHz sampling rate. Horiis current pulses occurred both as isolated events and in groups ( two or more pulses occurring with intervals of several tens of microseconds) and had amplitudes between 0.1 A to 100 A. Laroche et al.  observed current pulses and associated electric field pulses occurring p rior to the inception of a sustained upward positive leader with intervals of some tens of milliseconds in isolation or in groups, with the pulses with in groups occurring about every 25 s. H igher magnitude current pulses exhibited dampedoscillatory behavior, and the oscillation period increased with increasing wire length, leading Laroche et al.  to hypothesize that the current pulse oscillations represented the transient response of t he triggering
34 wire. Lalande et al.  observed that damped oscillatory current pulses were separ ated in time by 5 ms on average and lowered to ground several tens of microcoulombs. Willett et al.  gave examples of dampedoscillatory current pul ses before the initiation of a sustained upward positive leader along with corresponding dampedoscillatory ele ctric field signatures resulting in a static electric field change. Willett et al.  reported that the pulses occurred roughly every 10 ms and someti mes occurred in groups in which individual pulses occurred roughly every 30 s. The electrical breakdown that produces the current pulses preceding the inception of a sustained upward positive leader were first termed precursors by Willett e t al. . Lalande et al  speculated that the damped oscillatory current waveforms are caused by aborted leader channels developing from the wire tip. The leader channels stop elongating when the electric field intensity above the leader channel is below the level required to sustain the leaders propagation. Biagi et al  reported observations of two luminous channels at the triggering wire tip that were time correlated with two wire base current pulses, confirming that the observed curre nt pulses were associated with aborted leader channels at the wire tip. The aborted leader channels had observed lengths of 1.5 and 8 m at heights of 128 and 158 m above ground level, respectively, and had luminosity similar to that of the sustained upwar d positive leader. Biagi et al.  noted that no luminosity could be detected in association with several other precursor current pulses in the same triggering wire launch perhaps indicating that lower luminosity processes such as corona or corona st reamers produce at least some of the observed current pulses. New observations of luminous channels in association with precursor current pulses are given in Section 6.2.1.
35 22.214.171.124 The sustained upward positive l eader There are few reports in the literatu re of highly time resolved optical observations of the development of the sustained upward positive leader in artificially triggered lightning [ Rakov and Uman, 2003]. Laroche et al.  reported observing in streak photography stepped upward positive l eader developing with a mean step length of 14 m, a mean interstep period of 20s interstep, and a mean speed of 5 x 105 m s1. The upward positive leader discussed in Laroche et al.  was only imaged for heights above 1 km. A streak photograph of an upward positive leader in triggered lightning was taken by Dr. Vincent Idone at the Kennedy Space Center in 1988, and is presented in Rakov and Uman [2003, pg. 271]. The streak photograph shows the upward positive leader developing with pronounced stepping, and increasing speed and luminosity with increasing height. The upward positive leader image by Idone apparently switched from a stepped to a continuous propagation mode and back. Luminosity waves evidently began from the leader tip and traveled do wn the channel. Rakov and Uman  note that for Idones upward positive leader, the interstep period was about 20 s, the speed was 1.2 x 105 m s1 when it was first imaged, and 6.5 x 105 m s1 when it exited the field of view. Idones leader was apparently first imaged when it was about 300 m above the triggering wire, and when the leader was imaged, the wire length was unknown. Horii and Nakano  gave an example of an upward positive leader propagating continuously. Yoshida et al. [2010 ] us ing VHF interferometery, give observations of two upward positive leaders in a relatively intense thunderstorm. The VHF sources for the first upward positive leader (in flash UF0929) moved from an altitude of 1.1 km to 2.4 km and over a horizontal distance of 1.4 km with an average 3D speed of 2.2 x 106 m s1. The lower few hundred meters of the second upward positive leader was observed in high speed video. The 2D speed of the second leader increas ed in speed, from 1.2 x 104 m s1 to 2.1 x 105 m s1 for
36 heights from 123 m to 325 m above ground. The newly added channel segments for the second leader increased in length and luminosity in successive highspeed video frames, indicating the step lengths were increasing, or that steps were occurring with an increasing rate. The VHF source locations for the second leader (in flash UF0930) moved from an altitude of 1.5 km to 3.7 km and over a horizontal distance of 2.7 km with an average 3D speed of 3.3 x 106 m s1. Yoshida et al.  argued that the i ncreasing speed with increasing altitude was likely due to the decrease in air pressure and increase in electric field with altitude [ Stolzenburg et al., 2002]. The first and second upward positive leaders presented by Yoshida et al.  were associated with unusually intense channel base currents During the time when VHF sources were located for the first leader, about 620 s, the channel base current increased from about 3.3 kA to a peak of 6 kA, with 2 to 4 kA pulses occurring during this rise. D uring the time when VHF sources were located for the second leader, about 1.3 ms, the channel base current increased from about 3.1 kA to about 18 kA, with six large current pulses occurring during this rise, the largest having a peak magnitude of 9.7 kA ( ab ove the steady current level). The current s during the development of the upward positive leader s in Yoshida et al.  were significantly larger that the geometric mean and maximum of the average current reported by Wang et al. [1999a] ( 96 A and 1028 A, respectively ) and Miki et al.  (99.6 A and 316 A, respectively). Similarly, the largest current pulse peaks reported by Yoshida et al.  were significantly larger than the maximum current pulse peaks reported by Wang et al. [1999a] (2046 A), Miki et al.  (2179 A), and Rakov et al.  (up to 5 kA). The VHF sources associated with the first and second upward positive leader in Yoshida et al.  ascended to altitudes of 2.4 km and 3.7 km, which are below the typical freezing level altitude of 4 km, and several kilometers below the altitude, 7 to 8 km, where the main negative
37 charge of thunderstorms are thought to be located in typical Florida summer thunderstorms [ Koshak and Krider 1989]. Yoshida et al. [ 2010] argued their results indicated that the storm in which the two flashes were triggered was not a typical convective storm, but more like a mesoscale convective system. The latter are known to have a complex structure, with as many as five stratified charge layers [ Stolzenburg et al., 2002]. 2.2.2 Altitude Triggered Lightning A ltitude triggered lightning has been utilized less often tha n classical triggered lightnin g owing to a lower success rate and the lower chance of measuring channel base currents. A ltitude triggered li ghtning (or simply altitude triggers) involve s placing a long metallic wire (essentially the same type of wire used in classical triggering) in the air that is not connected to ground, but instead is isolated electrically. This is typically accomplished b y lifting the same type of triggering wire that is used in classical triggering, but with a gap between the bottom end of the upper wire and the top end of the grounded wire. The gap in the conducting wire can be tens to a few hundreds of meters in length The upper wire can unspool to be several hundred meters in length. The grounded wire is typically a few tens of meters in length and it increases the probability that the lightning will attach to the instrumented launcher so that channel base currents can be measured Altitude triggers sometimes occur when the grounded triggering wire unexpectedly breaks, as was the case for the altitude triggered lightning presented in this work Figure 24 illustrates the sequence of processes that occur during the initial stage of altitude triggered lightning. Altitude triggers have an initial stage involving a bi directional leader. An upward propagating positive leader initiates first from the upward tip of the upper wire. A few milliseconds after the initiatio n of the upward positive leader, a downwardpropagating negative leader initiates from the bottom end of the upper wire. The downward negative leader develops stepwise in a manner that is similar to the stepped leaders that precede
38 nature first return str okes in CG flashes. As the negative leader approaches ground, an upward connecting leader forms. Once the negative leader and upward connecting leader attach, a return stroke is initiated. When the return stroke begins, the overall channel length is only about 1 km (from the ground to the top of the upward positive leader) Further, the return stroke propagation speed is two to three orders of magnitude faster than the speed of the upward positive leader. Thus, the return stroke catches up with the upward positive leader tip in about 10 s. This results in an intensification of the upward positive leader [ Idone 1992]. At this point, the tr iggered lightning develops with a similar sequence of steps as classical triggered lightning (as illustrated in Figure 2 3 ) including the wire explosion, its replacement with a plasma channel, an initial continuous current, and possibly leader/return stroke sequences. There are many reports in the literature concerning altitude triggered flashes [ e.g., Hubert 1984; Rakov et al., 1998; Saba et al., 2005; Zhang et al., 2009] The review here will focus on observations pertaining to t he downward negative stepped leader that develops in the bi directional leader phase of the altitude trigger. The characteristics o f the stepped leader in altitude triggers have been inferred from electric field waveforms measured near the triggered lightning and streak photography Laroche et al.  described an altitude trigger in France with a triggering height of 670 m, and 200 m of dielectric thread. From electric field records, the y concluded that the upward positive leader began 3 to 4 ms before the downward negative leader began. They reported that the bi directional leader sequence occurred twice, with t he second seque nce occurring about 1 s after the first and leading to the full sequence of events described above. They inferred that the interstep time interval of the downward negative leader in both sequences was about 15 s.
39 Laroche et al.  reported observations of an altitude trigger at the Kennedy Space Center, Fl orida during the summer of 1989. The wire was extended between 450 m and 610 m above ground when the flash began. The upper portion of the downward negative stepped leader was observed with U.V. st reak photography developing into two branches with average step length s of 3 m, and steps occurring every 18 to 19 s. The estimated initial speeds for the two branches were 2.5 x 105 and 3 x 105 m s1, and they both accelerated to speeds of 3.1 x 105 and 3.8 x 105 m s1, respectively. Laroche et al.  observed, at 200 m from the channel electric field steps due to the deposition of charge with each leader step, and at 600 m, smaller steps with more significant oscillations. From these observations Laroche et al.  concluded that, for electric field, the effect of the space charge deposition by each step is more important at 200 m, while at 600 m, the transient response of the bi directional leader and wire is more important. Laroche et al. [ 1991] hypothesized that the reason for shorter negative leader step lengths in altitude triggers versus those in natural lightning results from the discharge being driven by the potential of the wire, and not the cloud charge. Lalande et al [ 1998 ] present ed electric field, current, and streak photography observations of an altitude trigger in 1995 at Camp Blanding (the ICLRT). Lalande et al.  observed that the downward negative stepped leader paused its development after eight steps for a time inter val of about 800 s even though the upward positive leader apparently continued to develop. The mean field change for these eight steps was 15 V m1 (consistent with 170 C being deposited at a height of 450 m) When the stepped leader resumed its devel opment, it stepped about once every 18.5 s, and the mean field variation of the steps was 23.5 V m1 (consistent with 270 C being deposited at a height of 450 m). The s treak photography show ed that the negative leader step lengths we re 3 to 5 m the mean stepping period was 21 us and the
40 stepped leader propagated with a longitudinal velocity of 1.3 x 105 m s1. Finally, Lalande et al.  inferred from electric field observations that the aver age charge per step was 300 C, and note d that in laborat ory sparks, this value of charge is associated with negative leader steps having peak currents of about 600 A Chen et al.  presented optical images from the A.L.P.S array and electric field observations of five altitude triggers in Guangzhou, Sourt hern China during the summer of 1998. They found that the negative stepped leader onset occurs 3 to 8.3 ms after the positive leader onset. The negative stepped leaders apparently paused and resumed their development several times, and had step int erval s ranging from 12 to 30 s that seemed to decrease as the leader developed closer to ground. Chen et al.  always observed a few isolated electric field steps prior to the onset of the bi directional leader, which they attributed to aborted positive leaders from the upper tip of the triggering wire ( apparently similar to precursors in classical triggered lightning). Lu et al.  reported highspeed video and electric field observations for an altitude trigger in August of 2005 at Binzhou, Shandong Province, China The upward positive leader propagated with a n estimated 2D speed of 3.8 to 5.5 x 104 m s1 from a height of 393 m to 452 m above ground. Three aborted downward negative stepped leader s were imaged over time intervals of about 1 ms The y first occurred about 952 s after the onse t of the upward positive leader The three aborted leaders propagated 37, 6, an d 20 m. The stable downward negative leader onset occurred about 4.1 ms after the onset of the upward positive leader, and apparently propagated to the upward connecting leader in 12 steps with an estimated 2 D speed of 1.9 x 105 m s1. The time intervals between steps ranged from 5 to 30 s, and the mean time interval was 15 s. The mean step length was estimated to be about 3 m.
41 2.3 Corona Space Charge Layer at Ground The ambient electric field of thunderstorms causes electrical discharge known as corona from various types of sharp objects located on the ground, often creating a space charge layer near ground. The usually upward directed electric field due to negative cloud charges is reduced near ground by the presence of the positive corona space charge layer. A space charge layer (of either polarity) prevents the quasi static (slowly varying over time scales of seconds to minutes) electric field at ground level from exceeding an absolute value of about 5 to 10 kV m1, while the field above the layer can be up to an order of magnitude higher [e.g. Standler and Winn, 1979; Chauzy and Raizonville 1982; Soula and Chauzy 1991; Willett et al. 1999]. When a significant space charge layer is present near ground, t he relatively large and fast field change from a lightning flash typically causes a polarity reversal at ground but not at altitude, and the field recovery following a large and fast field change occurs more rapidly at ground than aloft [ e.g., Standler and Winn, 1979; Chauzy and Soula, 1987; Chauzy and Soula, 1989]. Thus, inferences of for example, aspects of charge transfer and continuing current from electric fiel d measurements at ground may be compromised by the presence of a space charge layer. Additionally, when attempting to artificially initiate (trigger) lightning using the rocketand wire technique [ Rakov and Uman, 2003], the electric field at ground is us ed as an often inadequate proxy for the unknown triggering field at higher altitudes, and the variable field reduction of the space charge layer reduces the triggering efficiency. Although it would often be advantageous to measure the electric field above the space charge layer for the reasons given above doing so presents logistical difficulties. Nevertheless, several researchers have measured the electric field at various heights, and from these measurements, inferred the vertical profile of the space charge density near ground.
42 There are many reports of a significant space charge layer existing near the ground below thunderclouds. Thunderstorm electric fields have been found to have higher magnitudes over water, where a lack of sharp objects minimizes space charge production by corona current. Toland and Vonnegut  reported a maximum electric field intensity of 130 kV m1 over water (a lake). Chauzy and Soula  simultaneously measured the electric field on the shore of a lagoon and on a raf t that was 100 m away from land, and found that the electric field magnitude over the water was generally higher than over land. Several researchers have consistently reported measuring higher magnitude electric fields above ground using field mills carrie d by balloon or rocket. In experiments at the Kennedy Space Center (KSC) in Florida and Langmuir Laboratory in New Mexico, Standler and Winn  raised and lowered a field mill on a balloon between altitudes of 3 and 120 m altitude every few minutes to measure the electric field as a function of height while simultaneously measuring the groundlevel electric field. They reported that when the ground level field exceeded 3 kV m1 and 5 kV m1 at KSC and Langmuir, respectively, the field aloft increased with altitude to a maximum of about 20 kV m1. They inferred a maximum charge density of 0.8 nC m3 at a height between 30 and 50 m above ground, above which the charge density decreased. It is worth noting that Standler and Winn  also reported me asuring corona current flowing from small evergreen trees in New Mexico, and that the corona current level rapidly increased when the groundlevel electric field exceeded 5 kV m1. The maximum corona current from a tree measured by Standler and Winn  was 600 nA in an electric field of 12 kV m1. In experiments in southwestern France, Chauzy and Raizonville  reported five balloonborn electric field soundings with simultaneous groundlevel field measurem ents
43 underneath thunderclouds. Three o f the soundings were done with negative charge overhead and two with positive charge overhead. Their data showed that for both charge polarities overhead, the absolute value of electric field increased with altitude and became approximately constant at a height somewhere between 50 and 200 m above ground at levels between about 20 to 30 kV m1, while at the same time the absolute value of groundlevel electric field remained constant and never exceeded about 5 kV m1. They inferred average space charge d ensities of 2 to 4 nC m3 and spacecharge layer depths of about 100 to 200 m above ground when negative charge was overhead. When positive charge was overhead, they inferred a higher average space charge density of about 5 nC m3 in a more shallow spac e charge layer that extended only up to a height of a bout 50 to 100 m above ground. In experiments in two different locations in France and in different years, Chauzy and Soula , simultaneously measuring the electric field at ground and at a height of 15 m above ground, found that the field aloft was up to 10 kV m1 greater than at ground level and an inferred charge density between about 3 and 6 nC m3. Soula and Chauzy  simultaneously measured the electric field at ground and at four heights up to 803 m from an approaching storm at the KSC in Florida, during which there was no significant precipitation and four lightning flashes were triggered using the rocket and wire technique. The apparatus they used is described in Chauzy et al. . T hey found that ions created by corona at ground travel up to at least 600 m. They reported measuring a maximum electric field of 65 kV m1 at an altitude of 603 m, while the groundlevel field measured simultaneously did not exceed 5 kV m1. Their data i ndicated that the electric field became constant above 436 m. They inferred average space charge densities between the five electric field measurement heights that ranged from about 0.2 to 1 nC m3.
44 Chauzy and Soula , using the PICASSO model [e.g., Qie et al. 1994] with measurements made in Southern France, at KSC [ Soula and Chauzy 1991], and at the Camp Blanding Army National Guard Base, Florida [ Uman et al., 1996], examined the time evolution of corona space charge up to a height of 1 km within a 10 km x 10 km area. Chauzy and Soula  estimated that tens to a few hundreds of coulombs of corona space charge can be lifted to a height of 1 km via conduction or convection currents over periods of several tens of minutes, and thus the space charge may contribute to the development of the lower positive charge center in thunderclouds. Willett et al.  probed the vertical electric field up to an altitude of about 4 km at Camp Blanding using field mills carried by a rocket that was launched roughly five seconds prior to the launch of a separate wireextending rocket in 15 attempts to trigger lightning. They presented for two of their flights (flights 6 and 13, their Figures 14 and 18) the electric field versus altitude soundings that showed that the electric field increased with altitude, an observation from which they inferred the presence of a space charge layer. In their flight 6 the ground level electric field was about 7 kV m1, and it increased with height to about 15 kV m1 at a heig ht of about 60 m, above which the field stayed relatively constant. In flight 13 the groundlevel electric field was about 6 kV m1, and it increased with height to about 24 kV m1 at a height of about 500 m, above which the field stayed relatively consta nt. In both flights, the increasing electric field was attributed to space charge layers. For flight 13 they inferred an average space charge density of about 0.3 nC m3 and noted that the charge density in the lower 60 m was probably three times this va lue. Willett et al.  reported measuring a maximum electric field magnitude of 38 kV m1 at altitudes between 3.2 and 3.7 km above ground.
45 2.4 The Stepping Mechanisms of Long Negative Laboratory Discharges and Their Relationship to Lightning A signif icant portion of this work is based on observations of lightning leader propagation made with high speed video cameras and time correlated current and electric field measurements. Some of these observations show stepping mechanisms in negative polarity lightning leader s that appear similar to the stepping mechanisms of negative leaders in long laboratory sparks (Section 5.2) It is thus helpful to give the reader some background pertaining to long, negative leaders in laboratory sparks. There are relativ ely few reports in the literature focusing on the negative laboratory spark; most reports (of which there are many) focus exclusively on the simpler positive laboratory spark which requires a lower breakdown voltage and is more commonly encountered in high voltage engineering However much of the description of the long, negative leader is an extension of the description for its positive counterpart For both polarities, the corona streamers and leader channels are similar ; the two differ primarily in th e extension mechanisms [ Bazelyan and Raizer 1998]. T here are several key observational studies of the propagation of long, negative polarity laboratory sparks in air that have aided in the understanding of the stepping mechanisms exhibited by such sparks [e.g., Gorin et al., 1976; Les Renardieres Group, 1981; Ortega et al., 1994; Reess et al. 1995; Bazelyan and Raizer 1998; Gallimberti et al. 2002]. These reports are reviewed below, with emphasis placed on the stepping mechanism (the space stem, pilot and space leader) T he discharge begins with corona streamers [ Loeb and Meek 1941; Raether 1964] that begin when a free electron which can be produced by one of many processes (e.g., photoionization, radioactive decay, or cosmic rays), appears near t he electrode within the volume (called the critical volume by Gallimberti  and the ionization zone by Bazelyan and Raizer  ) where the convergent electric field is on the order of 30 kV c m1 or more. The
46 field value at which breakdown occurs, or the inception field, generally depends on the electrode geometry the gap distance, and the ambient air pressure [ e.g., Peek, 1929; Les Renardieres Group, 1972] Similarly, the inception voltage, defined as the voltage at which the first corona streamer burst appears, is somewhat random and depends on the voltage rise time and the electrode geometry [ Bazelyan et al., 1961; Les Renardieres Group, 1981]. The initial free electron gains more energy from the electric field than it loses through interactio ns with air, so it accelerates away from the cathode, and generates additional electrons via impact ionization These new electrons experience a similar acceleration and also generate new electrons, and so on, thereby creating electron avalanche breakdown There is also electron emission from the cathode which occurs via impact or photo ionization, and a wide range of chemical reactions occur that influence the ion density. C orona streamers consist of thousands of such avalanches and extend to several ten s of centimeters in length [ e.g., Les Renardieres Group, 1981; Reess et al. 1995] The mean charge injected into gaps by the first corona burst ranges from 107 to 106 C [e.g., Les Renardieres Group, 1981; Ortega et al., 2005]. The corona streamers pus h electrons from the vicinity of the electrode, and build up a positive space charge which produces a field reduction [e.g., Trichel 1938; Les Renardieres Group 1981]. Under the right conditions, t he negative corona streamers can form in a pulsed manner (Trichel pulses) with a frequency on the order of tens to a hundred MHz [ Trichel 1938; Reess et al. 1995]. More detailed descriptions of the complex physics and chemistry of the corona streamers can be found in the literature [e.g., Gallimberti, 1979; Les Renardieres Group, 1981; Wang and Kunhardt 1990; Alexandrov and Bazelyan, 1996; Marrow and Lowke 1997; Alexandrov and Bazelyan ,1999; Nudnova and Starikovskii 2008; Winands et al., 2008; Nguyen et al 2010]
47 As long as the applied voltage is suffici ently high (the level depends on the gap geometry and air thermodynamics), the corona streamers will continue, causing t he gas temperature to increase as a result of the Joule heating from the corona current The next step in the formation of the leader i s the development of one or more stem s (somet ime called space stem s if they form unattached to an electrode ) Th e physics of the space stem is not well understood. Reess et al  performed an observational study of space stem formation in discharg es in a 1.3 m point to plane gap which is summarized in the following text Reess et al.  observed that the first space stems form in the vicinity of the cathode (where negative corona streamers previously formed) w ith the inception of retrograde p ositive streamers from luminous spots (spots that apparently have an excess of positive ions) and that the luminous spots often correspond to the branch points of the negative corona streamers. The retrograde positive streamers contact the cathode and br ing forward the cathodes potential, and supply the stem with electrons, allowing the formation of new negative streamers extending further into the gap. Reess et al.  determined that about 300 nC of charge must be transferred to the stem before neg ative streamer s can develop Retrograde positive streamers grow from new space stems at branching points in the new negative streamers and travel back to the cathode (and through the previous space stem and positive streamers ) in effect moving the spac e stem further into the gap. This sequence occurs every few hundred nanoseconds [e.g., Gorin et al., 1976; Reess et al. 1995]. The space stem and its associated positive and negative streamers is sometimes called a pilot [ Bacchiega et al., 1994]. Les Renardieres Group , Ortega et al. , and Reess et al  all report a similar equivalent velocity for the space stem motion of 1 x 106 m s1. The corona streamer currents converge on the stem region (estimated to have a volume of about 1 cm3 by Gorin et al. ) and increase the local thermal energy, producing significant
48 effects, including : (1) a temperature increase of the gas and plasma by Joule heating from about 300 K to 1500 K, (2) a hydrodynamic expansion and reduction in gas de nsity (3) an increase in the electron detachment of the negative ions due to the increase in tempera ture and reduced electric field, (4) a sharp increase the conductivity of the stem and (5) an increase in the electric field at the stem tips If the tem perature in a stem reaches a critical temperature of about 1500 K, negative ions abruptly release their captured electrons. This causes a large and abrupt increase in the plasma conductivity, and the formation of a space leader. The space leader appears as a thin luminous channel connecting corona regions to the highvoltage electrode. The leader cross sectional area increases in time, and the longitudinal current is confined to a diameter between 0.5 mm and a 4 mm (the current diameter increases in time under by hydrodynamic expansion) Ortega et al. , studying negative discharges in a 16.7m gap, observed that the space stem became a space leader when it was typically between 1.4 to 2.2 m in front of the cathode or primary leader channel. It can be concluded that the space leader mechanism will not occur in gaps shorter than 1.4 m. The number of steps in Ortega et al.s 16.7m gap ranged from 4 to 7, which is higher than the number steps than was observed in 5 and 7 m gaps by Les Renardieres Grou p  Ortega et al.  reported estimates of the elongation speeds for the primary and space leader, and the propagation speed of the space stem, when the overall leader was less than 5 m in length. The speeds were apparently estimated from still photographs obtained with an image converter camera, but the rate at which the photographs were obtained is not stated. The primary leader elongated with an estimated mean speed in the range of 1.3 to 2.8 x 104 m s1. The estimated mean elongation speed was between 3.2 and 4.9 x 104 m s1 for the cathode directed end of the space leader (upper, positively charged end). The anode directed end (bottom, negatively charged end) elongated with a slower mean speed
49 between 1.2 and 2.9 x 104 m s1. When the positive end of the space leader merges with the cathode a wave carrying the higher cathode potential travels to the negative end of the space leader (forming a step) where it creates a relatively large corona streamer burst that contributes to producti on (heating and charging) of the following step. Ortega et al.  observed, with a shunt in the highvoltage electrode, that a current pulse with a peak current ranging from 100 to 600 A was associated with each leader step, although they noted that t he peak current may have been restricted by the external circuit. The values of peak current did not appear to be related to the step number. A step formed by a single space leader will produce a narrow, unipolar current pulse. A step formed by two or m ore space leaders will produce a multi peaked, unipolar pulse with a considerably longer width. In Figure 9 of Ortega et al. , it appears that there is a current peak for each space leader that contributes to a step, although they did not explicitly state this. Between 200 and 400 C flowed from the high voltage electrode with each step, but it is not clear what fraction of the charge contributes to the new step (some may develop and be swept away by the highelectric fields in the gap). The charge per unit length for the first four steps was determined to range from 100 to 130 C m1. Ortega et al.  extended the work of Les Renardieres Group  in relating the potential of the space stem just before space leader inception, USS, to the vol tage at the leader inception from the high voltage electrode, U1. The value of USS was calculated using the following relation: SSpL SSUUELEL 21 where UP is the peak high voltage electrode potential, Lis the length of the negative (primary) leader, LS+ is the length of the positive corona streamers connecting the space stem to the
50 neg ative leader, EL is the electric field in the negative (primary) leader (determined from the graph in Figure 6.5.2 in Les Renardieres Group ), and ES+ is the electric field of the positive corona streamers (assumed to be 500 kV m1). The values of U1 (the cathode potential at leader inception time) and USS increase with increasing distance between the high voltage electrode or space stem and the ground plane (anode), DSS, according to the following relation. 0.45 SS SSU0.8D1.5 22 The similarity between U1 and USS is an indication that the leader inception from the high voltage electrod e is preceded by the formation of a stem, as Bacchiega et al.  observed. Equation 22 is probably only valid for gaps larger than 2 m, since the spac e leader apparently cannot form in much smaller gaps [ Ortega et al., 1994]. With knowledge of the space stem and space leader in hand, it is possible to describe schematically the spatial and temporal development of the long negative laboratory leader afte r the leader has started from the cathode, and before the final jump, as is done in Figure 2 5. T he diagram in panel A of Figure 25 illustrates the streamer zone of a negative laboratory leader several microseconds after initiation from the highvoltage electrode, as first described by Gorin et al. : (1) primary leader channel that grows from the negative highvoltage electrode, (2) leader tip, (3) positive streamers (filamentary channels of low conductivity), (4) space stem, and (5) negative stre amers emanating from the space stem. The streamer zone extends from the primary leader channel intermittently [e.g., Reess et al. 1995]. Panel B of Figure 25 depicts negative leader development in time from left to right, as interpreted via streak photography, with electrod e current shown below (Figure 25C ). The negative electrode is at the top, and the leader develops downward toward a grounded plane. Numbers 1 through 5 correspond to the descriptions for Figure 25A The primary leader tip extends quasi continuously down curve 2
51 in Figure 25B with the space stem moving along the negatively sloped dashed line labeled 4. The space stem eventually thermalizes and becomes a space leader (6) that develops bi directionally. When the positive end (top) of the space leader merges with the negative leader tip (at 7), the higher potential of the leader channel is transferred to the negative end of the space leader (bottom), followed by a burst of negative corona (mobile, diffuse space charge) or corona st reamers (filamentary channels) (8). At this point, current and luminosity waves travel up the leader channel, completing the leader step. The spark propagation continues in the corona created at 8 with the development of a new space stem that initiates t he next leader step. Current pulses in the grounded electrode are associated wi th each step, shown in panel C of Figure 2 5. In the long negative laboratory discharge, the negative leader connects to the ground plane (anode) via an upward positive connec ting leader in the socalled final jump phase. According to Les Renardieres Group , there are three different final jump mechanisms. In type A, the negative corona streamers reach the ground plane during the propagation of the space stem. The spa ce step accelerates toward the anode, and upon reaching it, an upward positive connecting leader develops upward from the ground plane and connects to the establis hed leader channel. In t ype B after the downward negative corona streamers are in contact w ith the anode, a space leader develops between the primary downward negative leader and the upward positive connecting leader. In type B, the presence of the space leader alters the characteristics of the upward positive connecting leader. Finally, in ty pe C, which is similar to type A, the burst of negative corona streamers following the connection of a space leader to the primary negative leader channel reaches the anode. An upward positive connecting leader develops toward the negative leader without the presence of a space stem (as was the case for type A). Les Renardieres Group  observed, for negative discharges in a 7 m gap, that the upward
52 positive leader ranged between 0.7 to 3 m, or 10 to 45% of the gap distance. Based on the presence of channel loops, Ortega et al.  inferred that the length of the upward positive connecting leaders were about 4 m, or about 24% of the gap length (16.7 m) Les Renardieres Group  examine the variability in the upward positive connecting leader w ith gap distance, impulse shape, and overvoltage level.
53 Figure 21. The four types of cloud to ground lightning, defined by the charge transfer to ground and direction of the leader. Adapted from Rakov and Uman .
54 Figure 22. The sequence of e vents in a natural, downward negative cloudto ground lightning flash. Adapted from Jerauld .
55 Figure 23. The sequence of events in a classical triggered lightning. Adapted from Rakov et al. .
56 Figure 24. Sequence of events in altitude triggered lightning. Adapted from Rakov et al. [ 1998].
57 Figure 25. Schematics illustrating the stepped development of the negative leader. (A) Diagram (snapshot) showing the streamer zone structure ahead of a negative leader tip, (B) space time diagram of negative leader development with time increasing from left to right over 50 s, (C) the corresponding current in the ground electrode Diagrams are adapted from Gorin et al. .
58 CHAPTER 3 EXPERIMENT DESCRIPTION The data and observations described herein were recorded at the International Center for Lightning Research and Testing (ICLRT), a facility that is located at the Camp Blanding National Guard base, abo ut 5 miles east of Starke, FL. This work presents research on triggered lightning experiments performed at the International Center for Lightning Research and Testing (ICLRT). Beginning in 1993, many triggered lightning experiments have been performed at the ICLRT by many talen ted researchers from all around the world that have greatly advanced the understanding of lightning physics The ICLRT facility is a state of the art research facility which provides the means to study both natural and rocket triggered lightning at ranges of a few meters to h undreds of meters including: measuring electric and magnetic fields [e.g., Rakov et al., 2005; Jerauld et al., 2008; Howa rd et al., 2011], optical radiation [e.g., Wang et al., 1999a ; Olsen et al. 2004; Olsen et al. 2006; Biagi et al. 2009; Biagi et al. 2010; Hill et al. 2011], high energy radiation (x rays) [e.g., Dwyer et al. 2005; Saleh et al., 2009; Howard et al., 2008; Howard et al., 2010], source location s by VHF interferometry [e.g., Yoshida et al., 2010], highspeed spectroscopy [e.g., Walker et al. 2009; Walker et al. 2010] for the case of rocket triggered lightning, channel base currents [e.g., Wang et al., 1999b; Rakov et al. 2003; Shoene et al., 2009; Schoene et al., 2010], and the effects of lightning currents in electrical power distribution lines [e.g., Mata et al., 2000] and residential buildings [e.g., Rakov et al. 2002; Decarlo et al. 2008] The research presented in this work was performed at the ICLRT during 2008 and 2009. During these two years, several new major experiment s took place, requiring changes and additions to the existing instrument ation. Some of the key changes are briefly summa rized below.
59 Before 2008, six identically configured electric field sensors were operated in order to measure field changes that are produced by return strok es with strike points occurring on site; that is, within the confines of the physical area of the ICLRT facility at Camp Blanding In 2008, the network of electric field sensors was altered for the Positive Lightning Experiment (PLE). The goal of the PLE was to measure the electric fields produced by positive cloudto ground (CG) lightning occurring at ranges from on site to about 40 km. At these ranges, the positive CG processes of interest, namely the descending positive leader, return stroke, continuing current, and the overall charge transfer produce electric field changes with amplitude s varyin g up to five orders of magnitude, and time scales varying by up to seven orders of magnitude. Hence, multiple electric field sensors with different sensitivities and relaxation times were needed to measure properly the full ran ge of possible values. The number of electric field sensors was increased from 6 to 10 in 2008. The sensitivities and relaxation times of the six existing sensors were changed, and the f our new electric fi eld sensors had higher sensitivities and longer relaxation times. A new netw ork of digital storage oscilloscopes (DSOs) was constructed for the PLE so that data from off site positive CG lightning could be acquired without preventing the acquisition of data from onsite lightning by the Multiple Station Network (MSE). T he PLE DSO network had its own LabView control interface facilitating quick and easy operation of the common DSO functions (e.g., setting the trigger mode, loading s etup panels, and saving data). During attempts to trigger lightning, the configuration of the PLE DS O network was changed to acquire long records, up to 5 s in duration, of channel base currents, electric and magnetic fields, and a few x ray measurements. The PLE DSO network recorded data for nearly all rocket launches, regardless of whether or not lig htning was triggered (in the cases when lightning was not
60 triggered, transient currents in the triggering wire were still of interest). The PLE DSO network functioned as a backup data acquisition system for the rare instances when the MSE DSO network malf unctioned. In addition to changing the electric field sensor configurations, the current sensor configurations were also altered in 2008, primarily for the ball lightning experiment [ Hill et al. 2010]. In the ball lightning experiment, triggered lightn ing currents were made to flow through various materials with the goal of producing ball lightning. For this experiment, George Schnetzer and Mike Stapleton constructed a current intercepting wire system, which consisted of a rectangular wire located several meters over the top of the launch tower that was electrically connected to its own ground lead and ground rod located on a pole about 8 m to the west of the launch tower. The intercepting wire apparatus intercepted leader/return stroke sequences and provide d them with a current path to ground that was physically and electrically separated from the initial stage current path to ground (which is guided past the intercepting wire by the triggering wire). Figure 31 shows an image of the launch tower with the current interceptor installed. The intercepting ring may have encouraged the formation of upward positive connecting leaders, observations of which are analyzed below. The intercepting wire was removed on 21October 2008, and was not used in 2009. D igital high speed video cameras were first used to observe triggered lightning at the ICLRT in 2008. A Phantom V7.0 highspeed video camera, located in the launch trailer, recorded 500 fps (frames per second) video of the ball lightning samples that were located on the launch tower (about 50 m away) as they were struck by lightning. The framing rate of the Phantom V7.0 was too slow to resolve any processes associated with lightning, although the camera provided evidence of ball lightning forming above st eel plates [ Hill et al., 2010] A
61 Phantom V7.3 and a Photron SA1.1 were operated from the office trailer (about 440 m from the tower), and they provided video of the lower several hundred meters of lightning channel at framing rates up to 20 kfps (kilof rames per second), although they were generally operated at much slower framing rates, around 5 kfps. TheV7.3 and SA1.1 yielded original lightning observations of upward and downward leaders and the attachment process [e.g., Biagi et al. 2009]. In 2009, the high speed video cameras were optimally configured, as discussed in Section 3.8, and recorded video of lightning at framing rates up to 300 kfps [e.g., Biagi et al ., 2010; Hill et al. 2011]. The Multiple Station Experiment (MSE) operated throughout 2008 and 2009. Station 25 was added to the network in 2009. Station 25, located a few meters south of the launch trailer, had a dE/dt sensor and two new lanthanum bromide (LaBr3) x ray sensors which could resolve x rays occurring as often as tens of nan oseconds. In addition, 8 new plastic x ray/muon detectors replaced the unshielded sodium iodide measurements at the 8 TOA stations. The MSE recorded data nominally from six of the ten electric field measurements, 47 x ray sensors (including 8 plastic, 2 LaBr3, and 37 Sodium Iodide ), two optical sensors, two magnetic field sensors at a single location in the cross loop configuration, and up to six current measurements. A lengthy description of the MSE will be avoided here since only one dE/dt measurement and one x ray measurement recorded by the MSE are presented in this work However, a detailed description of the MSE can be found in the Ph. D. dissertations of Dr. Jason Jerauld and Dr. Joeseph Howard [ Jerauld 2007; Howard, 2009] 3.1 Experiment C ontrol The experiment at the ICLRT includes many field deployed measurements located at various stations around the facility. The physical layout of the experiment stations and buildings are identified in the map presented in Figure 32. Table 31 gives the location of the sensors at
62 the various stations. Each station is numbered, and measurements at a given station share the stations number (e.g. E2 is the electric field sensor at Station 2). Each measurement is controlled by a device called a PIC controlle r (because it uses a PIC brand microprocessor) which communicates with a central control computer in the launch trailer via fiber optics. Analog data are also transmitted via fiber optic cables from the sensors to the launch trailer, where they are digitized using digital storage oscilloscopes. 3.1.1 PICs Field measurements are controlled by PIC controllers (hereafter called simply PIC) that are in communication with a central control computer in launch control (HAL) through fiber optic link or RF link. T he PICs provide the ability to (1) switch power to itself and other enclosed electronics, (2) apply attenuation to the sensor output before being input to the data transmission fiber optic link, (3) probe the battery voltage and enclosure temperature, and (4) supply a calibration signal for the data fiber optic lin ks. The PICs are powered by 12V batteries. The PIC input and output impedances are each 50 electronics following an antenna) is fed through the PIC via BNC connectors, which can apply one or more of the fol lowing attenuations: 3, 6, 10, 14, and 20 dB. The PIC signal output is fed into a fiber optic transmitter dedicated to transmitting the data stream to a fiber optic receiver in the launch trailer. The PIC can block the signal from the sensor and out put a calibration wave; either a 1 Vpp or 0.1Vpp amplitude square wave with a frequency of 100 Hz The calibration wave is used to determine the gain of the fiber optic link. For the experiments of 2008 and 2009, the 2001 and 2006 PIC models were used, and they are pictured in Figure 33 and Figure 34, respectiv ely. The 2001 PIC and 2006 PIC connectivity is shown in schematically in Figures 35 and 36, respectively. Both provide power switching, attenuation, and calibration functionality described above. The 2006 PICs communicated with
63 the control computer via a single 62.5/125 m (core/cladding) glass fiber (called a control fiber to distinguish it from data fibers) for both received and transmitted commands, and could support two measurements (two s eparate data channels that could be configured differently with two correspondingly separate 12V power output ports). The 2001 PIC only supports one data channel and one power output. To communicate with the control computer, the 2001 PICs were connected via two 1mm diameter plastic fibers (one for receive and one for transmit) to either a 900 MHz radio frequency (RF) transceiver, or as a slave PIC to a 2006 PIC. The RF transceiver, also called an RF PIC, was powered by its own 12V battery connected t o a 10W, voltage regulated solar panel recharging system. By 2008, t he master slave functionality of the 2006 PIC had eliminated the need for the RF PICs at nearly all stations. By 2009, only the still photograph cameras were controlled through RF PICs except for the occasional circumstance when a 2006 PIC would fail and need to be temporarily replaced by and RF PIC Each glass control fiber was connected to one of two 24port fan out boards in the launch trailer, which itself was connected to the cont rol computer via RS 232. The control computer was also connected via RS 232 to a 900 MHz RF transceiver for communication with the RF PICs. Each PIC channel was assigned a 2 digit hex address for identification. PIC commands from the control computer we re pre ceded by the appropriate hex address and sent to all PICs, but only the PIC configured with the matching address would respond. Similarly, a PIC s transmissions were pre ceded with its hex address to distinguish their communications from other PICs 3.1.2 Fiber Optic L inks The Opticomm MMV 120C fiber optic links utilize frequency modulation with a 70 MHz carrier frequency, and operate at a wavelength of 1310 nm. The links were originally designed for transmitting video signals but the manufacturer a greed to make two modifications to better
64 suit them to lightning experimentation. First, the output and input resi stances were modified from 75 attained without compromising the functionality of the links. Second, the low frequency cutoff was modified from 5 Hz to DC, giving the links a nominal bandwidth of DC to 30 MHz. The nominal output range is 1 V, and the links saturate at about 1.2 V. The links are specified as having a signal to noise ratio as about 67 dB, a value determined using the short haul RS 250C standard in whi ch the signal is low pass filtered with a cut off frequency of about 5 MHz. In practice, the true signal to noise ratio is a few dB lower, and it depends on the fiber length. The Opticomm transmitters are powered by 12 V batteries (controlled by the PIC). The electrical signal is input via coaxial cable to a BNC port. The fiber output port is ST type. The Opticomm receivers in the launch trailer were placed in a rack mounted power supply in groups of 16. Like the transmitter, the fiber port on the rec e i ver is an ST type. The electric signal from each receiver is output from a BNC port to coaxial cable that is fed to one port of a BNC feedthough panel (with 32 ports, 2 rows of 16 columns) on the front of the rack, making it easily accessible inside the launch trailer. The Opticomm links were connected with 62.5/125 m (core/cladding) graded index multimode glass fibers with a nominal index of refraction of 1.483. Each fiber was covered, from cladding outward, by successive layers of plastic, Kevlar re inforcement, and additional plastic. Fibers were bundled in 6 or 8 strands on double armored cables with a fiberglass strength m ember at the center. Typically, one fiber bundle ran to each station, with one fiber being used as a PIC control fiber The fi ber optic links gains can be tuned by two internal potentiometers (one for broad adjustments and one for fine adjustments). Thus the link gain (which is ideally 1, or 0 dB) is
65 somewhat sensitive to temperature fluctuations and the gains for different li nks are variable. It is important to know the link gains for measurements with absolute calibrations. Thus, prior to and following data acquisition sessions, each link was calibrated using the 100 Hz 1Vpp square wave calibration signal generated by th e PIC. 3.1.3 Control Computers The primary control computer, often referred to as HAL, was located in the launch trailer. HAL continuously operated LabView virtual instrument (VI) software that controlled nearly every instrument on site, as well as the digitizing scopes in the Multiple Station Experiment (MSE). HAL displayed (and optionally recorded) the quasi static electric field sensed by the NASA field mill. The main VI running on HAL is used to arm the network, which generally consisted of sever al steps, including: turning on the field instruments and MSE DSO (but not the PLE DSO, which r a n separately from the MSE DSO) to calibration settings, instructing the DSO to record calibration shots for each instrument, and then putting the PICs and DSO i nto data acquisition mode, (a mode in which the DSA save data if lightning strikes on site). HAL also disarms the network; that is, executes the above stated steps in reverse order. The instruments and instructions for the PICs and DSO that HAL commanded were specified by a user in look up tables, thus allowing for quick and easy arming for different experimental conditions. For example, when collecting data from off site positive lightning in times when no on site lightning is expected, HAL could turn on only the measurements connected to the PLE DSO, and not arm the MSE DSO. Typically, the decision to arm/disarm the network was made by a human user. Alternatively, a user could enable HAL to arm/disarm the network automatically based on the quasi st atic electric field, sensed by the NASA field mill. Generally, HAL automatically armed the network when the electric field exceeded a level of 2 kV m1, and disarmed the network
66 when the field remained below this level for 10 min. The automation provide d by HAL allowed for the acquisition of data, at least from natural on site lightning, without personnel manning the site. A secondary VI was used to monitor the PICs and their associated measurements, and perform troubleshooting and diagnostics. HALs V Is were originally written by PhD student Rob Olsen III although helpful modifications were made by PhD student Jonathon Hill to add flexibility to the arming/disarming criteria, and to provide a signal that could be used to trigger the DSO in the PLE exp eriment upon firing a rocket. Since the PLE DSOs had a functionality that was different from the MSE DSO, they had their own control computer. The author created VIs on the PLE control computer only controlled the DSO. The VIs allowed a user to quickly s et the internal times (the Yokogawa scope times drifted a second every few minutes), save or discard data (after examination by the user), change the trigger state (auto, normal, single, off), and change data acquisition modes (for positive lightning or fo r triggered lightning). These configurations could be changed on individual DSOs, or all DSOs together. In addition, a user could use the PLE control computer to change the DSOs panels, or pre determined configurations. Using panels to change the DSO configuration was useful when switching operational modes that would otherwise have required many DSO settings to be changed by hand. By using panels, a user could change multiple settings with one mouse click on the control computer, which is faster and less mistake prone than changing individual settings by hand on the external DSO interface. 3.1.4 Rocket Launching Apparatus Figure 3 7 presents a close up view of the launch tube apparatus, and Figure 3 8 presents a view of the bottom of a launch tube wit h rockets loaded and ready to launch. There are a total of twelve launch tubes, although typically only five were loaded. The Kevlar coated, 0.2 mm diameter copper triggering wire wa s unspooled from the bottom of the rockets. Since classical
67 triggering was the desired outcome, the wires were electrically bonded to the launch tubes and grounding system (although in one instance a wire broke and led to an altitude trigger) The rockets initial acceleration was high, so the wire wa s i nitially un coiled by bungie that provide d strain relief to prevent the wire from break ing The rockets were 1 m long and 2inch diameter fiberglass tubes with plastic stabilization fins and nose cone. A parachute was stored in the rocket body and was ejected a few seconds after launch to safely lower the rocket to ground. The rocket motors were ignited by a 9 V battery shorted across a squib wire placed inside the motor. The connection of the squib wire to the battery, and thus the rocket firing, was controlled by pneumati c relays that were pressurized via air tube feeding from a compressor in the NASA trailer. A battery powered microcontroller was located on the launch tubes that opened the desired pneumatic relay upon receiving a command via fiber optic cable from the rocket launcher in the launch trailer. Thus, the rocket firing system was controlled solely by light and pressure signals, allowing the launch tower to be kept electrically isolated from the launch trailer for the safety of the personnel and electronics con tained within and discouraging the accidental launching of rockets by electrical pickup from nearby lightning There we re several factors to consider when deciding to attempt triggering lightning. The electric field at ground should be high, indicating t hat there is sufficient cloud charge overhead. At the ICLRT, ground level electric field values between 4 and 9 kV m1 (positive field pointing from ground to the cloud, indicating negative charge overhead) we re considered to be indicative of sufficient o ver head cloud charge, although the space charge layer near ground can make the ground level field reading misleading ( Section 7.1) In general, a higher success rate is achieved when attempts at triggering lightning we re made during a thunderstorms diss ipating stage, when there was still sufficient cloud charge and electric field strength, but when the natural lightning
68 flash rate wa s low (about one flash every few tens of seconds). Wind and rain must also be taken into consideration, since high winds c an cause a triggering rocket to veer off course horizontally, reducing the effective vertical speed and height that is achieved by the triggering wire T he presence of dense rain can prevent good photometri c observations from being made because the lightn ing channel is obscured. 3.2 Waveform Digitization and S torage The models of Yokogawa and Lecroy digital storage oscilloscopes (DSO) used to digitize and store data at the ICLRT are summarized in Table 3 2. The Yokogawa DSO are used to digitize long, cont inuous records of the electric and magnetic fields, channel base currents, optical luminosity, and x rays at a relatively slow sample rate (10 MHz). The Lecroy DSO s have a higher bandwidth than the Yokogawa DSO s and digit i ze with a faster sampling rate (2 50 MHz) short records of the derivative electric fields, currents, and x rays. The Lecroy DSO s have a memory segmentation feature, meaning that their acquisition memory can be partitioned and used by multiple triggers within a user specified time window. This feature is particularly useful for recording lightning return strokes and not the interval between stroke s which may not be of interest. 3.2.1 Yokogawa DL716 The Yokogawa DL716 is a 16 channel DSO that was always operated at its maximum bandwidth of 4 MHz ( 3 dB) and at its maximum sampling rate of 10 MHz. The DL716 can digitize up to 16 analog channels with 12bit amplitude resolution. The DL716 has a record length of 16 mega samples per channel, or a record length of 1.6 seconds when sampling at 10 MHz. The DL716 was operated with a 1V amplitude range, or 200 mV/division. The input impedance for all channels was 1 M
69 bus by Labview software. Data are offloaded via 10Base T Ethernet using standard File Transfer Protocol (FTP) software. 3.2.2 Yokogawa DL750 The Yokogawa DL750 is a 16 channel DSO that was always operated at its maximum bandwidth of 3 MHz ( 3 dB) and at its maximum sampling rate of 10 MHz. The DL750 can digitize up to 16 ana log channels with 12bit amplitude resolution. The DL750 is specified as having 25 mega samples per channel when using all 16 channels, but for an unknown reason, it only recorded 20 mega samples per channel, for a total record time of 2 s. The input im pedance for all channels was 1 M operated using only 11 channels, each having record length of 50 mega samples, for a total record time of 5 s. The DL750 is remotely controlled via 100Base T Ethernet using LabView software. Remote control was also possible over via GPIB. Data was download over 100Base T Ethernet using standard FTP software. As discovered by Dr. Joey Howard in early 2009 [ Howard, 2009] the DL750 divides its amplitude range in to 20 divisions, but only displays 10 of them. Since the voltage sensitivity is selected by adjusting the volts per division, the total amplitude range is normally twice that which is displayed on the DSO display. For example, when set to 200 mV/division, the DSO displayed 1 V ( 5 divisions), but it actually recorded 2 V ( 10 divisions). In such a case, half of the amplitude resolution of the DSO is wasted, since the nominal dynamic range of the fiber optic transmitters was 1 V (and saturated at abou t 1.2 V). Further, for voltage levels outside of the nominal range of the FO link (1 to 1.2 V and 1 to 1.2 V), the FO links may not behave linearly. In February of 2009, the DL750 configurations were all changed to have 100 mV/division so that their full dynamic range was 2 V, and the zoom of the vertical range was made x0.5 so that all 20 division would be displayed on the DSO screen. All data recorded
70 by DL750 before this change have half the expected vertical resolution, and waveform behavior outside a range of 1 V should be interpreted with caution. 3.2.3 LeCroy LT344 Waverunner The LT344 is a four channel DSO that samples with 8bit amplitude resolution. The LT344 was operated with sampling rate of 250 MHz using its internal low pass filter with a cutoff frequency of 25 MHz ( 3 db). The LT344 has a maximum record length of 1 MB per channel when all four channels are used, for a total record time of 4 ms, but was operated in segmentation mode, with two 2ms segments. The input impedance for each channel can be set to either 50 LT344 is controlled via 10Base T Ethernet by Labview software, and data is downloaded on the same connection using LeCroy proprietary file tra nsfer software. 3.2.4 LeCroy LT734 Waverunner 2 The LeCroy LT374 Waverunner2, which is the successor to the LT344 Waverunner, is a DSO that samples with 8 bit resolution. The LT374 was operated with a sampling rate of 250 MHz using its internal low pass filter with a cutoff frequency ( 3 dB) of 20 MHz. The LT374 had a maximum record length of 4 MB, and the DSO was configured to record up to 8 segments, each having 2 ms duration. The full amplitude range was 1 V with 250 mV per division. The LT344 is c ontrolled via 10Base T Ethernet by Labview software, and data is downloaded on the same connection using LeCroy proprietary file transfer software. 3.2.5 Lecroy 44Xi The LeCroy 44Xi represents a major improvement from the older LT344 and LT374 models, espe cially in the ease of operation thanks to its responsive touchscreen controls. The 44Xi was operated in essentially the same manner as the older LeCroy DSOs: with a sample rate of 250 MHz using its internal low pass filter with a cutoff frequency ( 3 dB) of 20 MHz, and a
71 full amplitude range of 1 V with 250 mV per division. The 44Xi has a maximum record length of 12.5 MB per channel, and the DSO was configured to record up to 10 segments, each having a 5 ms duration. The 44Xi is controlled via 100Base T Ethernet by Labview software, and data are downloaded on the same connection using LeCroy proprietary file transfer software. 3.2.6 MSE DSO N etwork All DSOs in the Multiple Station Experiment (MSE) were commanded by HAL via GPIB or Ethernet. The MSE DSO triggered i n two circumstances: (1) when the output of the two optical sensors, one at the northeast corner of the site (NEO), and the other located at the southwest corner of the site (SWO) exceeded 100 mV for at least 1 s, or (2) when the triggered l ightning channel base current exceeded a level of 6 kA. The first circumstance occurs when natural lightning occurs onsite, and both circumstances typically occur during triggered lightning. The DSOs in the MSE included two Yokogawa DL716 for recording the output of x ray sensors and one or two Yokogawa DL750 for recording electric fields, magnetic fields, current. All Yokogawa s in the MSE shared at least one channel for synchronization. Time derivative electric field, x ray incidence, and channel ba se currents were recorded on a combination of five Lecroy 44Xi, three Lecroy LT344, and one Lecroy LT3744, all operating with a sampling rate of 250 MHz (well above the Nyquist frequency) with the intent of finding source locations through time of arrival analysis [ Howard et al., 2008; Howard et al., 2010; Howard, 2009]. More detail regarding the operation of the MSE DSO network can be found in the Ph. D. dissertations of Joey Howard and Jason Jerauld [ Jerauld 2007; Howard, 2009]. 3.2.7 Pos itive Lightning Experiment DSO N etwork The PLE DSO network i s comprised of three Yokogawa DL750 and a single LeCroy 44Xi. The LeCroy 44Xi is used mainly to triggering the DL750, as detailed below, and does not store data. Two of the DL750 (called scope 22 and scope 25) have identical measurements connected
72 in parallel to identical channels (e.g., both record E2 on channel 1), and were configured to digitize all 16 channels for a total time of 2 s at a sampling rate of 10 MHz. The third DL750 (called scope 30) utilize s only 11 of 16 available channels, but digitizes them for 5 s while still sampling at a rate of 10 MHz. The channel configurations for the PLE DS O are summarized in Table 3 3. The PLE DSO network does not trigger with the MSE DSO, but instead triggers in one of two unique ways depending on its operational mode. The first operational mode (PLE mode) is designed to acquire data from off site positive CG lightning, and the 44Xi is set to trigger on electric field change (ideally return stroke field changes, sensed by E22 or E11), and also to output a TTL pulse that will trigger scope 22 and scope 25. The electric field record on the 44Xi can be quickly viewed (thanks to its responsive touchscreen interface) to determine if the data is worth saving. If it is, the control computer can command either scope 22 or scope 25 to save the data. The other scope can then be re armed and acquire data. By using two identically configured DL750, the overall amount of downtime due to data offloading was reduced, thus a llowing for more data acquisition. This design proved particularly valuable when recording data on positive CG lightning, which tend to occur only a few times within a time span of about 30 minutes or so at the end of storms. The second operational mode ( RTL mode) is used during triggered lightning experiments to acquire data for the entirety of the triggered lightning, including the wire ascent phase (which is of importance to this work). In contrast, the MSE typically triggers on return strokes, and doe s not acquire data from the wire ascent phase. When acquiring data on triggered lightning, the 44Xi served solely to provide a trigger signal for the three DL750: a 5 V, 1.8s long square pulse. The 44Xi itself was triggered by a TTL signal from HAL fol lowing a 1 s interval after a
73 pressing the launch button to fire a rocket (approximately 1 s elapses between pushing the button and rocket motor ignition), or by hand. Scope 30 and scope 22 trigger on the rising edge of the 44Xi trigger signal with no pre trigger. Scope 25 was triggers on the falling edge of the 44Xi trigger signal, with 200 ms of pre trigger. Thus, the measurements on scope 30 (mostly x ray measurements) were digitized for 5 s, and the shared measurements (currents and fields) on scopes 22 and 25 were effectively digitized for 3.8 seconds, with 200 ms of overlap between allowing for straightforward synchronization of the two records. 3.3 Electric Field Mill s A field mill is a device that has the capability to sense fields that do not v ary in time (DC or static field), and electric fields that vary slowly over periods of seconds to minutes (quasi static field change). Hereafter, the term quasi static electric field will refer to the DC or slowly varying electric field as measured by the field mills. In 2008 and 2009, the quasi static electric field at ground level was recorded at distances of 60 m and 350 m to the southeast and northwest of the launch tower, respectively, with tripod mounted Campbell Scientific CS110 field mills in th e inverted configuration (sensor is 2m above and facing ground, as shown in Figure 39). The analog field mill data were digitized and transmitted via fiber optic cable to a data s torage PC in the launch trailer (the same PC that operated the Symmetrico n GPS time card). The CS110 field mills use a reciprocating shutter, sample at 5 Hz, or every 200 ms (upper frequency response of about 2 Hz), and are specified by the manufacturer to have an amplitude accuracy of 5% of the reading. The amplitude resol ution of the field mill measurements used here are limited to 100 V m1. The CS110 field mill data are not recorded with GPS timing, although an approximate time is supplied by the data storage computer that is sufficiently accurate (within a few seconds) to distinguish between different lightning flashes. The sampling for the two field mills is not synchronous.
74 The NASA field mill was located a few meters outside of launch control, and its reading was displayed, but generally not recorded, on the HAL c ontrol computer. The NASA mill had a rotating shutter, and sampled at 100 Hz (upper frequency response of about 50 Hz). The field changes that the NASA field mill reported were consistent with but generally lower than the field changes reported by the Campbell Sc ientific field mills This difference is attributed to the NASA mill being shielded by the grounded catenary wire system that shields the launch trailer and NASA trailer. HAL could be configured to automatically arm experiments if the NASA field mill detected quasistatic electric fields exceeding a threshold value, typically 2 kV m1. 3.4 Broadband Electric Field and dE/dt 3.4.1 The Flat Plate A ntenna Broadband vertical component electric fields are sensed at ground using flat plate antennas, like those shown in Figure 3 10. The antenna consists of an electrically isolated circular plate that is mounted flush with the top face of a hollow aluminum housing. The circular plate has a radius of 22 cm, which is slightly smaller than the circular hole in the aluminum housing, so that the two are separated from each other by a 6mm annular ring. The area of the circular plate is 0.155 m2. The circular plate is mounted to the bottom face of the housing with nylon standoffs. The aluminum housing, which sits on the ground, is connected by a thick copper wire, or copper braid, to a 3m ground rod. Wire mesh is attached to the outer edge of the top face of the housing (and to the ground rod) that extends several meters horizontally. The wire mesh serv es to keep the circular flat plate, the top of the aluminum housing, and the Earths surface all flush with each other, and to increase the effective ground plane around the antenna, thereby leaving unenhanced the vertical electric field and minimizing hor izontal field components that may exist due to the Earths relatively poor conductivity (measured to be 2.5 x 104 S m1 at the ICLRT [ Rakov et al. 1998]). A coaxial cable on the inside of the housing
75 has its center conductor on one end connected to the circular plate, and the other end is connected to the internal side of a BNC bulkhead feed though on the side of the housing so that the outer conductor of the coaxial cable is at the housing potential (which is ideally ground potential). The antenna output voltage is fed from the external port of the antenna housing BNC feed though to a similar BNC feed through on a Hoffman box via 3m of coaxial cable inside copper shield braid. The Hoffman box itself is placed in a pit that is next to the antenna and about a half a meter deep, and the pit is covered by reflective insulation (tuff R) and the wire mesh that is attached to the antenna for protection from extreme temperatures from direct sunlight and electromagnetic interference. In addition to the standard control and communications electronics, the Hoffman box contains the sensor load impedance. The type of load impedance used depends on how the antenna is to be operated. The operation of the flat plate antenna can be understood from its Norton or Thevenin equivalent circuit. We begin by assuming that the flatplate antenna, surrounding ground mesh, and surrounding Earth are all perfect conductors. The boundary condition for the normal component of electric field on a perfectly conducting surface can be expressed by s En 31 m with units F m1, E is the electric field vector with units V m1s is the surface charge with units C m2. We are concerned with electric fields in air where the permittivity 0 = 8. 85 x 1012 F m1), and the normal component of the electric field at ground is Ez, so Equation 31 becomes Equation 32. 0zsE 32
76 The su s is the total charge on the circular plate, Qplate, divided by the plate area, Aplate, so Equation 32 can be expressed as Equation 33. plate0platezQA E 33 Equation 33 assumes that the smallest signal wavelength of Ez is much greater than the diameter of the flat plate, a conditi on that is satisfied for the signals of interest. The Norton equivalent short circuit current, isc(t), is equal to the time derivative of Equation 33 z sc plate0platedE d it[Q]A dt dt 34 Thus, the flat plate antenna can be viewed as a current source with a m agnitude that is proportional to the incident time varying electric field. The Norton equivalent current provides the basis for an equivalent circuit that is best analyzed in the frequency domain. Using the Fourier transform and the knowledge that differ entiation with respect to time corresponds to we find that the time domain expression for the equivalent current, Equation 34, can be transformed into a frequency domain expression given by Equation 35. 0platezIAjE 35 z component electric time t. Figure 3 11 shows the frequency domain equivalent circuit f or the flat plate antenna 35, Zs is the source (antenna) impedance and ZL is the load impedance, which will depend on the application.
77 The antennas output voltage signal in the frequency domain, Vout across the parallel elements of the equivalent circuit shown in Figure 3 11, given by sL out Total sL0platez sL ZZ VIZI(Z||Z)AjE ZZ 36 The voltage output of the flat plate antenna depends on its surface area Aplate, source impedance, and load impedance. For example, as noted in Howard , if the quantity sLsLZZ/ZZ is real and equal to unity, then Voutz independent gain 0Aplate. If sLsLZZ/ZZ outz frequency 0Aplate. The source impedance is dominated by the antenna capacitance, which has been measured to be about 80 pF for the typical flat plate antenna used at the ICLRT, allowing us to ignore the antennas inductive impedance and resistance. As noted in Jerauld , the impedance of the wire that connects the antenna to the load can be neglected. Thus, the source impedance is given by s ant1 Z jC 37 where Cant the is antenna capacitance. As mentioned above, the load impedance is specified by the application. For Vout proportional to the electric field, a capacitive ZL is required. In practice, the load impedance for an elect ric f ield sensor is a resistor placed in parallel with a capacitor, where the resistor serves to discharge the capacitor so that the output voltage decays to zero with a time constant RCint. For Vout derivative electric field, a resistor is used for ZL. When the load is a resistor and capacitor in parallel, the load impedance is given by
78 intL int int intR jC 11 Z||R 1 jC 1jRC R jC 38 where Cint is the so called integrating capacitance. All elements of the source and load impedances are in parallel, so the total capacitive impedance is 1/jw(Cant+Cint). Thus, the total impedance of the equivalent circuit, ZS||ZL, is given by Total intant intant11 Z ||R jCC1jR(CC) 39 Inserting Equation 39 into Equation 36 yields out 0platez intant1 VAjE 1jRCC 310 In the electric field configuration, Cant is on the order of microfarads, so Cant >> Cint, and the output voltage can be approximated by out,E 0plate z int1 VAj E 1jRC 311 After division int, Equation 311 becomes 0plate out,E z int intA 1 VE 1 C 1 jRC 312 The expression in the parenthesis on the right hand side of Equation 312 is the form of a single pole highpass filter with a cutoff frequency 0 int1 RC 313 For signals 0, the output voltage of the electric field sensor is
79 0plate out,E z intA VE C 314 E quation 314 is expressed in the time domain by 0plate out,E z intA VtEt C 315 Thus, the electric field sensitivity depends on both the flat plate area and the value of the integrating capacitance, and the low frequency roll off, f0, depends on the values of R and Cint. The high frequency response is limited by the digitizer. In the time domain, the low frequency roll off introduces an exponential decay step function input, given by int 01 RC 316 If the electric field output were a unit step function (equal to 1 at t = 0), the output would decay to e1 (~0. 37) after a 315 is valid only for measurement on times scales In practice, the product RCint can be made sufficiently large such that f0 is on the order of a the possible exception of very long continuing current. The value of R is typically on the order of megaohms, and the value of Cint is typically on the order of a microfarad or hundreds of nanofarads. However, there is an inherent trade off between the sensor sensitivity and low frequency roll off: while increasing Cint lowers the value of f0, it also lowers the sensitivity. This tradeoff is one reason that several electric field sensors were used, each having different sensitivities and values of f0 (the other being the limited dynamic range of the sensor).
80 As mentioned above, the flat plate antenna operates as a timederivative electric field sensor if a resistive load is used. In this case, Cint is set to zero in Equation 310 yielding out,dE/dt 0plate z ant1 VAR jE 1jRC 317 The expression in the parenthesis of the right hand side of Equation 317 is the form of a single pole low pass filter with a high frequency cutoff point of 0 ant1 RC 318 At the ICLRT, the load resistance is 50 ant = 80 pF, then f0 0 40 MHz, well above t he highest recorded frequency of 25 MHz. Thus, for the dE/dt 0, in which c ase Equation 317 becomes out,dE/dt 0platezV ARjE 319 Equation 319 is expressed in the time domain by z out,dE/dt0platedE VtAR dt 320 3.4.2 Electric F ield Sensor A schematic of the connections inside the Hoffman box for the electric field sensor is s hown in Figure 3 12. The antenna output voltage is fed from the Hoffmanbox BNC feed though to an RC box via coaxial cable. The RC box is connected directly to a BNC port on the amplifier, and the amplifier output is fed to the PIC input via coaxial ca ble. The PIC output is fed to the Opticomm fiber optic transmitter, which sends the data to the Launch trailer via 62.5/125 m fiber.
81 The RC box (a small Pomona box), shown in Figure 313, contains a printedcircuit board (PCB) on which the load capacit ors (integrating capacitors) and load resistors are surface mounted and connected in parallel. In practice, many parallel capacitors were used to reduce the inductance. Using surface mount devices as opposed to wire lead devices reduced lead inductance. Placing the antenna load in its own box provide s interchangeability: The antenna load can be quickly changed simply by swapping the RC box, without having to perform soldering or changing the amplifier circuit. Beginning in spring of 2008, new amplifiers with an updated design were used in the electric field sensors that could simultanesouly provide higher gain and increased bandwidth than the previously used amplifier (described in detail in Jerauld ). A circuit schematic is shown in Figure 3 14, and a picture of a constructed amplifier in a Pomona box is shown in Figure 3 15. The amplifier is based on the OPA657 opamp operating in the noninverting mode. There are two circuits shown in Figure 3 1 4: the top is the rail splitter circuitry and power switch (relay), and the bottom is the amplifier The negative and positive bias power pins on the amplifier are connected to the negative (0 V) and positive (+12 V) terminals of a battery. The rail splitter, which is simply a voltage divider (two 10 0k follower, creates a stable, 6 V reference for the amplifier, so that the amplifier bias is actually 6 V. If the same battery were used to power the PIC and Opticomm, the amplifier voltage would be 6 V above the comm on ground potential of the PIC and Opticomm, which is outside the Opticomm input voltage range (1.25 V). Therefore, it was necessary to power the amplifier with its own battery, and this power was relay controlled by the PIC power. Each amplifier was built with the same specification, and had a similar gain, with Gamp 42 (32 dB), with the exception of the amplifier for E2, which had a gain of 240 (48 dB). This allowed amplifiers to
82 be swapped without significantly changing sensitivity. In the case that the gain was too high, PIC attenuation, Gpic could be used to lower the overall signal gain. Equation 321 gives the complete equation relating the output voltage of the electric field sensor to the incident electric fiel d, taking into account the potential gain of the amplifier, attenuation provided by the PIC, and fiber optic link scaling factor (determined from the calibration signals). 0plate out,E ampPIClinkz intA VtGGGEt C 321 One way to increase the sensitivity of electric field sensors is to increase the surface area of the electrode exposed to the ambient field. Before t he new amplifiers with increased gain were available, the surface of the E6 and E22 antennas were increased to provide additional gain. The E6 antenna was similar to the flatplate design described above, but the circular sensing plate had a 61 cm radius and an area of 1.2 m2 (as opposed to 22cm radius and 0.155 m2 area). The E22 antenna was a not a circular plate in an aluminum housing, but instead was a square sheet of fine metallic screen supported by a rigid PVC structure. The square E22 antenna was 1.08 m on a side, and had an area of 1.17 m2. The E22 antenna is held several cm above ground, providing field enhancement and the metallic screen ed ges have many needlelike points However, it is possible to calibrate the sensitivity of E22 to an ant enna with a known calibration. As can be seen in Table 3 4, which summarizes the configurations of the ten electric field sensors, there were different sensitivity and relaxation times. As mentioned above, this was done in an attempt to measure the full r ange of field changes produced by positive CG lightning. The electric field sensors with a combination of high sensitivity and relaxation times (in particular E4, E5, E6, E9, E11, E22, E23) saturate upon exposure to rain because the rain is charged The E2 sensor had the highest sensitivity and a relaxation time of 10 ms; it also saturated when exposed to rain.
83 On 7 July 2008, thin plastic domes (trash can lids, about 1mm thick) were placed over some of the flat plate antennas, as shown in Figure 3 16, to shield them from rain and prevent saturation. The lids were secured to the edge of the aluminum housing by UVresistant zip ties. The larger E6 and E22 antennas were covered with corrugated plastic roofing material. Although the plastic covers solve the saturation issue, it is likely that they also distort the electric field above the sensor, and thus alter the amplitude calibration of the sensors. To estimate the effect of the plastic covers on the amplitude calibration, two flatplate antennas wit h similar loads and amplifier gains were placed about 2 feet from each other at station 23; one had a plastic dome, one did not. The intent was to compare their respective readings. However, this station suffered constant flooding, and no reliable data w ere acquired with which to make the comparison. As detailed in Section 7.3.3, the field change readings from E2 (with a plastic dome) were compared to the expected field changes from precursors. This comparison indicates that the plastic dome over the E 2 antenna may have enhanced the field strength by 29% at the sensor. It should be assumed that the same enhancement occurs for the other flat plate antennas that are similarly covered by a plastic dome. 3.4.3 dE/dt Sensor A schematic view of the connecti ons inside the Hoffman box for the dE/ dt sensor is shown in Figure 3 17. The antenna output voltage is fed from the Hoffmanbox BNC feed though directly to the PIC input, which applies 6 dB attenuation. The PIC output is fed to a 50terminator on the Opticomm input, which sends the data to the Launch trailer via 62.5/125 m fiber. Thus, the load impedance for the dE/dt antennas is 50 322 gi ves a complete equation relating the output voltage of the dE/dt sensor taking into account the PIC attenuation
84 GPIC, and fiber optic link scaling factor Glink (calculated from the calibration signals discussed in Section 4.2.1). z out,dE/dt0platePIClinkdE VtARGG dt 322 With GPIC = 0.5 ( 6 dB), R = 50 link = 1, the nominal cal factor for the dE/dt sensors is 29.2 kV m1 s1 V1, so a single volt corresponds to a dE/dt value of 29.2 kV m1. 3.5 Channel Base C urrents The channel base currents are measured using non inductive resi stors (shunts) and Pearson coils (current transformers). The lightning current is fed to a Hoffman box, either by copper braid wires or by connecting the box itself to the launch tubes. The current flows from the box to a shunt that is bolted to the exte rnal surface of the box, as shown in Figure 3 18. After passing through the shunt, the current flows from a lug that is outside of the box to a copper braid wire that is connected to a ground rod. Most of the shunts heat dissipating mass and its voltage (BNC) output are located in the box. The voltage output from the shunt is fed either directly to a PIC, or first to amplification electronics, and then to a PIC, depending on the application. The PIC voltage output is fed via coaxial cable to an Opticom m transmitter, which sends the signal to the launch trailer via fiber optic cable. Ideally, the current is confined to the external surface of the Hoffman box and shunt, and the electromagnetic fields inside the box are zero. However, the Hoffman box ha s a nonzero resistance and inductance, and a nonzero time varying voltage difference exists between any two points on the boxs inner surface. To reduce noise from electromagnetic interference, the amplification electronics, PIC, Opticomm transmitter, a nd battery are all contained inside of another sealed metallic electronics box that provides extra electromagnetic shielding. The electronics box is electrically isolated from the Hoffman box by mounting it to Plexiglass with
85 nylon hardware, and the Ple xiglass itself is attached to the Hoffman box. The electrical isolation prevents the formation of ground loops and the resulting distortion of the current signal. The voltage signal from the shunt enters the secondary box through a BNC bulkhead feedthrou gh. In the instances when a Pearson coil is used, it is clamped around the current carrying copper braid wire outside of the Hoffman box containing the shunt. The voltage output from the coil is fed into a Hoffman box (that is different from the box containing the shunt) through a BNC bulkhead feed through to a PIC terminated in 50 coaxial cable to an Opticomm tran s mitter, which sends the signal to the launch trailer via fiber optic cable. In 2008, IS currents and RS currents were separated through the use of a rectangular intercepting wire placed several meters above the launch tubes. The intercepting wire and the launch tube assembly, shown in Figure 3 1, are connected by different ground leads to different ground rods that were separated by a distance about 8 m. The locations at which the IS and RS currents are measured are identified in Figure 3 1. For each current, there are two shunt measurement at different amplitude scales, and a single Pearson coil measur ement. The configurations of the six current measurements in 2008 are summarized in Table 3 5. Note that the measurements of the IS are called the ICC measurements (for initial continuous current, the process of most interest in 2008). A diagram is gi ven in Figure 3 19 that illustrates schematically the ICC and RS current measurement configurations in 2008, which are essentially identical to each other. The ICC shunt, a T&M Research R 700010, has a constant resistance of 1 m frequencies ranging from DC to 8 MHz. The ICC shunts voltage is measured on two scales by applying its output in parallel to the inputs of two PICs; one applies 33 dB attenuation, and the
86 other applies 13 dB attenuation. The measurement with more attenuation is called the ICC high current measurement because it is designed to measure larger currents, in this case from about 1.4 kA to 28 kA. The measurement with less attenuation is called the ICC low current measurement because it was designed to measure current amplitudes that are a factor of 10 less than those measured by the high current measurement, in this case 140 A to 2.8 kA. The ICC low measurement was a custom built, model 6801 Pearson coil current transfor mer, with a linear frequency response from 8 Hz to 5 MHz, with a transimpedance of 1.2 x 102 V A1; it measured currents ranging from about 5 to 110 A. The RS current transformer was also a model 6801 Pearson coil, but it had a transimpedence of 1.3 x 102 V A1, and it measured currents ranging from about 6 to 115 A. The RS shunt was a T&M Research R 5600 8 with a constant resistance of 1.4 m ranging from DC to 12 MHz. Like the IS shunt measurements, the RS shunt had a high current and low current measurement. The RS high current measurement was attenuated by 23 dB; it measured currents ranging from about 3.2 kA to 65 kA. The RS low current measurement was attenuated by 3 dB; it measured currents ranging from 320 A to 6.5 kA. The tower current measurement setup was changed prior to the 2009 triggering season. The intercepting wire was not used, so the only current measu rements were attached directly below the launch tube assembly. The large, aging Hoffman box containing the old RS shunt and electronics was replaced by a larger, custom made stainless steel box. There was room for up to five separate electronics boxes in the new custom box, which is shown in Figure 3 20 (with only 4 electronics boxes, 1 of which was not used, and NASA operated digitizing equipment not discussed here). The configurations of the current measurements operated in 2009 are summarized in Table 36 and illustrated schematically in Figure 3 21.
87 The ICC shunt (R 7000 10) from 2008 was bolted to the center of the custom box in a similar manner to what was done in the old Hoffman box. The shunt voltage was fed to three different measurements: (1) the II high, (2) the II low, and (3) the II VLS (very low shunt). The II high measurement had 36 dB attenuation; it measured currents ranging from about 3 kA to 63 kA. The II low measurement had 16 dB attenuation; it measured currents ranging from ab out 300 A to 6.3 kA. The II VLS had no attenuation, but instead was amplified by a factor of 46.5 (33 dB). The amplifier circuit was the same as the amplifier used with the electric field sensors (pictured in Figure 3 15). An easily replaceable protecti on circuit, which included a current limiting resistor and zener diode voltage clamp to limit the input voltage to around 5 V was placed in front of the amplifier front end. The II VLS measured currents ranging from about 1 A to 21 A. The RS Pearson co il that was used in 2008 was used to measure mid range currents until 14Jul 2009. In an effort to keep the ground lead as straight as possible, a mount was built for the Pearson coil so it could be placed directly under the shunt lug, as shown in Figure s 37 and 320. The II VLP (very low Pearson) measurement was attenuated by 3 dB; it measured currents ranging from about 6 to 115 A. 3.6 High Speed Video Cameras 3.6.1 Photron SA1.1 The Photron SA1.1, shown in Figure s 322 and 3 23, detects light with a 1024 x 1024 pixel CMOS sensor. The dimension of each square pixel is 20 m x 20 m. T he Photron was operated from the office trailer with one of three lenses w ith different focal lengths: 50 mm, 24 mm, and 20 mm, yielding spatial resolutions of 0.18, 0.37, and 0.44 meters per pixel, respectively, at a range of 440 m, the approximate distance between the camera and the launch tower. The lens aperture was typically set as low as possible, up to f/2, to maximize the amount
88 of light collected by the sensor. Using the full pixel count (~1.04 megapixel), the Photron could record up to 5.4 kfps. However, the Photron was typically operated at much faster framing rates, up to 300 kfps, although with lower pixel resolution. The Photron acquired data on a continuous loop buffer, so it could record 100% pre trigger. The manufacturer specifications indicate that the Photron can operate with a shutter speed of (frame rate)1, meaning all light incident on the sensor during a frame time is integrated. However, it i s l ik e l y that the camera has a few hundred nanoseconds of dead time during each frame. The Photron digitizes grayscale with 12bit amplitude resolution. The Photron has 32 GB of internal memory, which can be divided into 64 memory segments, and the total duration of video that could be recorded depended on the framing rate and pixel count. During a triggering session, the Photron memory was divided into a number of segments equal to the number of rockets expected to be launched. The Photron was synchronized with IRIG B GPS time code. The Photron was cont r olled by computer via 100Base T Ethernet connection, and the same connection was used to offload each frame as individual lossless 16bit image files (the raw format). The Photron could be triggered by hand (using a short circuit switch) or by the trigger pulse generated by the MSE trigger system, which was sent from the launch trailer to the office trailer via Opticomm fiber optic link. The Photron is not absolutely calibrated, so radiometric measur ements were not possible. In 2008, two Photron SA1.1, called the UF Photron (owned by the University of Florida) and OU Photron (owned by the University of Oklahoma, and operated in collaboration with Professor William Beasley), were operated from the offi ce trailer, about 440 m from the launch tower. The OU Photron was only available for two storm sessions (17September 2008 and 10October 2009). It imaged the lower several hundred meters of lightning channel with a relatively slow framing rate (5.4 kfps), allowing the UF Photron to be operated at a faster
89 framing rate (up to 100 kfps). Before the OU Photron was made available, the UF Photron was only operated at a framing speed up to 50 kfps. The OU and UF Photron configurations for different storm se ssions in 2008 are given in Table 3 7 and Table 3 8, respectively. In early 2009, it was discovered that the Photron operates at faster frame rates for horizontal rectangular pixel areas than vertical rectangular pixel areas. For example, with a pixel area of 64 x 128 (vertical x horizontal), the Photron will operate as fast as 300 kfps, but with a pixel area of 128 x 64, the Photron will only operate up to 108 kfps. Before the 2009 triggering experiments, a custom tripod mount was built, shown in Figure s 322 and 3 23, in which the Photron could rest on its side so that the higher framing rate could be utilized. The horizontal images were rotated in post processing. In 2009, the Photron framing rate was increased incrementally (and the pixel resolution was correspondingly decreased) with each storm session, up to 300 kfps. For faster framing rates, the pixel resolution becomes too small to be of use. The UF Photron configurations for different storm sessions in 2009 are given in Table 3 9. From 7 July 2009 to 18August 2009, the OU Photron was returned to the ICLRT. It was placed in the launch trailer (a distance of about 50 m from the launch tower ) to image the lightning with increased spatial resolution; this camera was equipped with a 14 mm focal le ngth lens, which provided a spatial resolution of about 8 cm. Even with the relatively wide angle lens, the close proximity of the SA1.1 to the launch tower restricted its view of the triggered lightning to the lower 40 m or so of channel with a maximum f raming rate of 75 kfps. Unfortunately, a computer virus corrupted most of the data acquired by this camera, rendering it unusable It was discovered in August of 2009 that the Photron records a few frames less than the expected number of frames per second Further, the number of frames per second varies by
90 1 frame. For example, when the Photron is set operate at a framing rate of 300 kfps, it will actually record 299992 1 fps; that is, 299992 frames will be recorded for one second, and for the next second, the number of frames recorded may be 299993. Fortunately, this makes virtually no difference in the frame times, since the 1/299992 s 3.3334 s and 1/300000 s 3.3333 s. Only a few framing rates were tested to determine the actual number of frames that were recorded, and these are summarized in Table 3 10. Note that the deviation from the true framing rate increases with increasing framing rates. The Photron does not give correct time stamps. Although the GPS time stamp for the trigger frame is accurate, the time stamps assigned to successive frames (in either time direction) are progressively inaccurate. For example, if the Photron is operated at 300 kfps (actually about 299992 fps) for 1 second with no pre trigger, the time of the first fra me will be accurate, but the time reported for of the last frame will be 30 s less than 1 second. Thus, when analyzing Photron data, it is important to calculate the frame times independently, and not rely on the time stamps reported by the Photron. 3.6.2 Phantom V7.1 The Phantom V7.1, shown in Figure s 322 and 323 detects light with a 800 x 600 pixel CMOS sensor. The dimension of each square pixel is 22 m x 22 m. The Phantom was operated at framing rates between 5 kfps and 12 kfps. The Phantom acquired data on a continuous loop buffer, so it could record 100% pre trigger. There is a small amount of dead time associated with each frame, around several s (depending on the framing rate), an interval that is of little consequence since the frame time s are between 100 s and 200 s. The Phantom digitized grayscale with 14 bit amplitude resolution. The Phantom was computer controlled via 100Base T Ethernet connection using Phantom Camera Control software. The Phantom had 8 GB of internal memory, a nd videos were offloaded via Ethernet to the control computer as
91 cine files, a proprietary format, after which individual frames were saved for analysis and presentation purposes. The Phantom did not suffer the timing inaccuracies and variable framing r ate exhibited by the Photron. The Phantom was nearly always triggered by hand, although it could be triggered by the trigger pulse from the MSE trigger system. The Phantom was only used in 2009, and it was used in place of the OU Photron to image the lo wer several hundred meters of lightning channel with a relatively slow framing rate. The Phantom viewed in the direction of the launch tower from the office trailer (440 m away) through the same window as the Photron. The Phantom was equipped either with a 24 mm or 20mm focal length lens to give a spatial resolution of 0.40 and 0.48 m/pixel, respectively. The lens aperture setting depended on the background light conditions, but in general it was set as low as possible without saturating the camera, typically f/8. Like the Photron, the Phantom operated faster for horizontal windows than vertical windows, so it was mounted on its side. A list of the Phantom configurations utilized in 2009, including pixel resolutions, lens settings, spatial resolutions, and framing rates, are given in Table 3 11. .
92 T able 31. Sensor locations at the ICLRT. Designation Easting (m) Northing (m) Elevation (m) Latitude Longitude Distance to Tower b (m) Origin a 0.0 0.0 0.0 29.93899065 82.03648403 607.7 DE 1 137.1 4 99.6 3.0 29.94346957 82.03495231 318.1 T 1F 141.0 488.8 3.3 29.94337157 82.03491468 311.7 T 1U 138.2 489.2 3.7 29.94337560 82.03494311 314.5 E 2 424.4 570.2 3.8 29.94405042 82.03196110 156.3 T 2 427.5 580.4 4.7 29.94414255 82.03192649 166.1 DE 3 373.5 569.2 3.6 29.94405142 82.03248851 169.4 T 3F 370.9 575.0 3.5 29.94410482 82.03251415 175.8 T 3U 370.9 577.7 3.7 29.94412902 82.03251305 178.2 DE 4 680.8 493.8 4.7 29.94331163 82.02932329 249.6 E 4 683.6 492.5 4.7 29.94329927 82.02929405 251.9 T4 F 69 1.3 484.1 5.1 29.94322224 82.02921654 256.9 T4 U 692.2 486.6 5.4 29.94324471 82.02920611 258.5 DE 5 375.2 479.5 4.3 29.94324182 82.03249149 94.1 E 5 377.9 478.9 4.2 29.94323644 82.03246331 91.8 T5 F 382.0 468.7 4.4 29.94314365 82.03242317 81.8 T 5 U 379.3 468.7 4.7 29.94314415 82.03245086 83.9 E 6 101.8 310.5 2.3 29.94177175 82.03535988 357.6 T 6 104.9 301.4 3.0 29.94168893 82.03533024 357.5 T7 F 392.6 255.2 4.3 29.94121552 82.03236144 168.0 T7 U 389.5 254.6 4.4 29.94121138 82.03239285 169.4 DE 7 393.1 244.7 3.5 29.94112083 82.03235826 177.8 DE 8 570.3 286.1 4.9 29.94146024 82.03051350 180.6 T8 F 578.5 280.3 4.7 29.94140589 82.03043067 190.5 T8 U 576.0 279.0 5.2 29.94139507 82.03045638 189.7 DE 9 134.9 97.3 5.7 29.93984149 82.03506485 443.2 E 9 134.3 98.0 5.7 29.93984859 82.03507150 443.1 T 9F 133.8 104.9 6.0 29.93991034 82.03507496 438.6 T 9U 131.0 104.5 6.2 29.93990750 82.03510425 440.9 E 10 695.6 203.2 5.5 29.94068782 82.02923471 329.1 a) The southeast corner of the office tra iler. b ) With respect to T20, which is located on the launcher platform.
93 Table 31. Continued. Designation Easting (m) Northing (m) Elevation (m) Latitude Longitude Distance to Tower (m) T 10 695.7 194.1 6.3 29.94060558 82.02923595 335.1 E 11 165.9 26 2.5 2.1 29.94132629 82.03470770 317.1 DE 11 168.2 260.7 2.1 29.94130938 82.03468380 315.9 T 11F 173.4 252.6 2.3 29.94123483 82.03463147 315.5 T 11U 175.8 254.1 2.7 29.94124776 82.03460687 312.7 T 12 284.4 288.5 3.8 29.94153706 82.03347429 203 .6 T 13 463.8 324.2 5.6 29.94182414 82.03160836 93.1 T 14 506.7 447.4 6.1 29.94292722 82.03113612 70.7 T 15 507.9 547.1 4.5 29.94382576 82.03110204 146.7 T 16 261.4 496.3 3.7 29.94341599 82.03366567 199.7 DE 17 481.3 413.1 5.9 29.9426226 9 82.03140659 37.6 T 17 481.3 403.6 6.5 29.94253666 82.03140909 39.2 E 18 715.3 596.2 6.6 29.94422813 82.02894235 326.3 T 18 712.4 605.3 7.6 29.94431092 82.02897026 329.1 T 19 15.7 229.4 2.3 29.94105632 82.03626989 466.7 T 20 443.8 415.1 18.9 29.94264819 82.03179454 0.0 T 21 569.1 439.1 4.4 29.94283991 82.03049198 127.5 B 22 581.7 604.0 5.1 29.94432498 82.03032401 233.9 E 22 585.5 600.7 5.2 29.94429451 82.03028540 233.5 T 22 575.6 601.4 5.5 29.94430271 82.03038783 228.2 E 23 233.2 562.1 2.6 29.94401517 82.03394324 256.9 T 23 233.2 554.5 3.3 29.94394629 82.03394446 252.5 B 24 311.9 421.7 3.4 29.94273356 82.03315952 132.1 T 24 306.8 423.2 3.9 29.94274804 82.03321169 137.3 DE 25 445.6 454.5 5.0 29.94300302 82.03 176734 39.4 T 25 456.2 458.7 5.7 29.94303903 82.03165698 45.3 C ampbell OT 153.7 578.5 3.3 29.94417846 82.03476245 333.0 C ampbell LC 508.9 424.9 5.5 29.94272413 82.03111869 65.8
94 Table 32. Makes, models, and salient specifications of the DSO used at the ICLRT. Make Model Quantity Bit Depth Number of Channels Sample Rate Used (MHz) Bandwidth (MHz) Record Length (MS/ch) Yokogawa DL716 2 12 16 10 4 16 Yokogawa DL750 5 12 16 10 3 25 Lecroy LT344L 6 8 4 250 25 1 Lecroy LT374L 2 8 4 250 20 4 Lecroy 44Xi 4 8 4 250 20 12.5 Table 33. PLE DSO channel assignment Channel Scope 22/25 a Scope 30 b Scope 27 c 1 E2 E22 E11 2 E4 T2U E22 3 E5 T5U 4 E6 T12U 5 E6 T13U 6 E10 T14U 7 E11 T15U 8 E18 9 E22 T25U 10 E23 T20U 11 B24NS T24U 12 B24EW 13 B22NS II VLS 14 B22EW 15 II LO 16 II VLS a) Scope 22 and Scope 25 had the same channel assignments. b) Scope 30 only utilized 11 channels. c) Scope 27 is a LeCroy 44Xi with only 4 channels: only channels 1 and 2 were used.
95 Table 34. Electric field sensor configuration. Sensor Flat plate area (m 2 ) Load resistance ( Load capacitance (F) Relaxation time (s) Amplifier gain Nominal cal factor (kV m 1 / V) E2 0.155 5.0 x 10 5 2.20 x 10 8 0.011 240 0.0668 E4 0.155 2.1 x 10 6 2.19 x 10 6 4.60 41.9 38.1 E5 0.155 2.1 x 10 6 2.22 x 10 6 4.67 41.9 38.6 E6 1.166 2.0 x 10 4 4.54 x 10 7 0.009 41.8 0.588 E9 0.155 4.3 x 10 6 9.34 x 10 7 4.02 42.5 16.0 E10 0.155 2.1 x 10 6 2.08 x 10 6 4.33 41.9 36.2 E11 0.155 4.8 x 10 5 9.20 x 10 8 0.0092 51.1 1.3 E18 0.155 4.8 x 10 6 9.09 x 10 7 4.32 42.0 15.8 E22 1.166 2.0 x 10 4 4.39 x 10 7 0.0088 42.1 1.0 E23 0.155 4.3 x 10 6 1.02 x 10 6 4.38 41.1 18.1 Table 35. 2008 channel base current measurements configurations. Measurement Sensing device Nominal transimpedance (V A1) PIC attenuation Nominal cal factor (kA V1) ICC high R 7000 10 0.001 0.0224 ( 33 dB) 28.3 ICC low R 7000 10 0.001 0.224 ( 13 dB) 2.83 ICC VL Pears on Coil model 6801 0.001 0.707 ( 3 dB) 0.108 RS high R 5600 8 0.00125 0.0707 ( 23 dB) 64.7 RS low R 5600 8 0.00125 0.707 ( 3 dB) 6.47 RS UL Pearson Coil model 6801 0.025 0.707 ( 3 dB) 0.113
96 Table 36. 2009 channel bas e current measurements Measurement Sensing device Nominal transimpedance (V A1) PIC attenuation Amplifier gain Nominal cal factor (kA V1) II high R 7000 10 0.001 0.0158 ( 36 dB) 0.0 63.0 II low R 7000 10 0.001 0.158 ( 16 dB) 0.0 6.3 II VLS R 7000 10 0.001 0.0 46.5 (33 dB) 0.022 II VLP Pearson Coil model 6801 0.025 0.707 ( 3 dB) 0.0 0.108 Table 37. OU Photron configurations in 2008. Date Frame rate (kfps)a Pixel area, vertical x horizontal Lens focal length (mm) Lens aperture Spatial view, vertical x horizontalb Spatial resolution (m per pixel)b (Frame rate)1 (s) 17 September 5.4 1,024 x 1,024 24 unknown 376 x 376 c 0.37 185 9 October d 5.4 1,024 x 1,024 24 unknown 376 x 376 c 0.37 185 a) Nominal frame rate. b) At a distance of 440 m from the camera sensor. c) The camera viewing out of southfacing window; much of the image was blocked by office trailer wall. d) These settings were used for the second and third trigger on this date (UF 0820 and UF 0821).
97 Table 38. UF Photron configurations in 2008. Date Frame rate (kfps) a Pixel area, vertical x horizontal Lens focal length (mm) Lens aperture Spatial view, vertical x horizontal (m) b Spatial resolution (m per pixel)b (Frame rate)1 (s) 30 June 10 960 x 4 48 50 unknown 166 x 78 0.18 100 12 July 20 640 x 256 50 unknown 113 x 45 0.18 50 10 September 5.4 1,024 x 1,024 24 unknown 376 x 376 c 0.37 185 11 September 50 320 x 128 50 unknown 56 x 23 0.18 20 17 September 50 320 x 128 50 u nknown 56 x 23 0.18 20 9 October d 100 96 x 128 50 unknown 17 x 23 0.18 10 9 October e 67.5 192 x 128 50 unknown 35 x 23 0.18 148 a) Nominal frame rate. b) At a distance of 440 m from the camera sensor. c) The camera viewing out of sou th facing window; much of the image was blocked by office trailer wall. d) Settings for the second trigger of on this date (UF 08 20). e) Settings for the third trigger of on this date (UF 0821). Table 39. UF Photron configurations in 2009. Date Frame ra te (kfps) a Pixel area, vertical x horizontal Lens focal length (mm) Lens aperture Spatial view, vertical x horizontal (m) b Spatial resolution (m per pixel)b (Frame rate) 1 (s) 19 February 50 320 x 128 24 f/4 56 x 23 0.18 20.0 26 May 108 320 x 128 24 f/2.8 118 x 47 0.37 9.26 27 May 108 320 x 128 24 f/2.8 118 x 47 0.37 9.26 04 June 135 320 x 96 24 f/2.8 118 x 35 0.37 7.41 18 June 180 320 x 64 24 f/2.8 118 x 23 0.37 5.56 29 June 240 320 x 48 20 f/2.8 141 x 21 0.44 4.16 30 June 300 320 x 32 20 f/2.8 141 x 14 0.44 3.34 07 July 180 320 x 64 20 f/2.8 141 x 28 0.44 5.56 a) Nominal frame rate. b) At a distance of 440 m from the camera sensor
98 Table 310. Photron framing rates, specified and actual. Specified framing rate (fps) Actual framing rate (fps) 675,000 674,981 1 500,000 499,986 1 450,000 449,988 1 300,000 299,992 1 250,000 249,993 1
99 Table 311. Phantom configurations 2009 Date Frame rate (kfps) Pixel area, vertical x horizontal Lens focal length (mm) Lens a perture Spatial view, vertical x horizontal (m) a Spatial resolution (m per pixel) a (Frame rate)1 (s) Exposure time (s) 19 February 6.4 800 x 600 24 f/4 322 x 242 0.40 156.25 154.25 29 March 5 800 x 600 24 f/11 322 x 242 0.40 200.00 149.5 b 26 Ma y 5 800 x 304 24 f/11 322 x 123 0.40 200.00 190.0 27 May 10 800 x 208 24 f/11 322 x 84 0.40 100.00 98.0 04 June 10 800 x 208 24 f/8 322 x 84 0.40 100.00 98.0 18 June 10 800 x 200 24 f/4 322 x 81 0.40 100.00 98.0 29 June 8 800 x 200 24 f/8 322 x 81 0.40 125.00 120.0 30 June 8 800 x 200 24 f/8 322 x 81 0.40 125.00 120.0 07 July 8 800 x 200 20 f/8 387 x 97 0.48 125.00 123.0 14 July 6.4 800 x 200 20 f/8 387 x 97 0.48 156.25 150.0 18 July 6.4 800 x 200 20 f/8 387 x 97 0.48 156.25 150.0 18 August 6.4 800 x 200 20 f/8 387 x 97 0.48 156.25 150.0 a) At a distance of 440 m from the camera sensor. b) This exposure time was set manually
100 Figure 31. The launch tower with the current interceptor installed. Photograph taken by Dustin H ill.
101 Figure 32. The layout of stations and buildings at the ICLRT.
102 Figure 33. The 2001 PIC controller. A) Front view. B) Side view. Adapted from Howard .
103 Figure 34. The 2006 PIC controller. Adapted from Howard . Figure 35. Schematic of the typical 2001 PIC installation. Adapted from Howard .
104 Figure 36. Schematic of a typical 2006 PIC installation. Adapted from Howard .
105 Figure 37. The launch tube apparatus. Photograph taken by Dustin Hill.
106 Fig ure 38. The bottom of the launch tubes showing a loaded rocket installation
107 Figure 39. A Campbell Scientific field mill installation (LC field mill). The launch tower is visible in the background about 60 m away Photograph taken by Dustin Hill.
108 Figure 310. A field deployed flat plate antenna sensor. A) Picture showing the typical flat plate antenna installation. B) Diagram showing the side view of the installation, including the Hoffman box underground. Figure 311. The frequency domai n Norton equivalent circuit for the flat plate antenna.
109 Figure 312. Schematic of an electric field sensor configuration. Figure 313. Picture of an RC box. Photograph taken by Dustin Hill
110 Figure 314. Circuitry of the amplifier used in the electric field and II VLS current sensors. A) T he rail spitter circuit, and B) the non inverting amplifier. Note that typical circuit element values are shown for, and that in the noninverting circuit, C7, R3, C8, and R6 are not used (they were included i n the design but ended up not being needed). The gain of the amplifier is (1+R5/R4), which. If R5 = 1 k amplifier gain is about 42.6 (32.6 dB).
111 Figure 315. Amplifier circuit board mounted inside a Pomona box. Photograph ta ken by Dustin Hill.
112 Figure 316. Flat plate antenna covered with a plastic dome. Figure 317. Schematic of the dE/dt measurement configuration. Taken from Howard .
113 Figure 318. Inside the 2008 shunt box. The shunt is mounted to the box The lightning current travels through the box, through the shunt, and down the conductor to ground. Adapted from Howard .
114 Figure 319. Current schematic for the 2008 current setup. This schematic applies for both the RS path current measureme nt and the ICC path current measurement. Lightning current travels through the Hoffman box into the shunt, and then to ground.
115 Figure 320. The 2009 tower current measurement configuration. Note the NASA experiment is not discussed here. Photograph y taken by Dustin Hill.
116 Figure 321. Schematic of the 2009 tower current configuration. Lightning current travels through the Hoffman box into the shunt, and then to ground.
117 Figure 322. The highspeed video cameras setup in the office trailer. Figure 323. The Phantom V7.2 and the Photron SA1.1.
118 C HAPTER 4 DATA 4.1 Summa ry of Collected Data The data presented in this work were collected from triggered lightning flashes in 2008, 2009, and from a single flash (consisting of only an initial stage) that was triggered in September of 2010. In 2008, a total of 21 rockets were launched which resulted in 11 triggered flashes (52% success rate). Of these 11 triggers, 7 had at least one return stroke, and the total number of return strokes was 36. The other four triggers consisted of only the initial stage. In 2009, a total of 43 rockets were launched, which resulted in 26 triggered flashes ( 60% success rate). Of the 26 triggers, 18 had at least one return stroke, and the total number of return strokes was 75. The other 8 triggers consisted of only the initial stage. Data fro m one triggered lightning in the 2010 season was used (in Chapter 7) Table 4 1 summarizes th e triggered lightning statistics for 2008 and 2009. Table 4 2 summarizes for each triggered lightning in 2008 the dates, trigger times number of return strokes, the groundlevel quasi static electric field magnitude at launch, and the type of high speed video acquired. Tables 43 and 4 4 summarize the same information for each trigger ed lightning flash in 2009 and 2010. Tables 4 5 and 46 summarize the times an d peak currents for each triggered return stroke in 2008 and 2009, respectively. Rocket triggered flashes have been historically labeled with the nomenclature UFYY FF, where UF indicates a rocket triggered lightning, YY is the year, and FF identifies the shot attempt (rocket launch number) for that year; this convention is used in this work. 4.2 Data Processing The binary files recorded by the Yokogawa and Lecroy digital storage oscilloscopes (DSOs) and the RAW format images files stored by the highspeed video cameras were read using MATLAB scripts. Additional scripts were wr itten to create data displays, such as graphs
119 and image sequences. In general, a unique script was written for each graph or image sequence, although they had many common interchang eable algorithms. Some image processing, namely contrast enhancement and image intensity inversion, was performed using Adobe Photoshop. 4.2.1 Waveform D ata In order to use the waveform data (e.g. electric fields and current waveforms) for analysis and m odeling purposes, it was necessary to: (1) apply the nominal cali bration scaling factor, Gnom, to convert from digitizer volts to physical units (such as A for current), (2) adjust for the fiber optic link gain, Glink, and (3) remove artificial offset intr oduced by the fiber optic link and/or DSOs, Voffset. The resulting of this process, described by nomlinkscopeoffsetPGGVV 41 with Vscope being the voltage level digitized by the DSO, and P being the calibrated data in physical units. The value of Glink is determined from the 100 Hz, 1 Vpp square wave signal recorded before and after a data recor ding session as discussed in Section 3.2.3. The value of Voffset, when applicable, was typically determined by taking the average of at least 1000 sample points from an interval in which the true physical signal is believed to be zero, often at the begin ning of a record. The value of Glink was determined by the following : calexpected link calprecalpostV G 0.5VV 42 where Vcal expected is the expected amplitude of the calibration signal (1 V) and Vcal pr e and Vcal post are the actual amplitudes of the calibration signals recorded before and after a storm session, respectively. The values of Vcal pre and Vcal po st were nearly always within a few tens of millivolts of each other. Note that in instances when only one calibration signal was recorded, its voltage
120 value was used for both Vcal pre and Vcal post in Equation 42. In cases when the calibration signal was not recorded, Glink wa s assumed to be the expected value. 4.2.2 Image Data The image analysis performed in this work was essentially visual, and not numeric al (such as using edge finding algorithms) Visual analysis is subject to interpretation, and it is important to do analysis using good quality displays. I mages will appear to the eye with more contrast on a liquid crystal display ( LCD ) monitor than a cathode ray tube ( CRT ) monitor. Further, LCD monitors using inplane switching (IPS) or pattern vertical alignment ( P VA) technologies have far better contrast than an LCD using twisted nematic (TN) technology. Indeed, some features that are visible on an I PS or PVA display might not be evident on a TN display even with contrast enhancement. Ambient background light can reduce the effect contrast of a computer display so it is best to do computer image analysis in a dark room. All of the image analysis was performed on the raw images on an S PVA (super pattern vertical alignment) LCD monitor, ( Dell 2408WFP) with a maximum contrast ratio of 3000:1, typically in a darkened, windowless room. Paper or photo hardcopies of images will clearly be influenced by the type of printer and paper that is used. In this work and in the associated publications, the reproductions of high speed video i mage s were typical ly enlarged and contrast enhanced for improved visualization In addition, the images were typically cr opped horizontally to show only the region containing the lightning channel. A ll resolutions given throughout this work are vertical x horizontal. When making enlargements, a n effort was made to use the same integer multiple in the vertical and horizonta l direction, thereby retaining the resolution aspect ratio. For example, to double the size of an image (enlarge by 200%) the number of pixels in the horizontal and vertical direction were increased by a factor of two. Nearest neighbor interpolation (NN I) was used to determine
121 new pixel intensity values, which does a good job of preserving edges, and does not alter the intensity information. For example, In the case of 200% enlargement, 1 pixel becomes a 2 x 2 area of 4 pixels with the same intensity as the original pixel. NNI does not use any potentially distortion introducing anti aliasing filters which can distort the image. However, the high speed video images and image sequences were often arbitrarily resized so that the horizontal dimension fit the page width, thus maximizing the image size and increasing the visibility of the luminous phenomena of interest. Any resized image displayed in a figure was compared with the raw image to ensure that the display faithfully represe nted the data in the raw image. Unfortunately, there were some mistakes made when saving the high speed video data. First, s ome of the Photron data were saved in RAW file format, which, for the Photron, only support ed 8bit amplitude resolution, even though the data were recor ded with 12bit amplitude resolution. The Photron data must be saved using a special file format, designated RAWW, in order to preserve the 12bit amplitude resolution. In the RAWW file format, each 12bit sample (corresponding to 1 pixel from 1 fram e) were written to 2 bytes, with either the first or last four bits being set to zero. Second, t he Photron software (PV3.2) allows the user to alter the intensity contrast, brightness and gamma, and features an option to save the data with these alteratio ns, or without them. Before this save option was discovered, s ome Photron data were erroneously saved with altered intensity settings. The events for which these datasaving errors were made are noted in Tables 42 and 4 3.
122 Table 4 1. Summary of triggering in 2008 and 2009. Description 2008 2009 Number of rockets launched 21 43 To tal number of triggered lightning flashes 11 26 Number of flashes with initial stage only 4 8 Number of flashes with return strokes 7 18 Total number of return strokes 36 75 Table 4 2. Summary of data acquired in 2008. Flash ID Date (mm/dd/yy) Time Number of Strokes E at launch (kV m 1 ) a UF Photron Data OU Photron Data UF08 02 0 6/10/08 19:32:16 5 N/A No No UF08 04 0 6/29/08 21:36:29 IS only 5.2 No No UF08 08 0 6/30/08 18:41:24 5 5.7 Yes b No UF08 11 0 7/12/08 17:52:49 3 5.9 Yes No UF08 12 0 7 /23/08 18:40:21 IS only 5.8 No No UF08 13 0 7/27/08 20:22:21 IS only 6.2 No No UF08 17 0 9/11/08 20:36:56 IS only 5.3 Yes No UF08 18 0 9/17/08 22:04:15 9 6.3 Yes b Yes UF08 19 10/ 0 9/08 18:11:39 3 5.4 No No UF08 20 10/ 0 9/08 18:24:15 9 5.3 Yes Yes UF08 21 10/ 0 9/08 19:17:48 2 5.2 Yes b Yes a) Ground level electric field 60 m from the launch tower ( physics sign convention). b) Data saved with altered intensity values .
123 Table 4 3. Summary of data acquired in 2009. Flash ID Date (mm/dd/yy) Time Number of Strokes E at launch (kV m 1 ) a UF Photron Data Phantom data UF09 01 02/19/09 12:40:53 IS only 4.5 No Yes UF09 04 02/19/09 13:04:05 IS only 4.6 Yes Yes UF09 06 03/28/09 01:56:06 5 6.0 No No UF09 11 05/26/09 20:13:25 3 5.7 Yes b Yes UF09 12 05/26/09 20: 31:21 1 5.1 Yes b No UF09 13 05/27/09 20:19:37 9 6.0 Yes b Yes c UF09 15 06/04/09 20:20:09 IS only 6.0 No Yes UF09 17 06/04/09 20:37:13 5 6.0 Yes c Yes UF09 20 06/18/09 16:35:03 4 7.4 Yes Yes UF09 21 06/18/09 16:44:42 IS only 3.2 No Yes UF09 22 06/18/09 16:58:11 8 5.6 Yes c Yes UF09 25 06/29/09 21:09:17 5 5.9 Yes No UF09 26 06/29/09 21:18:32 5 5.5 Yes Yes UF09 27 06/29/09 21:31:18 7 4.9 Yes Yes UF09 29 06/30/09 13:49:17 5 8.5 Yes Yes UF09 30 06/30/09 14:01:04 1 7.2 Yes Yes UF09 31 06/30/09 14:12:14 5 8.1 Yes Yes UF09 32 07/07/09 15:12:54 1 6.5 Yes Yes UF09 34 07/09/09 17:15:34 4 5.6 No No UF09 35 07/14/09 21:07:58 IS only 6.4 No Yes UF09 37 07/14/09 21:21:21 IS only 6.6 No Yes UF09 38 07/14/09 21:25:15 1 6.7 No No UF09 40 07/18/09 15:25:01 IS on ly 5.2 No Yes UF09 41 08/18/09 16:22:25 IS only 6.4 No No UF09 42 08/18/09 16:24:42 1 7.6 No Yes UF09 43 08/18/09 16:30:09 5 7.3 No No a) Ground level electric field 60 m from the launch tower (physics sign convection). b) Data save with 8 bit resolut ion. c ) Data saved with altered intensity values. Table 4 4. Summary of the triggered lightning flash from 2010. Flash ID Date (mm/dd/yy) GPS time E at launch (kV m1)a UF 10 25 09 / 27 / 10 18:34:20.558752 5.1 a) Ground level electric field 60 m from the launch tower (physics sign convention).
124 Table 4 5. Summary of return stroke times and peak currents in 2008. Instances when return stroke peak currents were not available are marked with N/A. Flash ID Date (mm/dd/yy) Hour Minute Second Stroke Peak Current (kA) UF08 02 0 6/10/08 19 32 16.546405 1 18.7 19 32 16.677830 2 8.0 19 32 16.708177 3 22.0 19 32 16.818693 4 14.0 19 32 16.828135 5 4.3 UF 08 08 06/30/08 18 41 28.958560 1 23.5 18 41 29.013714 2 13.3 18 41 29.078171 3 10.8 18 41 29.204311 4 13.4 18 41 29.293099 5 11.4 UF 08 11 07/12/08 17 52 49.133847 1 17.7 17 52 49.161172 2 10.7 17 52 49.188131 3 11.7 UF 08 18 09/17/08 22 4 17.637823 1 11.1 22 4 17.661084 2 8.5 22 4 17.695004 3 20.5 22 4 17.757405 4 15.6 22 4 17.810386 5 N/A 22 4 17.895307 6 7.3 22 4 17.909987 7 N/A 22 4 18.079641 8 N/A 22 4 18.094242 9 N/A UF 08 19 10/09/08 18 11 42.973488 1 16.0 18 11 43.032189 2 15.0 18 11 43.208505 3 19.0 UF 08 20 10/09/08 18 24 18.355067 1 8.1 18 24 18.361326 2 4.7 18 24 18.387358 3 9.1 18 24 18.393885 4 5.3 18 24 18.440662 5 12.4 18 24 18.534700 6 11.2 18 24 18.610483 7 11.8 18 24 18.703408 8 6.2 18 24 18.837247 9 13.4 UF 08 21 10/ 0 9/08 19 17 51.975022 1 8.6 19 17 52.060087 2 18.0 .
125 Table 4 6. Summary of return stroke times and peak currents in 2009. Instances when GPS times or return stroke peak currents were not available are marked with N/A. Flash ID Date (mm/dd/yy) Hour Minute Second Stroke Peak Current (kA) UF 09 06 03/28/09 N/A N/A N/A 1 16.8 N/A N/A N/A 2 7.6 N/A N/A N/A 3 11.9 N/A N/A N/A 4 6.0 N/A N/A N/A 5 8.9 UF 09 11 05/26/09 20 13 28.061461 1 N/A 20 13 28 .087430 2 N/A 20 13 28.219430 3 N/A UF 09 12 05/26/09 20 31 23.496924 1 34.5 UF 09 13 05/27/09 20 19 37.082304 1 N/A 20 19 37.084693 2 N/A 20 19 37.091822 3 N/A 20 19 37.094276 4 N/A 20 19 37.097406 5 N/A 20 19 37.098878 6 N/A 20 19 37.457390 7 N/A 20 19 37.498066 8 N/A 20 19 37.569844 9 N/A UF 09 17 06/04/09 20 37 13.416051 1 22.8 20 37 13.562980 2 21.0 20 37 13.571341 3 4.9 20 37 13.583893 4 21.9 20 37 13.650808 5 44.8 UF 09 20 06/18/09 16 34 3.11 9539 1 14.4 16 34 3.215808 2 20.0 16 34 3.266208 3 14.6 16 34 3.357608 4 7.9 UF 09 22 06/18/09 16 58 10.997707 1 15.5 16 58 11.027656 2 11.6 16 58 11.153341 3 9.4 16 58 11.161657 4 8.9 16 58 11.225880 5 10.7 16 58 11.229780 6 3.1 16 58 11.398570 7 2.9 16 58 11.419171 8 10.8 UF 09 25 06/29/09 21 9 17.612277 1 15.7 21 9 17.778748 2 9.1 21 9 18.232577 3 16.3 21 9 18.280832 4 18.8 21 9 18.641641 5 31.6
126 Table 4 6 Continued. Flash ID Date (mm/dd/yy) Hour Minute Second Stroke Peak Current (kA) UF 09 25 06/29/09 21 9 17.612277 1 15.7 21 9 17.778748 2 9.1 21 9 18.232577 3 16.3 21 9 18.280832 4 18.8 21 9 18.641641 5 31.6 UF 09 26 06/29/09 21 18 36.30 6798 1 26.6 21 18 36.327519 2 11.4 21 18 36.605640 3 11.6 21 18 36.716802 4 23.2 21 18 36.786340 5 13.7 UF 09 27 06/29/09 17 31 23.005941 1 8.4 17 31 23.049751 2 15.4 17 31 23.080486 3 11.8 17 31 23.097855 4 10.1 17 31 23 .111993 5 5.6 17 31 23.230472 6 15.6 17 31 23.320614 7 28.3 UF 09 29 06/30/09 13 49 17.096270 1 10.5 13 49 17.253414 2 11.5 13 49 17.281337 3 11.4 13 49 17.427614 4 15.6 13 49 17.487826 5 18.9 UF 09 30 6/30/09 14 1 4.391149 1 30.6 UF 09 31 6/30/09 14 12 24.486065 1 6.4 14 12 24.510480 2 13.6 14 12 24.568247 3 11.1 14 12 24.583725 4 6.4 14 12 24.596714 5 7.5 UF 09 32 07/07/09 15 12 57.261135 1 19.5 UF 09 34 07/09/09 17 15 40.445418 1 11.5 17 15 40.45 7757 2 6.3 17 15 40.752652 3 15.2 17 15 40.842385 4 16.4 UF09 38 07/14/09 21 25 18.526361 1 28.0 UF 0942 08/19/13 16 24 41.585945 1 14.7 UF 09 43 08/19/13 16 30 12.252596 1 24.9 16 30 12.309397 2 9.5 16 30 12.432971 3 9.5 16 30 12.500518 4 9.6 16 30 N/A 5 N/A
127 C HAPTER 5 OBSERVATIONS OF LIGHTNING LEADERS WITH HIGHSPEED VIDEO AND CORRELATED CHANNEL BASE CURRENT, REMOTE ELECTRIC FIELDS, AND X RAY EMISSION Streak photography on film has historically been the most common met hod of obtaining time and space resolved optical measurements, both for rocket and wire triggered and natural lightning [e.g., Schonland, 1956; Berger and Volgensager 1966; Orville and Idone 1982; Jordan et al., 1992; Rakov et al. 2003; Olsen et al., 2006]. The use of photodiode arrays has offered an alternate method of obtaining highspeed optical measurements [e.g., Yokoyama et al ., 1990; Wang et al ., 1999a, 1999b, 1999c; Olsen et al. 2004; Lu et al ., 2008], generally exhibiting an order of magnitude faster time resolution than streak photography, but with poorer spatial resolution and more ambiguity in the data interpretation. High speed digital video photography is a relatively new technology that provides optical data with both relatively high time and spatial resolution [e.g., Ballarotti et al. 2005; Qie and Kong, 2007; Saba et al., 2008; Zhang et al., 2009; Kong et al., 2009; Warner et al. 2011] .. In this chapter, original observations of lightning leaders with high speed video observations al ong with correlated channel base current, remote electric fields, and x ray emissions are presented T he major finding s of the work presented in this chapter include: (1) Observations showing that negative lightning leaders do in fact develop through ste pping mechanisms that are very similar, if not identic al to, laboratory long spark leaders. (2) An upward positive leader was observed with high speed video and correlated wirebase current developing in a stepped manner from a triggering wire. (3) P osit ive upward connecting leaders (in triggered lightning) have been imaged for the first time with high speed video cameras including eight strokes in a single flash. One image was recorded just prior to the attachment process, when the streamer zone of the downward negative leader was close to or in contact with
128 the positive upward connecting leader. Much of the content in this section has been published by the author in two journal articles [ Biagi et al. 2009; Biagi et al. 2010] and, at the time of writ ing this dissertation, some of the other material is being prepared for publication. In this chapter, a positive electric field at ground corresponds to the electric field vector pointing downward (atmospheric sign convention), and positive current and positive electric field change at ground correspond to the removal of negative charge from or the deposition of positive charge in the atmosphere. 5.1 Observations of a Stepped Upward Positive Leader Init i atin g Triggered Lightning The upward positive leader that initiated the triggered flash UF0930 began its development when the wire tip height was about 123 m. As a result, the lower 1 2 m of the upward positive leader was imaged by the Photron camera that was operating at 300 kfps (3.3 s per frame) In a ddition, the lower 200 m or so of upward positive leader was imaged by the Phant om camera operating at 8 kfps (120 s per frame). Example images from the Phantom and Photron are shown in Figure 51 A and Figure 5 1B, respectively. The Photron camera was s lightly tilted with respect to the Phantom, and its field of view is identified in Figure 5 1A as a darker region As is evident in Figure 5 1, the Photron viewed mostly triggering wire. The upward positive leader developed only in the upper right region of the Photron image. The Photron recorded a total of 60 images in 200 s before the upward positive leader propagated out of the cameras field of view. The upper right, 13 m x 5 m region view ing of the upward positive leader in these 60 images are arr anged in a sequence of three rows in Figure 5 2, increasing in time from left to right and from top to bottom. The leader channel lengths after each new step are displayed in Figure 5 2, and given in Table 51. T he wirebase current recorded by the II VL S measurement is also shown in Figure 52 (with a time scale that is aligned with the high speed video frames) T he II VLS measurement saturated at about 21 A.
129 However, most of the current pulses were resolved b y the II Lo current measurement, which is shown in Figure 53 on approximately the same time scale as the current plots in Figure 5 2. The steps in Figures 5 2 and 53, and Table 51, are identified by lower case letters near the respective current pulses. S everal interesting observations can be made from the data presented in Figure s 5 2 and 53 and the measurements summarized in Table 5 1. T he upward positive leader developed to about 11 m in length in 8 distinct steps (steps a through h) with step lengths that rang ed from 0.8 m to 2.2 m wi th a mean value of 1.5 m The channel diameter for the first step appears to illuminate two pixels, or a width of up to 0.88 m It is difficult to resolve the channel diameter in successive st eps, but it appears to never exceed two pixels However, t he channel appears to have lower luminosity on each side extendi ng out 1 pixel, or about 0.44 m. This luminosity may be camera blooming or evidence of a corona sheath T he leader extended upward with an overall speed of 5.5 x 104 m s1 in its first 11 m of development, and by the time the leader exited the Phantom field of view at an altitude of about 310 m, the leader development speed had increased to 2.1 x 105 m s1. Steps e, f, g, and h developed i n two highspeed video frames. In the first frames for S teps f, g and h, isolated luminosity appears first at the top of previously formed channel segment (with no separation between the two) followed by a re illumination of the previously established channel in the following frame, indicating that a current wave was generated at the leader tip that travels down the channel The bottom end of the newly formed steps was always at the upper end of the previously established leader. The interstep time interval (determined from the time between current pulses) ranged from 16.6 to 30.4 s with a mean value of 21.1 s.
130 It is evident in Figures 5 2 and 53 that a single current pulse is detected at the wire base for each step observed i n the highspeed video images. The incident current pulse that is injected int o the leader and wire by each step is likely unipolar with a full width on the order of several microseconds, as is shown in the modeling detailed in Section 6.4 of this work for similar current pulses produced by precursors (precursors are usually leader channels that stop developing after a few meters) Owing to transmission line effects, w hat is measured at the wire base is a single current pulse exhibiting more or less damped oscillatory behavior. The first peak of the damped oscillatory signature tha t is measured at the wire base is the superposition of the current pulse that was generated at the wire tip after having traveled down the wire, and a reflected current pulse of the same polarity from the approximately short circuit termination at the grou nd rod. During the time when the first current pulse is flowing through the wire base, t he re are several sequences of current pulse reflections from the ground and wire tip, and a polarity reversal occurs with each wire tip reflection These reflected cu rre nt pulses superimpose with the original unipolar pulse, yielding the oscillatory behavior. The magnitude of successive reflected current pulses are increasingly smaller due to energy losses associated with the wire, and absorption by the leader and ground. With the exception of Steps d and e, the current pulses detected at the wire base become smoother and less oscillator y as the leader grows in length. It is reasonable to assume that the electrical characteristics of the triggering wire d id not change in the 200 s during which the steps occurred, nor does the wire length or the grounding impedance. Under these assumptions, the change in the current pulses detected at ground can be attributed to the upward developing leader channel increasingly attenu ating successive current pulse reflections.
131 The measured peak currents for Steps a through j, determined from the II Lo current record shown in Fig ure 5 3, are given in Table 51, and they ranged from 17 to 15 3 A with a n arithmetic mean of 59 A. As discus sed above, and shown via the modeling in Section 6.4, the current peak at the wire base is most likely not the same as the peak of the incident current due to transmission line effects The incident current peaks can be estimated by scaling the measured w ire base current peaks to account for the propagation losses in the wire and the current reflection from ground using Equation 616. Using the values determi ned in the analysis of Section 6.4.3, = 8.2 x 104 Np m1, G = 0.9, and a wire length of 123 m, Equation 616 predicts that the currents should be scaled b y a factor G = 0.58. The scaled peak current amplitudes are given in Table 51, and they ranged from 10 to 89 A with a n arithmetic mean of 34 A The apparent charges associated with Steps a, b, d, e, f and g were estimated by computing the time integra l of the current signature in the II Lo measurement from the beginning of the current pulse to the time when the reflections drop below the noise floor. The charge for Step i was computed from the II VLS measurement. The charge cannot be computed for Ste ps c, h, and i because their signal to noise ratio is too low. The unscaled current is used for this computation, and it is assumed that, by the end of the damped oscillatory signature, a charge is lowered to ground that is equal to the charge deposited b y the new leader step (but of opposite polarity). This computation is similar to what is done for precursors in Section 6.3.2. The charges for the current pulses associated with the ten steps in Figure 5 2 and 53 are given in Table 5 1, and ranged from 22 t o 107 C with an arithmetic mean of 64 C. The ratio of the step charges to the step lengths ranged from 26 to 110 C m1 with an arithmetic mean of 51 C m1.
132 5.2 Observations of Leader Step ping Mechanisms 5.2.1 Dart Stepped Leaders in Classical Triggered Lightning UF08 18. There were two downward negative dart stepped leaders in two different triggered lightning flashes for which the streamer zone (as defined in Section 2.4) ahead of the leader tip and stepping mechanism s w ere particularly well res olved. The first was the eighth return stroke of flash UF0818, which is presented in Biagi et al. . This stroke occurred about 444 m s after the first stroke, 170 ms after the fourth stroke and 830 m s after the triggering wire exploded during the i nitial stage of the flash. Two 20s frames of the dart stepped leader were imaged by the Photron preceding this stroke T rue value and intensity inverted value images for both frames (not subtracted) are shown in Figure 54, along with 100 s of current (RS VL) and electric field (E6) data (in Panel E) with time zero corresponding to return stroke 8. The corresponding pulses in electric field and current seen in 5 4E confirm that the leader in fact developed through steps. Note that the second frame in Figure 5 4 (shown as panel C and D) is also shown in Figure 518 As seen in Figure 54, a 7 m long streamer zone is visible at the top of the second frame before return stroke 8 (panels A and B) In the next frame, the downward leader extended about 25 m into the frame. If the leader is just above the image two frames before the return stroke, the leader traveled 25 m in two frames (20 40 s), and hence its speed was between 1.25 x 106 2.5 x 106 m s1. The downward leader observed one frame prior to the return stroke in Figure 54 has several short branches along its path that emanate corona streamers up to 5 m long. An upward connecting leader that is 16 m long is also visible (and discussed further in Section 5.4) The downward and upward connecti ng leaders are about 1 5 m apart in the frame, and there is a low level of luminosity connecting them (that was not remnant channel luminosity from return stroke 7), apparently indicating that the downward streamer zone has reached the upward connecting lea der. In the frame prior to the eighth return stroke of
133 UF08 18 (panels C and D of Figure 54) a luminous segment about 2 m in length that is brighter than the surrounding streamer zone is apparent with its lowest point being about 4 m below the downward leader. It is thought this is a space stem or space leader that helped initiate the next step of the downward stepped leader ( Biagi et al.  termed it a space stem) As is noted in Section 2.4.2, the positive, cathode directed end of the space lead er (the upper end) develops with a speed about three times greater than that of the negative, anode directed end (the bottom end) [e.g., Les Renardieres Group, 1981; Ortega et al., 1994] Thus, if the upper end developed 3 m upward before connecting to the primary leader, then the lower end likely developed downward an addition 1 m. Based on these rough calculations, the space leader is thought to have extended the channel by 5 or 6 m, and it probably was not involved with the attachment to the upward pos itive connecting leader. UF09 25. The second dart stepped leader in a triggered lightning flash with wellresolved stepping mechanisms preceded return stroke 5 of UF0925. This stroke occurred about 1.029 s after the first stroke, 361 ms after the fourth stroke and 1.560 s after the triggering wire exploded during the initial stage of the flash. The long time interval between the wire destruction and the fifth stroke makes it unlikely that significant copper residue from the destroyed triggering wire was present along the leader path. Figure 5 5 shows a sequence of the ten high speed video frames depicting the leader descending from 150 m to 11 m above ground level with time increasing from left to right in 4.17 s intervals. The frames span about 21 m horizontally, and have heigh ts labeled in 10 m increments. In the first nine frames the leader descended from 150 m to 47 m with an average speed that was between 2.7 x 106 and 3.4 x 106 m s1, depending on when the leader first reached 150 m and 46 m during the integration times of F rames 1 and 9, respectively. The leader speed may have increased in the lower 45 m of development during the
134 integration of F rames 9 and 10, either because the leader accelerated (an actual increase), or because an upward positive connecting leader intercepted the downward leader (an apparent increase), although there is no optical evidence of the latter having occurred. The large increase in lu minosity in the lower 40 m seen in F rame 10 is from the beginning stage of the upward propagating return stroke current wave. Frame 11 (not shown here) was completely saturated by return stroke luminosity. The features of most interest in Figure 5 5 are the luminous segments of channel (identified by white arrows and labeled with low er case letters ) that are separate from and below the primary leader channel The sections of the frames just below the leader tip are shown expanded by a factor of 4 and contrast enhanced in Figure 56. Table 52 gives the distances between the lower ti p of the primary channel and the lower tip of the segment, and the length of the segments. The luminous segments ahead of the leader tip in F rames 4 ( segment d ), 5 ( segment g ), 7 ( segments h and i ), and 8 ( segment j) had a luminance about equal to that of the leader channel ; these are thought to be space leaders When they were imaged, t he lengths of the space leaders ranged from 1 to 4 m, and their lower tips were between 4 and 12 m below the primary channel. The other luminous segments in F rames 1, 2, 3, 4 ( segments a, b, c, and e ), 5 ( segment f ) and 8 ( segment k ) were less well defined and significantly less luminous than the leader channel, although still more luminous than the surrounding corona streamers ; these are thought to be space stems When t hey were imaged, the lengths of the space stems ranged from 1 to 2 m, and their lower tips were between 2 and 8 m below the primary leader channel. Lower luminosity corona and forked corona streamers are present in the vicinity of the leader tip that appa rently did not develop in a direction greater than 60 degrees from vertical, best seen in the expanded and contrast enhanced image 2 in Figure 56.
135 Figure 5 7 shows the deposited x ray energy (A), time derivative electric field (B), and launch tower curren t (C) during the time when the ten high speed video frames were recorded (frame intervals are shown at the top of the figure, 4.17 s). Positive dE/dt and current correspond to negative charge moving downward or positive charge moving upward. The return stroke began just after time zero. There were 10 distinct pulses in the dE/dt record that were likely produced by leader steps, and there was a leader burst [ Howard et al., 2010; Murray et al., 2005] about 1 s before the return stroke began. In each of the 10 dE/dt pulses, there were one to three secondary peaks following and/or preceding the largest peak. Corresponding current pulses were measured between the launch tubes and ground before the current sensor electronics saturated (at about 10 s), and each had one to two peaks with timing that matched that of the peaks in dE/dt. A low amplitude, steady state current apparently began to flow after the pulse at 30 s, most likely due to corona emission from the tower since there was no optical evide nce of an upward positive connecting leader Corresponding x ray pulses were recorded for five of the dE/dt and current pulses, although the timing of the secondary x ray peaks did not always match that of the dE/dt peaks. For example, the inset plots in Figure 5 7 show on a 2s time scale a pulse in x ray, dE/dt, and current that occurred at 17 s. The dE/dt pulse had one primary and two secondary peaks, the current had two corresponding peaks, and there was only one x ray peak. 5.2.2 Downward Negat ive Stepped Leader in Altitude Triggered Lightning UF09 13. Event UF0913 was an attempt at classical triggering lightning that resulted in an altitude trigger after the wire broke during the rocket ascent. The wire extension began when the electric fiel d magnitude at ground was about 6 kV m1. The triggered lightning included 9 leader/return stroke sequences Figure 5 8 shows a picture of the lightning channel from a high definition (HD, 1080i resolution) camera operating at framing rate of 30 fps (33 ms per
136 frame). The HD image shows the lower portion of the exploded triggering wire with its bottom at a height around 133 m. The downwardnegative stepped leader developed from the bottom of the triggering wire and developed towards the launch trailer (about 50 m to the north of the launch tower). T he lightning struck one of the lightning rods connected to the catenary wires that protect the launch trailer from a strike. The white box in Figure 58 shows the approximate view of the Photron camera (th e Photron was about 10 m south of the HD camera). Unfortunately, the upward positive leader was not imaged because the upper end of the triggering wire was above the field of view of the cameras. The Photron, operating at a framing rate of 108 kfps, recor d ed about 586 s of the downward leader development below a height of about 123 m in 63 frames, (9.3 s per frame), and these frames are shown in Figure 59. Images 2 through 63 shown in Figure 59 have the background luminosity subtracted; each image is the recorded image minus the luminosity that was recorded in image 0 (not shown). In effect, what is shown is the change in the luminosity from I mage 0. T he images in Figure 5 9 have also been intensity inverted and contrast enhanced for improved visuali zation. The tower can be seen in the lower right corner of I mages 1 and 64. The leader develops from the upper right corner downward and to the left in a stepwise manner. A leader branch apparently extends outside of the Photrons FOV in I mage 18 at a height of about 106 m. The primary leader channel (the channel that connected to ground) extends outside of the Photrons FOV during I mage 38 at a height of about 69 m. The leader develops outside of the Photrons FOV during the time when I mages 39 through 49 were recorded. In I mage 50, the tip of a leader branch barely enters the Photrons FOV at a height of about 48. In I mage 56, another leader branch develops into the Photrons FOV at a height of about 32 m. This branch
137 develops an additional 10 m or so in length, and then apparently ceases. The return stroke occurs in image 64, producing heavy bloom ing N o branches were observed in the HD video. T he features of most interest in Figure 5 9 are found at the leader tip in I mages: 7 through 11, 33, 34, 36, 37, and 56 through 59. Expanded views of the leader tip in these images are given in Figures 510, 5 11, and 512 (enlarged by a factor of 4) Secondary segments of luminosity that are believed to be space stems or space leaders are identified by l ower case letters. Table 5 3 gives the distances between the lower tip of the primary channel and the lower tip of the segment, and the length of the segments. Note that all length and distance measurements are made assuming that the luminosity is a distance of 440 m from the camera. The length measurements would change by up to 12% i f the luminosity were 50 m farther or closer than 440 m. Moreover, there can be significant errors in the length measurements if the luminosity ha d significant development towards or away from the camera (i .e. perpendicular to the camera sensor plane). In the following descriptions, the primary leader channel, or just primary channel, will refer to any portion the main channel that connects to ground, including branches. Fi gure 5 10 shows expanded views of the leader tip in I mages 7 though 11. In I mage 7, it is clear that a space leader has formed that is about 3 m in length, with the farthest tip being about 4 m from the primary channel. The space leader in I mage 7 apparently failed to connect to the primary leader channel since no luminosity is evident in the following image In I mage 8, a space stem has formed that is about 1 m in length, with the farthest tip being about 3 m from the primary leader channel C onnecting corona streamers are evident betw een the space stem and primary channel In I mage 9, the primary leader extends in length to about the position of the space stem in I mage 8, and fanshaped corona streamers are emanating from the leader tip.
138 Another spac e stem forms in image 10 that is also about 1 m in length, with the farthest tip being about 5 m from the primary channel. Again, connecting corona streamers are evident between the space stem and primary channel The space stem in I mage 10 has a higher luminosity than that in I mage 8, making it more distinct. In I mage 11, the primary leader extends in length to about the position of the space stem in I mage 10, and corona streamers are emanating from the leader tip. Figure 511 gives a view of the leader tip in I mages 33 through 37 that is enlarged by a factor of 4. In I mage 33, a space stem has formed that is about 1 m in length, with the farthest tip being about 4 m from the primary channel. In I mage 35, corona streamers can be seen emanating from the left leader tip ; i n I mage 36, a space leader has formed in these corona streamers that is about 2 m in length, with the farthest tip being about 4 m from the primary channel. Connecting streamers are evident between the space leader and the primary chann el. In I mage 37, the primary channel has extended into the region where the space leader formed in I mage 36. Figure 512 gives a view of the leader branch in I mages 56 through 59 that is enlarged by a factor of 4. In I mage 56, the leader branch enters th e Photrons FOV from the left side, and corona streamers emanat ing from the leader tip are evident. In I mage 7, two space stems have formed apparently simultaneously and in parallel. Both of these space stems are about 2 m in length, and there farthest t ips are about 5 m from the primary channel Connecting streamers are evident between the space stems and the leader channel. In I mage 58, the leader channel has extended to the spot where space stem g formed, and it has corona streamers emanating from its tip. In I mage 59, a space leader formed in the vicinity of space stem f. This space leader is about 6 m in length, and its farthest tip is about 8 m from the primary channel. Like the space
139 leader in image 7 (Figure 5 10), t he space leader in imag e 59 apparently never connected to the primary leader channel T he dE/dt record from dE 5 (about 94 m west of the tower) during the time when the stepped leader was imaged is presented in Figure 5 13. About 36 distinct dE/dt pulses were detected by dE 5. The time between the pulses ranged from 3.6 to 26.6 s, and the mean time between pulses was 12.9 s. These times are similar to the inter step time intervals reported by others for negative stepped leaders in altitude triggered lightning [ Laroche et al., 1988; Laroche et al. 1991; Lalande et al., 1998; Chen et al., 2003; Lu et al., 2009]. Moreover, the mean interstep time interval determined from the dE 5 record is greater than the frame times of the high speed camera, confirming that it was possible f or the camera to resolve individual steps and their associated processes. Some of the pulses occurring close in time were lik ely associated with the same step, as was reported by Howard et al. . The large dE/dt pulse at time zero was produced by the return stroke that occurred when the leader attached to ground. Note that the return stroke was not a typical return stroke since, as described in Section 2.2.2, the height of the upper end of the channel was limited to the height attained by the upward positive leader. 5.3 Upward Positive Connecting Leaders Of the 36 return strokes triggered in 2008, 19 were imaged in high speed video. Upward positive connecting leaders were observed preceding 12 of these 19 return strokes (63%), in three different flashes: return strokes 1 and 2 of UF808 (shown in Figures 514 and 515, respectively), return strokes 2 and 3 of UF0811 (shown in Figures 516 and 5 17, respectively), and return strokes 1 through 8 in UF0818 (shown in Figure 518, and panels C and D of Figure 54 show the upward positive connecting leader for the eight stroke ). Of the 75 return strokes triggered in 2009, a total of 64 were imaged in highspeed video. Upward positive connecting leaders were observed preceding only 3 of these 64 return s trokes (4.7%), each in a different
140 flash: return stroke 9 of UF0913 (shown in Figure 519), return stroke 2 of UF0917 (shown in Figure 5 20 ), and the return stroke 7 of UF0927 (shown in Figure 5 21). As noted in Section 3.6, the tower current configura tion was different in the two years ; a grounded rectangular intercepting wire was placed several meters above the launch tubes in 2008, but not in 2009. Table 5 4 summarizes the lengths of the upward positive connecting leaders and the estimated attachment height assuming that the upward and downward leaders propagated with the same speed (so that they met in the middle of the gap between them) As can be seen in Figures 5 14 through 5 21 and Table 5 4, the lengths of the upward positive connecting leaders in the highspeed video images vary from 5 m to 74 m with a mean length of 23 m The estimated attachment heights for the leaders were essentially the same for retur n strokes within the same flash: about 96 and 98 m f or the two strokes in UF0808, about 52 m for the two strokes in UF08 11, and between 41 and 44 m for six (of eight) of the strokes of UF08 18. The estimated attachment heights for s trokes 6 and 8 of flash UF0818 were similar and lower than the attachment heights of the other six strokes about 34 and 36 m, respectively I nterestingly, strokes 6 and 8 of UF0818 are believed to have been preceded by dart stepped leaders. The leader channels were significantly less luminous for strokes 2 and 7 tha n for the other strokes of UF08 18, possibl y because only streamers were imaged, or alternatively, because less charge was deposited along the leader channel resulting in less current and thus less luminosity [ Idone and Orville 1985]. For all 15 return strokes for which an upward positive connect ing leader was observed, the estimated attachment heights varied from 24 to 98 m with a mean of 50 m. Unfortunately, no upward positive connecting leader was imaged in two consecutive frames, so it is impossible to estimate their development speed.
141 Of t he 15 downward negative leaders imaged with upward positive connecting leaders 11 are inferred to be dart leaders because (1) they produced smooth electric field changes without pulse activity, (2) the y produced no appreciable current (or current pulses) in the launching apparatus, and (3) no clear streamer zones, corona streamers or stepping processes were evident in the highspeed video images. T he downward negative leaders for return strokes 5, 6 and 8 of UF08 18 (Figure 518) and return stroke 2 of UF 09 17 (Figure 5 20) are inferred to be dart stepped leaders because there were pronounced pulses in electric field and corresponding current pulses were detected in the launching apparatus. The current pulses observed for these leaders were likely the res ponse of the rocket launch ing apparatus and the grounding conductor acting as an electricfield derivative (dE/dt) antenna located directly beneath the approaching downward propagating leader, while the electric field pulses were radiated from the downward steps. In this view, there is no evidence that the upward connecting leaders were stepped. Alternatively, the current pulses detected in the launching apparatus may in fact be due to the upward connecting leader stepping, but only when, and in response to, corresponding downward leader stepping. The observations for the dart stepped leader preceding return stroke 5 of UF0925 (Figure 55) supports the view that the current pulses are due to the downward leader and not an upward connecting leader that i s stepped For this leader, pronounced current pulses were detected in the launching apparatus during the 30 s interval leading to the return stroke. However, as seen in Figure 55, no upward positive connecting leader was imaged in any of the nine 4.2s high speed video frames recorded during the time when the current pulses were detected. Considering that streamers emanating from the downward leader were detected by the camera, one might expect that if an upward positive connecting leader were presen t, it would also be detected. In
142 this view it can be concluded for the case of the fifth return stroke of UF09 25 that the current pulses must have been induced by the downward negative leader steps. 5.4 Discussion The upward positive leader discusse d in Section 5.2 developed in a stepwise manner. As noted in Section 126.96.36.199, other researchers using streak photography, have similarly observed upward positive leaders in triggered lightning developing intermittently [e.g., Laroche et al., 1988; Idone 1992; Rakov et al. 2003; Idone in Rakov and Uman, 2003]. Intermittent development of positive leaders has also been observed in upward negative lightning from tall buildings and towers [ e.g. McEchron 1939; Berger and Vogelsanger 1966; Berger and Voge lsanger 1969] in downward positive lightning [e.g., Wang et al., 2011], and in long laboratory sparks [e.g., Gorin et al., 1976; Les Renardieres Group, 1977; Gallimberti, 1979; Domens et al., 1991; Bazelyan and Raizer 1998; Bazelyan and Raizer 2000; Gu et al. 2010]. The high speed video images presented in Figure 52 are the first images from a framing camera of a positive leader clearly stepping and as it first develops from a triggering wire with wire base current pulses precisely correlated with each step. The luminosity waves that appear to propagate downward from the leader tip are consistent with similar observations by Idone  and Rakov et al. . The currents determined for each leader step, both measured and scaled (on average 59 and 34 A, respectively) are consistent with other reports of first current pulses associated with the upward positive leader at low altitudes [ Laroche et al., 1988; Lalande et al., 1998; Willett et al. 1999; Biagi et al. 2009] but are up to two orders of magnitude less than the peak currents (on average 1.6 kA) reported for individual steps in an upward positive leader at higher altitudes (probably somewhere around 300 to 500 m) by Rakov et al. . The individual steps of the upward positive leader e xamined by Rakov et al.  transferred on
143 average 31 mC of charge, which is significantly (a thousand times) more than the average charge per step 64 C, for the upwa rd positive leader in UF0930. The measured charge s for the upward positive leader st eps in UF09 30 are consistent with charge measurements of long positive laboratory sparks which range from about 35 to 50 C m1 [e.g., Les Renardieres Group, 1972; Les Renardieres Group, 1974; Les Renardieres Group 1977; Domens et al., 1991] Domens et al. , who studied the 3D development and charges of positive leaders in a 16.7m spark gap, determined that 50 C of charge flow ed through the high voltage electrode for each meter of leader growth. For the upward positive le ader of UF09 30, the charge per unit length was computed for each step by dividing the total charge per step by the steps length. The computed charge per unit length ranged from 26 to 110 C m1 with a arithmetic mean of 51 C m1, which is essentially the same value determin ed for the long laboratory spark by Domens et al.  T he upward positive leader developed from the wire tip at a height of about 123 m with a speed of 5.5 x 104 m s1, and its speed had increased to 2.1 x 105 m s1 when it reached a height of 310 m. The speed at 3 10 m is consistent what has been reported by Idone in Ch.7 of Rakov and Uman  and Laroche et al.  for leaders at altitudes around 1 km It is worth noting that Yoshida et al. , who presented a detailed description of the s ame upward positive leader as it developed to higher altitudes using 3D interferometric images, reported that the leader develop ed from 1.5 to 3.7 km with a three dimensional speed of 3.3 x 106 m s1. The lengths of the leader s first steps between heigh ts of 123 and 134 m (0.8 to 2.2 m), were smaller than those measured by Laroche et al.  (14 m) for a lea der at a height of about 1 km. T he mean interstep time intervals for the upward positive leader in UF09 30 was about 21 s, which is consistent w ith the average interstep time interval reported by Laroche et al.  of 20 s
144 but less than the average interstep time of 50 s that Rakov et al.  inferred from current and electric field records for an upward positive leader at a height of 300 to 500 m. The apparent diameter of the upward positive leader (0.88 m) is likely the diameter of the leaders corona sheath, whereas the longitudinal current is confined to a small core several millimeters in diameter as is observed for long positive polarity laboratory leaders [e.g., Gorin et al ., 1976; Gallimberti, 1979] The luminous segments of secondary channel depicted in Figures 54 through 56 and 59 through 512, that were below and separated from the primary leader channel have spatial dimensi ons that are similar to or slightly larger than the space stems and space leaders observed in long laboratory sparks. The lengths of the observed s pace leaders ranged from 2 to 6 m, and their farthest tips were between 4 and 12 m from the primary channel. Ortega et al.  reported that space leaders in a 16.7 m spark gap develop a distance of 1.4 to 2.2 m ahead of leader channels and extend the leader channel by 1 to 5 m. Les Renardieres Group  reported similarly that space leaders in 5 m and 7 m gaps develop 1 m to 2.5 m ahead of leader channels and extend the leader channel by about 1 m. Les Renardieres Group  observed multiple simultaneous space leaders in long laboratory sparks, with the number of space leaders that develop simultane ously increasing with increasing voltage rise times. Ortega et al  reported the simultaneous development of several space leaders from different space stems, in series (co linear) or parallel (side by side), and noted that a space stem may develo p into a space leader only if an additional space stem develops further ahead of the leader channel. Ortega et al.  reported that current pulses from laboratory leader steps exhibited two distinct peaks when they formed with two space leaders. Space stems and space leaders were observed forming in series and in parallel ahead of
145 the leaders in UF09 13 and UF0925. For UF09 13, two space stems were observed to have existed in parallel, or side by side, in Frame 57 (best seen in Figure 512) For UF 0925, it is evident in F rame 7 of Figure 55 and Figure 56 that two well defined segments of luminosity appear in series ahead of the leader channel that we re about as luminous as the leader channel, suggesting that they were probably space leaders. Add itionally, there were two segments of luminosity ahead of the leader in F rames 4, 5, and 8. In Frames 4 and 8, it appears that there is a space stem ahead of a space leader, and in Frame 5, it appears that there is a space leader ahead of a space stem T he observations of space stems and space leaders forming in series and in parallel are consistent with the observations of laboratory sparks noted in above Howard et al. , using a dE/dt time of arrival network to locate sources of natural and tr iggered lightning steps with an accuracy on the order of meters, reported that the location of subsidiary peaks in a single overall leader step dE/dt pulse were grouped within a few tens of meters, indicating that the causative leader step was formed throu gh a complex series of breakdowns. This hypothesis is supported by the observations presented in Section 5.3. F or the dart stepped leader preceding return stroke 5 of UF0925, all of the dE/dt pulses that were measured during the time when the leader was imaged had one to three secondary peaks, and the corresponding current pulses (the current system was likely acting in part as a dE/dt antenna) had similar peaks (Figure 5 7) Many of the dE/dt pulses recorded during the time when the downward negative l eader developed to ground in the altitude trigger, UF09 13, also had secondary peaks (Figure 5 13) If there were 10 steps observed for the dart stepped leader in UF0925 (Figures 55 and 56) as the dE/dt record indicates (Figure 5 7) then the average step length was about 11 m, which is close to the 5 to 10 m reported by Orville and Idone  for steps of dart stepped
146 leaders in triggered lightning. Schonland  reported that leader step lengths in natural dart stepped leaders near ground were on average 12.7 m, and Idone and Orville  report ed step lengths of 10 to 30 m. The average downward speed s for the dart stepped leader s in UF0913 ( Figure 5 5) and UF09 25 w ere between 1.25 x 106 and 2.5 x 106 m s1, and 2.7 x 106 and 3.4 x 106 m s1, respectively. These values are consistent with the observed range of speeds, between 2 x 106 m s1 and 8 x 106 m s1, reported for dart stepped leaders in previous studies [ Schonland, 1956; Orville and Idone,1982; Wang et al., 1999b]. Although it a ppears likely that the steps in the dart stepped leader discussed here developed through mechanisms similar to those in long laboratory sparks, it is not clear that such mechanisms operate on the longer spatial scales usually reported for stepped leaders i n natural lightning, between 10 and 200 m [ Schonland, 1956; Berger and Vogelsanger 1966; Chen et al., 1999]. The l onger leader steps observed by others may be produced through multiple space leaders developing in series and nearly simultaneously. Altern atively, as noted by Hill et al. , it is possible that observed steps with lengths up to 200 m are in fact observations of upward propagating luminosity waves that we re produced by steps of short lengths. The time coincident x ray, dE/dt, and current pulses, along with the optical observation of step formation support the well established fact that x ray emissions are produced during the leader phase of lightning and are associated with the leader steps [e.g., Dwyer et al., 2004; Dwyer et al., 2005b; Howard et al., 2008]. The high electric fields of corona streamer tips that develop from leaders are presently thought to produce cold runaway electrons that cause x ray emission via bremsstrahlung radiation [ Dwyer, 2004; Moss et al., 2006]. X ray emissi on has also been observed in laboratory sparks smaller than 2 m, but apparently only in association with corona streamer development [ Dwyer et al. 2005a ; Rahman et al., 2008; Dwyer et al. 2008].
147 The streamer zone of negative laboratory leaders can be several meters in length, and in gaps shorter than 2 meters the streamer zone connects to ground without the development of space leaders [ Gorin et al., 1976; Ortega et al., 1994; Reess et al. 1995]. A detailed study of laboratory spark leaders that develop step wise via the space leader mechanism (gaps greater th a n 2 m length and with long voltage rise times) using microsecond or submicrosecond highspeed video and synchronized x ray measurements might help to clarify when and where x rays are produced in lightning and long laboratory spark leaders. The high speed video images presented in Figure 514 through 5 21 represent the first photographic observations of upward positive connecting leaders in lightning The image presented in Figure 5 4 (and Figure 518) showing the upward positive connecting leader and downward negative dart stepped leader preceding return stroke 8 of UF08 18 is the only known image in which the streamer zone of the downward negative leader is in contact with the upward positive lea der in lightning It is curious that so many upward connecting leaders were observed in 2008 while so few were observed in 2009. In 2008, upward positive connecting leaders were observed for 12 of the 19 (63%) return strokes imaged by high speed cameras whereas in 2009, only upward positive leaders were observed for only 3 of the 64 (4.7%) return strokes imaged by high speed cameras. Two theories are presented to explain this disparity. First, the rectangular intercepting wire placed above the launch t ower only in 2008 (not in 2009) may have enhanced the local electric field in such a way as to encourage the development The second theory involves how the camera framing speed relates to its sensitivity The Photron was generally operated at higher framing rates in 2009 than in 2008. Since the time per frame decreases with increasing framing speed, the amount of light that is integrated in each frame may also decrease, rendering faint objects undetectable. Wang et al. [1999a], using the ALPS photodiode array,
148 reported that the luminosity of one upward connecting discharge was an order of magnitude lower than that of the downward negative leader. However, it seems unlikely that upward positive connecting leaders would be completely undetectable when the following is considered: (1) corona and corona streamers are evident in many of the downward negative leaders, even those imaged at a framing speed of 300 kfps and (2) upward positive leader steps developing from the triggering wire were imaged for flash UF09 30 (Figure 5 2) that were of low luminosity Thus, the author favors the first theory.
149 Table 5 1. Salient information for the stepped upward positive leader of UF0930. Step Step length (m) Total leader length (m) Interstep time interval (s) Meas ured peak current (A) Scaled peak current (A)a Step charge (C) Ratio of step charge to step length (C m1) a 1.8 1.8 n/a 123 71 47 26 b 0.8 2.6 21.4 37 21 22 28 c 0.9 3.5 21.7 25 14 n/a c n/a c d 2.2 5.7 30.4 153 89 107 49 e 1.8 7.5 18.6 122 71 99 55 f 0.4 7.9 17 32 19 44 110 g 2.1 10 20.5 41 24 70 33 h 1.8 11.8 19.0 17 10 n/a n/a c i n/a b n/a 16.6 23 14 60 d n/a c j n/a n/a 24.9 20 12 n/a n/a c arithmetic mean 1.5 n/a 21.2 59 34 64 51 a) The measured pe ak current is scaled to take account of reflections at ground and attenuation along the wire ( using Equation 616 in Section 6.4.3) b) T he leader was developing outside of the cameras field of view for Steps i and j. c) Only the first peak of these cur rent pulses was resolved, the rest of the pulse was below the noise floor so the charge could not be determined. d) The charge for Step i was determined from the II VLS shunt measurement (the others were determined from the II Lo measurement).
150 Table 5 2. Lengths and distances for the space stems and space leaders observed in event UF09 25. Segment (type) a Mechanisma Distance between the lower tip of the primary channel and the lower tip of the segment (m) Segment length (m) a ss 4 1 b ss 7 1 c ss 2 1 d sl 4 2 e ss 8 2 f ss 2 1 g sl 12 2 h sl 7 4 i sl 12 4 j sl 4 2 k ss 8 1 arithmetic mean 6.4 1.9 a) The mechanism thought to have been observed, either space stem (ss) and space leader (sl). Table 5 3. Lengt hs and distances for the space stems and space leaders observed in event UF09 13. Segment Mechanisma Distance between the lower tip of the primary channel and the lower tip of the segment (m) Segment length (m) a sl 4 3 b ss 3 1 c ss 5 1 d ss 4 1 e sl 4 2 f ss 5 2 g ss 5 2 h sl 8 6 a) The mechanism thought to have been observed, either space stem (ss) and space leader (sl).
151 Table 5 4. Upward positive connecting leader lengths. Flash ID Stroke Length (m) Estimated a ttachment h eight (m) a UF08 08 1 35 96 2 74 98 UF08 11 2 16 52 3 5 52 UF08 18 1 9 43 2 16 43 3 10 42 4 22 43 5 13 41 6 15 34 7 12 44 8 16 36 UF09 13 9 64 64 UF09 17 2 10 24 UF09 27 7 22 37 Arithmetic Mean 23 50 a) Note that the upward connecting leaders initiated from the top of the intercepting wire (17 m above ground level) in 2008, and the launch tubes (14 m above ground level) in 2009.
152 Figure 5 1. High speed video images of the channel during the initial stage of UF0930. A) Image reco rded by the Phantom camera at 8 kfps (120 s per frame) showing the destroyed triggering wire that has been replaced by a plasma channel and the upward positive leader (UPL) channel. The darker region of the image identifies the Photron field of v i ew. B) Image recorded by the Photron camera at 300 kfps (3.3 s per frame) showing the plasma channel that replaced the destroyed triggering wire and about 12 m of the upward positive leader channel.
153 Figure 5 2. The sequence of 60 Photron images containing the UPL for UF09 30, along with the synchronized wire base current. The part of the Photron image containing lightning channel is shown on the left for reference. All of the images are intensity inverted and contrast enhanced. Each image in the sequence v iews about 13 x 5 m of space, and is an integration of luminosity over a time of 3.3 s. The numbers next to the leader channel is the total length of the leader channel at each step. The current measurement from the II VLS sensor saturated at about 21 A (also shown in the panel B of Figure 5 3 ).
154 Figure 5 3. The w ire base current associated with the ten upward positive leader steps in UF0930 that were imaged with high speed video. A) The II Lo measurement. B) The II VLS measurement (also shown in Figure 5 2).
155 Figure 5 4. High speed video images, and correlated electric field and current pulses for the dart stepped leader preceding return stroke 8 of UF08 18. The current (RS VL) and electric field both (E6) saturated before the return stroke In images C and D, zipper like luminosity is evident to the right of the channel that is camera artifact.
156 Figure 5 5. Ten highspeed video frames depicting the leader for the fifth stroke of UF0925 developing from 150 m height to ground during a time of 41.7 s. The frames were recorded at a framing rate of 240 kfps (4.17 s per frame). The top of the launch tower (the top of the launch tubes) is 14 m above ground. T he luminous segments that formed separately from and below the downwardextending leader channel are pointed to by white arrow and identified by white, lower case letters (some of them may be too faint to be seen in this reproduction, but are readily identifiable in the data and in the reproductions in Figure 56). The return stroke began during frame 10.
157 Figure 5 6. Expanded and contrast enhanced reproductions of t he bottom of the downwardextending leader channel seen in the first nine frames in Figure 5 5. Each image shows about 20 m x 20 m. The white arrows and white lo wer case letters correspond to those in Figure 55, and point to the luminous segments of interest.
158 Figur e 5 7. The x ray emission, dE/dt, and tower current that were recorded during the time when the 10 images shown in Figures 55 and 56 were recorded. Frame intervals shown at top. The return stroke began at time zero. The inset plots show the pulses that occurred at 17 s on a 2s timescale. Note that the lower case letters that are shown here to make clear which pulses are correlated do not re present the lower case letters used in Figures 5 6 and 57.
159 Figure 5 8. An image of the lower 200 m of channel for UF0913 recorded by the HD camera. The straight green segment is the remnant of the exploded triggering wire that has been replaced by a plasma channel. T he channel below was forged by negative downward stepped leader. The lightning struck a lightning rod on the system of protecti ve catenary wires over the launch trailer. The white box shows the approximate Photron FOV.
160 Figure 5 9. A sequence of 64 images recorded at 108 kfps (9.3 s per image) showing the first downward negative stepped leader in UF09 13. There are three rows of 21 images, each showing heights spanning from about 12 to 125 m above ground, and each about 26m horizontally. Each row of images has the heights marked on the left. Images 2 through 64 have had the background luminosity removed by subtracting image 0 (not shown). The light gr a y shadow channel above the real channel (most visible in images16 and 17) is camera artifact. Figure 5 10. The leader tip seen in Images 7 through 11 from Figure 59 enlarged by a factor of 4. Black arrows point to features of interest, and red, lower case letters identify space stems and space leaders. A space leader is evident in Image 7. Space stems are evident in Images 8 and 10. S mall black lines identify the measurements of the approximate distances between the lower tip of the space stem and the lower tip of the primary leader.
161 Figure 5 11. The leader tip seen in images 33 through 37 from Figure 59 enlarged by a factor of 4. Black arrows point to features of interest, and red lower case letters identify a space stem and space leader that are evident in images 33 and 36, respectively Small black lines identi fy the measurements of the distances between their lower tips and the corresponding leader channel. Figure 5 12. The tip of a leader branch seen in images 56 through 59 from Figure 59 enlarged by a factor of 4. Black arrows point to features of inter est, and red lower case letters identify space stems and space leaders. Note that the height scale is displayed on the right. Two space stems are evident in image 57, with the lower tips being about 4 m from the leader tip (indicated by thin black line). A space leader is evident in image 59 that is about 5 m in length.
162 Figure 5 13. The dE/dt record from dE 5 during the time when the downward negative stepped leader in UF09 13 was imaged. The return stroke occurred at about time zero.
163 Figure 5 14. High speed video images of the leader preceding return stroke 1 of UF0808. The 320 x 48 pixel images were recorded by the UF P hotron at a framing rate of 10 kfps (100 s per ima g e). Image C is obtained by subtracting the luminosity in A from the lumin osity in B. All images are intensity inverted and contrast enhanced.
164 Figure 5 15. High speed video images of the leader preceding return stroke 2 of UF0808. The 320 x 48 pixel images were recorded by the UF P hotron at a framing rate of 10 kfps (100 s per image). Image C is obtained by subtracting the luminosity in A from the luminosity in B. All images are intensity inverted and contrast enhanced.
165 Figure 5 16. High speed video images of the leader preceding return stroke 2 of UF0811. The 640 x 101 pixel images were recorded by the UF P hotron at a framing rate of 20 kfps (50 s per image). Image C is obtained by subtracting the luminosity in A from the luminosity in B. All images are intensity inverted and contrast enhanced.
166 Figure 5 17. High speed video images of the leader preceding return stroke 3 of UF0811. The 640 x 101 pixel images were recorded by the UF P hotron at a framing rate of 20 kfps (50 s per image). Image C is obtained by subtracting the luminosity in A from the luminosity in B. All images are intensity inverted and contrast enhanced.
167 Figure 5 18. High speed video images of the leader preceding return strokes 1 through 8 of UF08 18. The 320 x 60 pixel images were recorded by the UF P hotron at a framing rate of 50 kfps (20 s per image). Each image is obtained by subtracting the two frames prior to the corresponding return stroke leaving primarily the leader luminosity. All images are intensity inverted. Return stroke 8 is also shown in Figure 5 4. In some of the images, zipper like luminosity is evident to the right of the channel that is camera artifact.
168 Figure 5 19. High speed video images of the leader preceding return stroke 9 of UF0913. The 320 x 70 pixel images were recorded by the UF P hotron at a framing rate of 108 kfps (9.3 s per image). Image C is obtained by subtracting the luminosity in A from the luminosity in B. All images are intensity inverted.
169 Figure 5 20. High speed video images of the leader preceding return stroke 2 of UF0917. The 320 x 96 pixel images were recorded by the UF photron at a framing rate of 135 kfps (7.41 s per image). Image E is obtained by subtracting the luminosity in A from the luminosity in D. All images are normal intensity (not inverted). The darker, rectangular region below the leader tip is a camera artifact.
170 Figure 5 21. High speed video images of the leader preceding stroke seven of UF0927. The 320 x 48 pixel images were recorded by the UF photron at a framing rate of 240 kfps (4.2 s per i mage). Image C is obtained by subtracting the luminosity in A from the luminosity in B. All images are intensity inverted and contrast enhanced.
171 C HAPTER 6 TRANSIENT CURRENT PULSES IN ROCKET EXTENDED WIRES USED TO TRIGGER LIGHTNING In rocket and wire triggered lightning, transient current pulses in the triggering wires are observed at ground before the development of a sustained upward positive leader from the wire tip. The current pulses are caused by electrical breakdown at the tip of wire where the electric field is significantly enhanced The triggering wire behaves like a transm ission line with the precursor pulse round trip propagation time on the wire being greater than the pulse width. Current pulse reflections are produced at the ground and at the wire tip. As a result, t he current signature from a single precursor observed at ground is a sequence of pulses of alternating polarity and decreasing in amplitude during some tens of microseconds. The electrical breakdown that produces the current pulses preceding the inception of a sustained upward positive leader were first term ed precursors by Willett et al. . The relatively little information in the literature regarding precursors has been su mmarized in Section 188.8.131.52. In this chapter, new observations and measurements of precursor luminosity, currents, and remote el ectric fields will be presented. Then, wirebase precursor current measurements are analyzed to estimate current pulse propagation speeds on the triggering wire and the current pulse attenuation due to propagation losses and reflections at both ends of the triggering wire. Finally, a transmission line model is presented and used to predict wire base current signatures, and make inferences regarding the electrical characteristics of the triggering wir e, and the ground termination. In this chapter, a posit ive electric field at ground corresponds to the electric field vector pointing upward (physics sign convention). Positive current and negative electric field change at ground correspond to the removal of negative charge from or the deposition of positive charge in the atmosphere.
172 6.1 Data and Observations The luminosity, wire base current, and electric field signatures for 410 precursors in 15 wire launches have been examined. In this section, the luminosity that was often observed at the wire tips in ass ociation with the precursors is described Then examples are presented of the wire base current and electric field signatures of precursors from two separate wire launches. Finally, a description is given of the variability in precursor behavior that wa s observed. 6.1.1 Luminosity Associated with Precursor Current Pulses Of the 410 precursor current signatures examined, 339 (83%) were correlated with observations of luminosity at the wire tip in high speed video recordings that varied from a meter or so of dim, diffuse glow that often appeared fan shaped, to distinct leader channels of several meters length. In seven cases, leader channel extended from the wire tip in two consecutive high speed video frames (or a time of a few hundred microseconds) to a maximum length from 3 to 8 m. Each observation of leader channel corresponded to bursts of precursors (2 to 7 precursors occurring in rapid succession within tens of microseconds of each other) indicating that the aborted leaders developed stepwise. T he type of luminosity that was observed, or lack thereof, certainly depended on the general visibility conditions ( e.g., background light, rain) as well as the camer a frame rate and lens aperture. 6.1.2 Precursor Current and Electric Field Signatures Fig ure 6 1 presents an example of the wirebase current for a precursor observed when the wire top height was 339 m, for which the current pulse width was clearly shorter than the round trip propagation time (the time between successive peaks). As a result, the current pulses produced by successive reflections at the wire base and wire tip are easily distinguishable, and measuring the amplitudes and timing of the precursor signature features is straightforward. The
173 first pulse (and peak peak 1i ) of the dampedoscillatory signature measured at the wire base is the superposition of the current pulse that was generated at the wire tip, after having traveled down the wire, and a reflected current pulse of the same polarity from the approximate ly short circuit termination at the ground rod. The reflected current pulse propagates up the wire to the wire tip where it encounters approximately open circuit conditions, and a n opposite polarity (negative) current pulse reflection is produced that tr avels down the wire to ground. T he second peak of the damped oscillatory signature measured at the wire base is the superposition of the negative current pulse and another ground reflected current pulse (that is also of negative polarity) This sequence of reflections repeats with the current polarity reversing with each wire tip reflection, explaining the oscillatory nature of the wire base measurement. E nergy losses associated with the wire (resistance, radiation, and corona leakage current ) and imper fect reflections at the wire tip and at the ground attenuate the current and hence damp the oscillatory current pulse signature observed at ground. The shape of each successive pulse appears increasingly distorted, or smoothed, indicating that there is some frequency dependence in the process. Figure 6 2 presents the current and electric f ield signatures for a precursor that occurred at a wire top height of 168 m (about half that of the precursor shown in Figure 6 1). Note that the individual pulses for the precursor signature of Figure 6 2 are not well separated in time. A low level, steady current flow s for about 40 s and reaches a level of about 1 A before the much larger damped oscillatory signature begins. A slow ramp in the electric field begin s with the steady current flow, and ends when the damped oscillatory signature begins. These features were observed in 126 (31%) of the 410 precursors analyzed. It is certainly possible that t hese features always occur but are sometimes below the noise f loor of the measurement s (a current level of about 1 A and a field change of about 1 V m1) and thus are undetect able.
174 The precursor signatures presented in Figures 61 and 62 are relatively simple in shape. The majority of the precursor signatures anal yzed displayed more complexity in the pulse structure, such as two or more peaks (like the third current pulse in Figure 63C ) nonmonotonic rising and falling edges, and/or irregular oscillations, indicating a more complex electrical breakdown at the wir e tip. T he current pulses in most precursor signatures overlapped; that is, they we re not clearly separated in time In addition, since the pulse structure is more distorted with each successive reflection cycle, distinguishing features, such as two peak s, are often lost, typically by the fourth pulse. Precursors tended to occur in bursts more frequently with increasing wiretop height. There was no obvious relationship between the height at which the precursors occurred and the precursor features, such as low level steady current of pulse shape. Figure 6 3 shows how the precursor signatures change as the triggering wire extends with three examples of precursor signatures in wire base current and electric field from wire launch UF09 11 (the 11th launch of 2009) at the beginning (26.20435 s), in the middle (26.77435 s) and just before the UPL (27.59095 s) when the wire top heights were 31 m, 90 m, and 200 m, respectively (the full record for Launch UF0911 is shown in Figure 6 4). As the wire top height increased, the number of current reflections increased, and the pulses increased in width. Note that for the precursor that occurred when the wire top height was 200 m, the initial current pulse has a multipeak structure that is lost by the fourth pulse 6.1.3 Precursor Rates Precursors occur at different rates in different wire extension As an example, data are presented for two launches within a time of about 18 minutes in which precursors occurred at significantly different rates, even though the wi res were extended upward beneath the same thunderstorm at similar extension rates, and initiated sustained upward positive leaders at about the same heights. As can be seen in Figure 6 4, precursors in launch UF09 11 occurred quasi -
175 periodically (with a pe riodicity that was regular, but with slightly different times from precursor to precursor) throughout the wire ascent, generally every several hundred microseconds to a few milliseconds. Based on the total time during which precursors occurred in launch U F09 11 (about 1.4 s), somewhere between 5,000 and 10,000 individual precursors occurred during the wire ascent. In the second wire launch ( UF09 12) shown in Figure 6 5, precursors occurred quasi periodically only during a 250ms interval for wire top hei ghts from about 30 m to 60 m, followed by a 380ms interval with no measurable current in the wire and then a 680ms interval in which 41 precursors without obvious periodicity In Figure 6 4, the precursor current pulses began at about 26.1 s, when the w ire tip was at a height of about 30 m AGL. Note that the pulses in electric field before time 26.1 s were not produced by current in the wire. Between times 2 6.1 and 26.3 s, the current pulses occur sporadically and are unipolar while the corresponding electric field pulses are bipolar The pulses begin occurring quasi periodically just after time 26.3 s. Figure 6 6 presents a 300ms expanded view of pulses from 26.35 s to 26.65 s showing that the amplitude envelope of the current pulse s exhibits somew hat periodic variations, and that the current pulses occur less frequently when the pulse amplitudes are larger, a general feature of all the launches. A fter time 26.8 s in Figure 6 4, the amplitude envelope of the current pulses varies with more distinct periodicity. At time 26.9 s, current pulses and pulse bursts begin occurring, somewhat randomly, with magnitudes many times that of the pulse s occurring quasi periodic ally. 6.1.4 Negative Polarity Precursors In one launch (UF09 01), made when the groundlevel electric field was 4.5 kV m1 indicating that predominately posit ive charge was overhead, observations were made of negative polarity precursor signatures in current and electric field occurring quasi periodically every several hundred microseconds in a manner similar to those from UF09 11 ( Section 6.2.3).
176 These negative polarity precursor signatures are presented in Figure 6 7. Launch UF0901 was not recorded in video, so there was no measurement of the wire top height versus time or observations of luminosity corresponding to the precursors. However, based on the time when the rocket was launched and the modeled trajectory in Section 7.3.1, it is estimate d that the precursor signatures presented in Figure 6 7 occurred when the wire top height was somewhere between 75 and 125 m. The observed negative polarity precursors do not appear much different in rate and shape from positive polarity precursors. The negative polarity precursors occurred at a rate of about one every 1 ms, and generally had pe ak currents of several amperes and electric field changes of a few volts per meter. 6.2 Analysis This section contains analysis of measured precursor current signatures. First, the current pulse propagation speed along the wire is measured. Then, informa tion is developed from which the apparent attenuation of the current pulses due to propagation losses and imperfect current reflections with each round trip on the wire can be estimated and compared to the model predictions in Section 6.4.3. Finally, the charges in the first current pulse and in the entire precursor current signature, as measured at the wire base, are compared. 6.2.1 Propagation Speed The current pulse propagation spe ed on the triggering wire is measured from wire base current measurements by dividing the wire top height by one half of the average of the times between the successive peaks (round trip propagation times) for the first six peaks. For most precursors, the peakto peak times were equal within 200 ns, or 2 sample points. There were 27 1 precursor signatures with single peaked pulses that were not saturated and hence suitable for current pulse propagation speed measurement. The speeds of the current pulses for these precursors are plotted versus wire height in Figure 6 8. There is uncertainty of at least 200 ns
177 (one sample point time for each peak time measurement) in the round trip propagation time that introduces a margin of error in the calculated current pulse speed (shown as blue bars in Figure 68) that depends on the wire top height (the longer the wire length, the longer the peakto peak time is, and thus the 200 ns timing uncert ainty becomes less of a factor) The current pulse propagation speed is roughly between 2.7 x 108 and 2.8 x 108 m s1 (disregarding the 200ns uncertainty) for wire top heights from 80 m to 200 m. The speed decreases for larger wire top heights, to as low as about 2.3 x 108 m s1, or about 20% lower, for a wire top height of 340 m. The measured speeds of three specific precu rsors used in the mode ling ( Section 6.4) are identified in Figure 6 8 by red circles None of the six wires studied here exhibited a tilt angle of more than a few degrees or had a significant curvature. It is estimate d that the wire tops did not deviate horizontally from the launch tower more than 10 m. 6.2.2 Precursor Charge and Current The precursor signature in Figure 6 1 is one of 19 signatures of the 410 analyzed in which the starting point of the successive pulses were clearly distinguishable so that pulse amplitudes cou ld be measured accurately. For these 19 precursor signatures, which occurred at wire tip heights between 135 m and 340 m, t he peak amplitudes of the first four current pulses peak ni where n = 1, 2, 4 (as identified in Figure 6 1), w ere measured. Figure 6 9 is a scatter plot of the computed ratios peakpeak 21ii peakpeak 32ii and peakpeak 43ii versus wire top height for the 19 precursors signatures. The ratios were roughly normally distributed from 0.45 to 0.75, and the arithmetic mean of all the ratios was 0.60 with standard deviation of 0.08. There was no apparent relationship between ratios of current peaks and wire top height. There was a clear relationship between the charge in the first current pulse, Q1, and the total charge delivered to ground by the end of the entire precursor current signature, QT otal.
178 These charges were determined by computing the time integral of the current from the beginning of the precursor signature to: (a) the beginning of the second pulse for Q1, and (b) the point when the current attenuates below the measurement noise floor for QTotal. The charges Q1 and QTotal were computed for 15 of the 19 precursor signatures analyzed in Figure 6 9 in which there was little to no overlap of pulses, so that the charge of the first current pulse could be accurately determined. Figure 6 10 is a scatter plot of Q1 versus QTotal for the se 15 precursors There is linear relationship between the two, with a correlation coefficient of 0.99. Neglecting the non zero intercept, the ratio Q1/QTotal is 1.64. Figure 6 10 also shows the charges Q1 and QTotal that were computed for the model predicted current signatu res for precursors 2 and 3 (s Section 6.4). Precursor 1 was not used for the calculation because its pulses overlapped, making it impossible to determine accurately the charge in the first pulse. 6.3 Modeling In this section, three representative precursor current signatures (referred to as precursors 1, 2 and 3) are modeled. These three precursors occurred on the same triggering wire (UF09 37) when the wire top was at heights of 205 m, 307 m, and 339 m, respectively. First, a description is given of the assumed model input incident current waveforms, which are inferred from the wire base measurements. Next, a description is given of t he distributed (transmission line) circuits and the characteristic electrical parameters used to model the precursor current propagation on the triggering wire, ground lead, and ground rod, as illustrated in Figure 6 12, summarized in Table 6 1, and discussed in Section 6.4.2. Finally, in Section 6.4.3 the model predictions are presented and compared to the measurements. 6.3.1 Model Input Panels A B and C of Figure 611 present the model input incident current pulses for precursors 1, 2 and 3, respectively. The shape of the incident current pulse is assumed to be
179 identical to the shape of the measured precursor from time zero to the time when the second pulse begins. In each precursor modeled here, a power law relation is fit to the smooth current decay from the first pulse peak time to the time when the second pulse begins. The input current from the time when the second pulse begins to a time 25 s after the pulse begins is an extrapolation of the power law relation, and the last point of the input current is set equal to zero. The first pulse of the precursor signature measured at ground is the superposition of the incident wave and a reflected wave at ground, and as a result is larger in amplitude (almost twice) than the current pulse arriving at ground (and could be potentially different from the input pulse in shape, which is assume d to not be the case) which itself is attenuated from its initial value by propagating down the wire. Thus the assumed input current pulse s were reduced in amplitude by multiplying the entire input waveforms by scaling factor s The scaling factors, given in Figure 6 11 and Table 6 1, were found through trial and error by running the model and checking the m atch between the model predicted first pulse amplitude and the measured first pulse amplitude. 6.3.2 Model Description The transmission line model [e.g., Sadiku, 1994, Ch 11], shown in Figure 6 12, consists of three interconnected sections representing the triggering wire (top), the groundlead (middle), and the ground rod (bottom). Each is considered to be a straight, vertical, and uniform transmission line with different parameters. The transmission line sections shown in Figure 6 12 are implemented in Pspice using the lumped element lossy transmission line model (TLUMP128) [ Roychowdhury and Pederson, 1991; Roychowdhury et al., 1994]. The Pspice model predictions for propagation on the triggering wire were verified in several cases by multiplying the discrete Fourier transform of the input signal wi th the propagation constant ( Equation 62) in the frequency domain, and then taking the inverse discrete Fourie r transform of
180 the result. The result of the frequency domain multiplication yielded results that were identical to the time domain convolution performed by the Pspice model. The Pspice software provided a straightforward way to connect the three transmi ssion lines so as to be able to model the complex reflections at the transmission line connections (triggering wire to ground lead, and ground lead to ground rod). The incident precursor current pulse (at the top of the circuit in Figure 6 12) is input to the circuit using an ideal current source, making the current reflection coefficient at the wire tip 1. Note that the actual current measurement is made and the presented model output is calculated at the top of the ground lead, which is located at the bottom of the triggering wire. Nevertheless, the model predicts essentially the same current waveform at the bottom of the ground lead as at the top of the ground lead, but slightly delayed in time (by about 40 ns). The complex sinusoidal current jtIze on the transmissionlines used to represent the j1 is described by the single frequency timeharmonic, wave equation in the frequency (or phasor) domain [ Sadiku 1994]: 2 2 2Iz Iz z 61 w here z is the propagation distance, and is the propagation constant, defined in terms of the distributed circuit parameters as jRjLGjC 62 where R, L, G and C are the series resistance, series inductance, shunt conductance, and shunt capacitance, respectively, all per unit length. In Equation 62 is the phase constant, given by:
181 1 22 2 222ReRGLCRGLCLGRC2 [Np m1] 63 1 2 2 2 2 22ImLCRGRGLCLGRC2 [radian m1] 64 The attenuation constant unit Np is a Neper, the commonly used dimensionless unit of attenuation. The transmission line characteristic impedance, the ratio of the voltage to the current for a wave traveling in the +z direction, is given by: RjL Z GjC [ 65 The time domain solution to Equation 61 for a wave propagating in the +z direction is: zjt z 00Iz,tReIeeIecostz [A] 66 where Re means the real part, and I0 is the current amplitude at z = 0 (assumed to be real). The current wave propagation speed (phase velocity) predicted by Equation 61 is: pv [m s1] 67 T he following is a description of how the values of transmissionline parameters for the triggering wire, ground lead, and ground rod were determined. The triggering wire has characteristic per unit length values of: series resistance RTW due to the finite conductivity of the copper, series inductance LTW due to the magnetic flux around the wire per unit current in the wire and shunt capacitance CTW due to the charge on and around the wire (in a corona shea th) per unit voltage. For the vertical wire above ground transmission line, one can visualize the return path (the second conductor required for any transmission line) as being the wires image below ground. Such a transmission line is necessarily non uniform, particularly near ground, with the per unit length values of shunt capacitance and series inductance varying with height
182 [e.g., Baba and Rakov 2003; Theethayi and Cooray 2005; Baba and Rakov 2005; Visacro and De Conti 2005]. However, as a simplifying approximation, it is assumed here that all transmission line parameters are constant with height and independent of frequency, some aspects of these assumptions being discussed later in this section and in Section 6.4.3. The DC value of per unit l ength resistance of the 0.2 mm diameter triggering wire, RTW, was measured to be 0.5 1. The measured series resistance of the triggering wire was found via the model to be insufficient to attenuate the current pulses to the extent observed in the meas ured precursor signatures. Additional current attenuation was provided in the model by using a n effective shunt conductance per unit length GTW ( associated with radial leakage current). It is important to note that the GTW does not represent the true phy sical configuration since, in reality, transverse conduction current exists only within the corona sheath, but not in the space between the outer boundary of the corona sheath and ground. T he value of GTW (constant with height) was chosen in the model so that the model predicted precursor signature amplitude attenuation matched that of the measurement. Thus, the shunt conductance should be viewed as a means to apply additional attenuation to the current pulse as it propagates on the transmission line. The inductance per unit length LTW is calculated using the relation given for a vertical conductor above ground by [e.g., Bazelyan et al ., 1978; Rakov 1998] : 02h Lln 2r [H m1] 68 where h is the height above ground, r is the conductor radius, and 0 is the permeability of free space. Equation 68 describes LTW as a weak function of height that varies little over the heights of interest. The value used in the modeling is LTW = 3.0 H m1, which is the value yielded by Equation 68 for a 0.2 mm diameter wire for intermediate heights around 150 m.
183 G << 6.4.3 to be the case for the primary frequencies present in the pulses, the attenuation and phase constants described in Equations 63 and 64 can be approximated as: TW TW TW TW TW TWCL 1 RG2LC [Np m1] 69 2 TWTW TWTW TWTWGR 1 LC1 8CL [radians m1] 610 If the squared term in the brackets of Equation 610 is assumed to be zero, which is a good approximation in the low loss case, then Equation 67 becomes: p TWTW1 v LC [m s1] 611 where vp is the current propagation speed along the wire, and LTW is the per unit length inductance of the wire given by Equation 68. The values of capacitance per unit length, CTW, that are used in the modeling are inferred from Equation 611 and the measured current propagation speeds from Section 6.3.1. The inferred values of CTW are larger than the values expected from the relation given by Bazelyan et al  for a vertical conductor of radius r at a height h ab ove ground: 02 C ln2hr [F m1] 612 0 is the permittivity of free space. As expected, using the values of L and C given by equations 68 and 612 in place of LTW and CTW in Equation 611 yields a propagation speed vp = c. The CTW is often viewe d as being given by Equation 612, but for a value of radius that is larger than the conductor (wire) radius and equal to that of the corona sheath [e.g., Baz elyan et
184 al., 1978; Kodali et al., 2005]. The value of LTW computed from Equation 68 is unchanged by radial expansion of charge since the inductance depends on the longitudinal current, which flows solely in the wire [ Rakov 2007]. The corona sheath and the lower than light current pulse propagation speed are discussed further in Section 6.5. T he ground lead that connects the bottom of the triggering wire to the ground rod has per unit length values of series resistance RGL, series inductance LGL, and shunt capacitance CGL. The ground lead (2.5cm wide copper braid) has a measured series resistance per unit length RGL 1. The shape of the copper br aid was somewhere between flat and cylindrical, but as a simplifying approximation it is a ssume d to be uniformly cylindrical with an effective radius of 1.25 cm. Under this assumption, it is expected that the electric field on the ground lead surface (whi ch is estimate d to be on the order of 105 V m1 in Section 6.5) is below the level necessary for corona inception. T he ground lead shunt conductance is assumed to be zero, and the current propagation speed on the ground lead wire is assumed to be equal to the speed of light. The per unit length values of series inductance and shunt capacitance for the ground lead, determined from Equations 68 and 6 12 using h = 11 m (the upper height of the ground lead) and an effective radius of r =1.25 x 102 m, are LGL = 1.5 H m1, and CGL = 7.4 pF m1, respectively. T he buri ed ground rod is modeled in two different ways: as a lumped resistor of 20as a 25 m long buried transmission line with series resistance RGR, series inductance LGR, shunt capacitance CGR, and shunt conductance GGR. The value of series resistance RGR is DC resistance for a 16 mm diameter steel rod, approximately 8 m 1. The values of LGR, CGR, and GGR are adapted from a model used in Mata et al [ 2000] for similar ground rods at the ICLRT. The shunt conductance is the inverse of the low freque ncy, low magnitude current resistance between the ground rod and the reference ground (surrounding soil), which has been
185 measured to be 20 Crawford et al., 2001]. To determine the shunt conductance per unit length, the total measured resistance was fir st converted to a parallel resistance per unit length via multiplication by 25, yielding 500 GR = 2 mS m1. The total value s of C and L of the ground rod are determined using the following relations from Mata et al.  : 9 rl C 10 18ln4ld [F] 613 74l L2lln10 d [H] 614 where l is the length of the ground rod (25 m) r is the relat ive permittivity of the soil ( assume d to be 10), and d is the diameter of the ground r od (16 mm). The total values of C and L for the grounding rod according to Equations 613 and 614 were 1.6 nF and 44 H, respectively. The total values of C and L were converted into per unit length values via di vision by 25, or the number of 1m segments for the ground rod, yielding values of LGR = 1.8 H m1 and CGR = 64 pF m1. 6.3.3 Model Predictions Table 6 1 summarizes the parameters of the triggering wire transmission line that yielded the model predictions used to fit the measurements, the scaling factor needed to match the first pulse amplitude of the model output and measurements, the wire top heights at which the precursors occurred, and the measured current propagation s peeds on the triggering wire ( Se ction 6.3.1). Figure 6 13 presents the three measured precursor signatures and the corresponding model predictions for the case that the grounding system is represented by a lumped resistor and for the case that the grounding system is represented by a 25m transmission line. Each of the three rows of Figure 6 13 shows a different precursor on a 25s time scale on the left, and an
186 expanded view from 4 s to 9 s on the right. Overall, the model predictions matched better the measurements when the grounding system was represented by a 25 m transmission line than when the grounding system was represented by a lumped resistor: (1) the model predicted current pulse peaks occurred later in time, and matched better the times when the measured current pulse peaks occurred, (2) the model predicted current pulse shapes were smoother, and matched better the shapes of the measured current pulses, and (3) the model predicted current pulse amplitudes matched better the measured current pulse amplitudes. For either grounding system, the model predicts that all the precursor charge eventually leaves the bottom of the triggering wire by the end of the 25s model run. As evident from Figure 6 8, the measured current pulse propagation speeds were lower for precursors oc curring at greater wire top heights. This observation was reproduced in the modeling by using greater triggering wire capacitance per unit length for longer wire. As can be seen in Table 6 1, the measured current propagation speed for precursors 1 and 2 was 2.6 x 108 m s1, and according to Equation 611, the capacitance per unit length of the triggering wire, CTW, for these precursors 1 and 2 was 4.9 pF m1. The measured current propagation speed for Precursor 3 was 2.5 x 108 m s1, or about 4% slower than the speed for Precursors 1 and 2, and according to Equation 611, the value of CTW was 5.3 pF m1, or about 8% higher than the value of CTW for precursors 1 and 2. For precursor 2, there is timing mismatch between the model predicted current pulse peaks and the measured current pulse peaks, most notably in Fi gure 6 13 for the seventh current pulse at 16 s, possibly indicating that the value of CTW used for precursor 2, 4.9 pF m1, was too low. Using a CTW value of 5.1 pF m1 in the model yields a signature with current pulse reflection timing that matches be tter that of the measured current pulse reflections.
187 The values of RTW, LTW, GTW, and CTW for the triggering wire that yielded the best model predictions satisfy the low loss conditions for frequency content TWTWfR2L30kHz and TWTWfG2C40kHz so Equations 69 and 610 are good approximations for the main portion of the pulse since a transient pulse having a full width of 3 s, like that of the input current pulses, approximately corresponds to a primary sinusoidal wave in the Fourier spectrum having a period of 6 s, or a frequency of about 170 kHz, above the low loss frequencies noted above. Clearly, however, the input current pulses contain low frequency components that do not satisfy the low loss criterion, and a DC component to which the transmission line theory does not apply. Low loss r estrictions were not used in the model solutions presented in Figure 6 13 (or Figure 6 14 discussed below). The calculations above indicate that the primary current pulse frequency content is sufficiently high to propagate on the triggering wire in the low loss mode, which justifies the calculation of CTW from the propagation speed using Equation 611 for lossless transmission lines (in Section 6.4.2). Furth er justification that the current pulses propagate on the triggering wire in the low loss mode can be found by comparing the exact attenuation constant given by Equation 63, to the low loss attenuation constant, given by Equation 69, using the characteristic values found via modeling. The attenuation constant for propagation on the triggering wire yielded by Equation 63 is 8.2 x 104 Np m1 for frequencies less than about 10 kHz, and for greater frequencies, the att enuation constant increases by less than 1% at the highest measured frequency of 3 MHz. The attenuation constant is essentially identical for the three values of CTW in Table 6 1. The low loss approximation for the attenuation constant yielded by Equation 69, which is frequency independent, is the same, 8.2 x 104 Np m1. The attenuation constant value of 8.2 x 104 Np m1 for the triggering wire was determ ined by comparing the model current pulse peak amplitudes
188 after the current pulses have traversed 25% and 75% of the triggering wire length. The pulse peak decreases by 8% for 100 m of propagation on the triggering wire. The characteristic impedance of t he triggering wire, ZTW, yielded by Equation 65 using the characteristic values found via modeling, is about 600 increases for higher frequencies, and becomes constant at about 800 than 200 kHz. The characteristic impedance of the ground rod, ZGR, is 2 below 100 Hz, and increases to about 120 ground lead between the triggering wire and ground rod has a negligible effect on the current entering the grounding system transmission line, as the model predicts, then the current reflection coef ficient at the bottom of the triggering wire (as though it were connected directly to the 25m transmission line grounding impedance) is given by: TWGR TWGR TWGRZZ ZZ 615 According to Equation 615, the current reflection coefficient is slightly l ess than 1 at frequencies below 10 kHz, and it decreases with increasing frequencies to a value just below 0.8 at a frequency of 3 MHz. The current reflection coefficient at the bottom of the triggering wire can be inferred by taking the ratio of the peak amplitude of the first upward, ground reflected current pulse to the peak amplitude of the first downward current pulse. These two pulses overlap near the bottom of the triggering wire, so the peak amplitudes were measured in the model at the mid point of the triggering wire, and then adjusted appropriately to account for the expected attenuation after propagating a distance equal to half the triggering wire length by multiplication with exp( an inferred current reflection coefficient at ground of about 0.9, which is in the range of values calculated using Equation 615.
189 The ratio of the input inci dent current pulse amplitude and the first current pulse amplitude measured at the wir e base (the scaling factor described in Section 6.4.1) increased with increasing wiretop height. For precursors 1, 2 and 3, the amplitude scaling factors determined by trial and error were 0.62, 0.68, and 0.72, respectively. If the current reflection coefficient at the bottom of the triggering wire of length l is G and the attenuation constant is then the scaling factors that were used for pr ecursors 1, 2 and 3 can be approximated by Equation 616. 1 GG1exp() l 616 For = 8.2 x 104 Np m1 and G = 0.9, Equation 616 yields scaling factors of 0.62, 0.67, and 0.69 for precursors 1, 2 and 3, respectively. The analysis of Section 6.3.2 was performed on precursors 2 and 3 (precursor 1 did not meet the criterion for inclusion in the analysis because the successive pulses overlapped and the starting points of successive pulses were not distinguishable). The m odeled peak current amplitude ratios ( peakpeak 21ii peakpeak 32ii peakpeak 43ii ) are similar to those in Figure 6 9, ranging from 0.51 to 0.74 with an arithmetic mean of 0.62. The charges Q1 and QT otal from the modeled and measured current signatures for precu rsors 2 and 3 were similar ( Figure 6 10). The ratios of Q1/QTotal for the model predicted signatures 2 and 3 were 1.63 and 1.47, similar to the ratios for the measured signatures, 1.62 and 1.47. The similarit ies in the measured and modeled signatures for precursors 1 and 2 discussed above demonstrates the validity of the model. 6.4 Discussion There is a good match between the model predicted and measured precursor current signatures for all three representat ive precursors. The precursor current signatures from the distributed circuit model match better the measured precursor signatures when the grounding system is represented by a 25 m transmission line, rather than a lumped resistor. T he apparent
190 frequency dependence of the groundrod characteristic impedance may be compensating for neglected frequency dependence elsewhere in the model, such as the tendency for highfrequency currents to flow closer to the conductor surface, thereby lowering the cross secti onal area through which the current flows and increasing the effective resistance, known as the skin effect [ Sadiku 1994, Ch. 10]. For the copper triggering wire, the skin depth (the conductor depth at which the current density is about a factor e1 smaller than at the conductor surface) is equal to the wire radius (0.1 mm) at a signal frequency of about 425 kHz. As noted in Section 6.4.3, the current pulse frequency content is mostly greater than 170 kHz, so the true value of RTW is expected to be higher than the measured DC value, but only up to a factor of 1.6 higher at 3 MHz (the low pass filter 3 dB point cutoff frequency of the digitizer). If the model value of RTW were made higher, then the additional current pulse attenuation provided by the nonz ero value of GTW might not be necessary for the modeled pulse amplitudes to match the measured ones. As noted in Section 6.4.2, in the transmission line representation for the vertical wire above ground, the shunt capacitance and series inductance, and hence the characteristic impedance must vary with height. A non uniform transmissionline model may reproduce better some of the observed current pulse attenuation and shape change (dispersion) due to the distributed reflections that are expected when the characteristic impedance varies in the longitudinal direction [ Baba and Rakov 2005]. However, it is likely that a nonzero series resistance would still be necessary to reproduce the observed current pulse attenuation. Figure 6 14 presents model predicti ons for precursor 3 when the value of either RTW or GTW is varied by factors of 0, 1, 2, 5 and 10, to illustrate the range of behavior that might be expected if triggering wires of different dc resistance were used, or if the value of GRW were different. The top plots show, on different time scales, five model predictions for five values of
191 RTW: 0, 0.5, 1, 2.5 and 5 1, with LTW, CTW and GTW being equal to the values used for the model predictions in Figure 613. The bottom two plots show, on different time scales, five model predictions for five values of GTW: 0, 1.3, 2.6, 6.5 and 13 S m1, with LTW, CTW and GTW equal to the values used for the model predictions in Figure 6 13. In all cases the grounding system is modeled as a 25 m transmission line. Note that the measurements are not shown in the plots of Figure 6 14. It is evident from Figure 6 14 that changing either RTW or GTW changes the amplitudes of the model predicted current pulses, but does not noticeably change the current pulse shapes, or the times at which they occur. If the value of either RTW or GTW is a factor of 5 higher than the value used to obtain the model predictions in Figure 6 13, then the current is attenuated to essentially zero by the third reflection. If the value of either RTW or GTW is higher by a factor of 10, then the current is attenuated to essentially zero by the first reflection. If the value of either RTW or GTW is zero, then the reflections continue past the time of 25s to which the model calculations were made. The model predictions presented in Figure 614 show that the current propagation speed is not appreciably changed for the different values of RTW or GTW that produce reasonable current attenuation, or for the case that RTW and GTW were zero, and the observed current attenuation is a result of some other factor, such as charge deposition to an extending plasma channel at the wire tip (as suggested for the stepped upward positive leader discussed in Section 5.5) The waveform measurements (and necessari ly the modeling results because CTW is chosen to give the measured speed) show that the current propagation speed on the triggering wire is less than the speed of light, and that the current propagation speed decreases with increasing wire top height. A c urrent propagation speed less than the speed of light on a vertical conductor can be viewed as a result of the increased capacitance per unit length, as per Equation 612, due to the
192 existence of a corona sheath that increases the effective charge radius [ Rakov 2007]. As discussed in Chapter 7 of this work a corona sheath surrounding the wire is likely created via radial corona streamers initiated by the enhanced radial electric field on the thin wire surface. The modeling results of Chapter 7 ( Section 7.5) predict a substantial corona sheath extending out to about 5 meters that, in the time necessary to extend a grounded triggering wire to a height of 285 m, builds up to several millicoulombs of charge with the line charge density on the order of tens of C m1 that increases with height. The prediction of a corona sheath around the grounded triggering wire in Chapter 5 is supported by the results present ed here, namely that the current propagation speed is less than the speed of light. In the following, the radial electric field strength on the wire surface due to the precursor charge on the wire is inferred and the issue of corona charge surrounding the wire due to the precursors radial electric field is discussed The line charge density on the wire from the precursor current, can be estimated by dividing the precursor current by the current propagation speed. The charge density for a single cu rrent peak of 50 A traveling at a speed of 2.6 x 108 m s1 is on the order of 200 nC m1, much smaller than the charge per unit length of tens of C m1 induced by the quasi static ambient field. However, according to Gausss law for the radial electric field Er from a line charge [e.g., Sadiku 1994, Ch. 4]: r 0E 2r 617 a line charge density of 200 nC m1 can produce an electric field of 36 MV m1 at the triggering wire surface, well above the threshold for corona discharge. It takes a time of about 400 ns for the current to propagate 100 m at a speed of 2.6 x 108 m s1. During a single wire traversal, t he intense radial electric fields on the wire surface from the precursor charge exist for about 1 s (for a 300 m wire top height). If the radial corona streamers propagate at a speed of 0.1 m s1
193 [ Cooray 1993], there is little time for space charge dev elopment from precursor current electric fields. Further, whatever space charge is created, it is mitigated by the oscillating current polarity, that is, charge is deposited along the wire when the current pulse is of negative polarity, and charge is remo ved when the current pulse is of positive polarity. Nevertheless, there will be some deposited corona charge around the wire, with some, if not most, of it flowing back into the grounded wire. The argument above is supported by the circuit model which pr edicts that essentially all of the charge input at the top of the triggering wire leaves the bottom of the triggering wire by the end of the 25s model run. In the model, the charge deposited on the transmission line capacitors by the decrease (attenuati on) in peak current with distance in propagation flows off those capacitors to ground within the 25 s duration of the model run. If all of the precursor charge is brought to ground, it is reasonable that precursor charge can be inferred from nearby stati c electric field change using a point charge at the wiretip approximatio n, as is done in Chapter 7 ( Section 7.3.3) According to Equation 617 the electric field on the surface of the ground lead, with an assumed effective radius of 1.25 cm, will be about 3 x 105 V m1, so the assumption that the shunt conductance per unit length for the ground lead GGL is zero is a reasonable one. The following text contai ns some speculation regarding the observed variability in the number and rates of precursor s in different wire extensions and the periodicity of the ir peak amplitude envelope. The observed variability in the number of precursors may indicate that wires ex tend through different vertical profiles of space charge density, and thus different profiles of electric field. T he periodicity exhibited in the ampl itude envelope of the precursor pulses in UF0911 may be a result of the wire tip travel ing through layer s of periodically increasing and decreasing electric fields Alternatively, the variability in rates of precursor
194 occurrence may instead be due to different vertical profiles of humidity. It is well known that positive polarity c orona processes in labor atory spark gaps require a higher electric field strength in air with high humidity than in air with lower humidity [e.g., Griffiths and Phelps 1976; Gallimberti, 1977].
195 Table 61. Precursor information, triggeringwire transmission line parameters corresponding to the model predicted precursor signatures that best match the measured precursor signatures, and the amplitude scaling factor of the input current pulse. Precursor GPS time Wire top height (m) a R TW 1 ) L TW (H m 1 ) G TW (S m 1 ) C TW (pF m 1 ) Measured Speed (m s 1 ) Amplitude Scaling Factor 1 21:21:24.089508 205 0.5 3.0 1.3 4.9 2.6 x 10 8 0.62 2 21:21:25.351162 307 0.5 3.0 1.3 4.9 2.6 x 10 8 0.68 3 21:21:25.940685 339 0.5 3.0 1.3 5.3 2.5 x 10 8 0.74 a) The wire length is this value minus 11 m
196 Figure 6 1. Current signature of a precursor in which the first current pulse, and subsequent current pulses resulting from reflections from the wire base and wire top, are clearly separated in time and easily distinguishable. Peak amplitude measurements that are used in the analysis of Section 6.3.2 are identified along with the roundtrip propagation time (peak to peak time). This is precursor 3 that is modeled in Section 6.4.
197 Figure 62. Current and electric field s ignat ures produced b y a precursor that exhibited an initial low level, steady current, and corresponding electric field ramp. A) wire base current shown on full scale, B) wire base current shown at 2 A scale, and C) electric field
198 Figure 63. The wire base current, and respective electric field measured by E2 at 156 m for three precursor signatures from event UF 09 11. Each column shows the current in the top panel and the electric field in the bottom panel. Each plot is 20 s full scale. The wire top heights were a bout 31 m, 90 m, and 200 m for the left, middle, and right panels, respectively. As the wire top height increased the number of current reflections increased, and the pulses increased in width.
199 Figure 64. The wire base current, and respective electri c field measured by E2 at 156 m for three precursor signatures for wire launch UF09 11 on a 2 s time scale. The wirebase current and electric field measurements saturate at about 125 A and 85 V m1, respectively. The sustained upward positive leader be gan at time 27.604 seconds when the wire tip height was about 234 m. The solid envelope in the current record that varies with a period around 200 ms is composed of thousands of individual pulses that are not resolvable on this time scale, some of which are shown in Figure 66.
200 Figure 65. The wire base current, and respective electric field measured by E2 at 156 m f or UF09 12 on a 1.3s time scale. The wire base current and electric field records began when the wire tip was at a height of about 40 m, and they saturate at about 125 A and 85 V m1, respectively. The sustained upward positive leader began at about 22.85 s when the wire tip height was about 190 m. Note that much of the recorded electric field change from time 21.6 s to 22.4 s is due to separate and unrelated lightning process (signatures corresponding to distant preliminary breakdown and cloud discharges are evident when the field record is examined on an expanded time scale.
201 Figure 66. An expanded view of the wire base curren t and electric field of the precursors in UF09 11 viewed at 300 ms full scale. (A) The wire base current. (B) The electric field from E2 at 156 m. Pulses generally occur less frequently (the interpulse time is greater) when the pulse amplitudes are larg er.
202 Figure 67. Wire base current and electric field signatures of negative polarity precursors during wire launch UF09 01. The wire base currents are shown in the top plots (A and B), and the remote electric fields are shown in the bottom plots (C an d D). The left plots show the precursors on a 100ms time scale The right plots shows, on a 15s time scale, the largest precursor signature that occurred at time 1.76066 s. It is estimate d that these precursor signatures occurred when the wire top hei ght was some where between 75 and 125 m ( Section 6.2.4).
203 Figure 68. A scatter plot showing the measured current propagation speeds (the ratio of wire top height to one half of the average peak to peak times) versus wiretop heights for 271 precursors. The blue vertical lines show the margins of error that result from the peak time measurements having a timing uncertainty of 200 ns ( 100 ns). The data points for precursors 1, 2 and 3 that are modeled in Section 6.4 are plotted as red circles, and pointe d to by black arrows numbered 1, 2 and 3. Note that the vertical scale starts at 2 x 108 m s1 and that many data points overlay.
204 Figure 69. A scatter plot of the current peak ratios Red diamonds, blue x, and black plus marks show the values peakpeak 21ii peakpeak 32ii peakpeak 43ii for 19 measured pr ecursor current signatures ( Section 6.3.2).
205 Figure 610. A scatter plot of the charge transferred to ground during the initial precursor current pulse versus the total charge transferred to ground by the end of the precursor current signature. Data points are shown for 15 measured precursors (blue circles and triangles, Section 6.3.2), and modeled precursors 2 and 3 (red tr iangles, Section 6.4). The black line is the linear regression for the 15 measured precursors.
206 Figure 611. The i ncident current pulses that are used as inputs to the distributedcircuit model shown in Figure 6 12. The red dashed lines are the inputs and the corresponding measur ements are shown with black lines for Precursors 1, 2 and 3 in panels A, B, and C, respectively The incident current pulses are a scaling factor smaller in amplitude than the measured initial pulses ( Section 6.4.1).
207 Figure 612. The distributed circ uit used to model the current propagation on the triggering wire, ground lead, and ground rod. The precursor incident current is represented by an ideal current source at the triggering wire top. In the case when the grounding impedance was assumed to be purely resistive, the ground rod distributed circuit is replaced by a resistor. Current is measured at the junction of the triggering wire and ground lead.
208 Figure 613. Measurement and modeling results for three precursors for two m odel grounding configurations. T he grounding system is modeled as a 25 m transmission line (dash dot red line) and the grounding system is modeled as a lumped resistor (dashed blue line) Precursors 1 2, and 3 are shown on a 25s time scale in panels A C and E resp ectively. Precursors 1, 2, and 3 are shown on a 5s time scale in panels B D and F respectively.
209 Figure 614. The m odel predictions for precursor 3 with varied values of GTW and RTW. The model predictions using different values of RTW are show n in panels A and B. The model predictions using different values of GTW are shown in panels C and D. In both cases the grounding system is modeled as a 25m transmission line. For each case, the left plot (panels A and C ) shows the model predictions on a 25 s time scale, and the right plot (panels B and D ) shows an expanded 5s time scale from 4 to 9 s. In each case, increasing values of RTW or GTW correspond to the curves with smaller first peak amplitudes. Note that the measured current signature is not shown here. The red curves are the same model predictions as sh own in Figure 613.
210 C HAPTER 7 DETERMINATION OF THE ELECTRIC FIELD INTENSITY AND SPACE CHARGE DENSITY VERSUS HEIGHT PRIOR TO TRIGGERED LIGHTNING The ambient electric field of thunderstorms causes electrical discharge known as corona from various types of sharp object s located on the ground, often creating a space charge layer near ground. This layer produces its own electric field that at ground level opposes the clouds electric field. Space charge produced by ground corona plays an important role in atmospheric el ectricity. The usually upward directed electric field due to negative cloud charges is reduced near ground by the presence of the positive corona space charge layer. A space charge layer (of either polarity) prevents the quasi static electric field at gr ound level from exceeding an absolute value of about 5 to 10 kV m1, while the field above the layer can be up to an order of magnitude higher [e.g., Standler and Winn, 1979; Chauzy and Raizonville, 1982; Soula and Chauzy, 1991; Willett et al., 1999]. A s pace charge layer near ground can influence inferences made from ground based measurements of quasi static electric fields regarding cloud charge structure and lightning parameters. When a significant space charge layer is present near ground, the relativ ely large and fast field change from a lightning flash typically causes a polarity reversal at ground but not at altitude, and the field recovery following a large and fast field change occurs more rapidly at ground than aloft [e.g., Standler and Winn, 1979; Chauzy and Soula 1987; Chauzy and Soula 1989]. Thus, inferences of, for example, aspects of charge transfer and continuing current from electric field measurements at ground may be compromised by the presence of a space charge layer. Additionally, when attempting to artificially initiate (trigger) lightning using the rocket and wire technique [Rakov and Uman, 2003, Ch. 7], the electric field at ground is used as an ofteninadequate proxy for the unknown triggering field at higher altitudes, and the variable field reduction of the space charge layer reduces the triggering efficiency. Finally, space charge produced by corona at ground may play an important role in
211 thundercloud electrification (at heights greater than 1 km or so). The lower positive c harge center in thunderclouds may develop through accumulation of corona space charge lifted from ground level by conduction or convection currents [e.g., Malan 1952; Chauzy and Soula 1999]. Although it would often be advantageous to measure the electri c field above the space charge layer for the reasons given above, doing so presents logistical difficulties. On the other hand, the effect of the space charge density on ground based measurements of electric field might be accounted for in principle if the vertical profile of the space charge layer were known. T his chapter describes a novel method to infer the vertical profiles of space charge density and electric field intensity above ground by comparing modeling and measurements of the ground level electric field changes caused by elevating grounded lightning triggering wires. M easurements are presented of the groundlevel electric field intensity versus time prior to initiation of the triggered lightning upward positive leader at distances of 60 m and 350 m for six triggered lightning flashes (named Launches 1 through 6, with the UF event ID for each listed in Table 7 1) The measurements (accounting for precursor charge transfer) are then compared to numerical solutions of Poissons equation for the electric field change everywhere in the computational domain as the wire is extended upward in assumed space charge layer with an assumed uniform electric field intensity far above this layer. T he induced charge on the wire as a function of height is infe rred from the model predicted radial component of electric field along the wire, as is the current from ground that supplies it. Finally, the relationship between the measured pre launch values of the groundlevel electric field and triggering height are analyzed and compared to similar relationships presented by other researchers. In this chapter, a positive electric field at ground corresponds to the electric field vector pointing upward (physics sign
212 convention). Positive current and negative electric field change at ground correspond to the removal of negative charge from or the deposition of positive charge in the atmosphere. 7.1 The Wire Shielding Effect Panel A of Figure 7 1 illustrates the cloud charge, the space charge layer near ground, and the g rou nd surface charge assuming that (1) the cloud charge is uniformly distributed on an infinitely thin boundary at constant height of several kilometers with a horizontal extent that is much greater than its height above ground and (2) the space charge lay er near ground is horizontally homogeneous. Under these approximations, the lines of equal potential ( colored lines in Figure 7 1) are horizontally uniform Correspondingly, the ambient electric field lines ( the negative gradient of the potential, shown as solid black arrows ) point vertically from the ground to the cloud (with no horizontal component), and the ambient electric field strength ( represented by density of field lines) increases with increasing height in the space charge layer. Panel B of Figu re 7 1 illustrates the ambient electric field profile when a thin and grounded conductor is quickly extended vertically from ground, as is done during the launch of a grounded wire to trigger lightning (this electric field profile is similar to that around a stationary tall object). As the wire ascends, an induced charge develops on the wire surface to cancel the tangential component of the ambient electric field on the surface of the conducting wire [ Griffiths 1981, chap. 2]. The line charge density on the wire surface is proportional to the radial field magnitude at the wires surface according to Gausss Law. The ground supplies the induced charge needed to keep the wire at ground potential. Corona from the wire pushes the induced charge radially out wards, creating a corona sheath around the wire extending out several meters. In the modeling it is assume d that the shielding effect at ground is the same if the charge is on the wire or in the corona sheath. The induced charge on the wire and in the corona sheath creates an electric field outside the wire that distorts the ambient electric field
213 depicted in Figure 7 1, forcing some of the ambient electric field lines that were vertical before the wire was launched to originate on the surface of the w ire (or corona sheath) in the normal (radial) direction instead of originating on the ground. This results in a reduction of the electric field magnitude at ground near the wire. The induced charge per unit length on the wire (and surrounding electric f ield intensity) is highest at the top of the ascending wire. Eventually, current pulses at the wire tip (precursors) occur as the air undergoes significant dielectric breakdown [e.g. Lalande et al., 1998; Willett et al., 1999; Biagi et al. 2009] Each precursor deposits charge in the air (and delivers opposite charge to ground via current on the wire) that causes a field reduction at ground of the same polarity as the field reduction from the wire charges. As described in Section 7.3.3, measurements sh ow that the charge of a single precursor is on average about 34 C which can reduce the electric field at ground by up to several tens of V m1 or more depending on the charge height and the horizontal distance of the sensor from the wire and the number of precursors that occur If as few as several tens of precursors occur during the wire ascent, the cumulative groundlevel electric field change from precursors is significant, and the total electric field reduction at ground during the wire ascent is t hen a combination of the presence of the induced wire charge the wire corona charge in the surrounding air, and the precursor charge in the surrounding air. 7.2 Data 7.2.1 Rocket Height and Wire Extension Rate The triggering wires were unspooled from the bottom of rockets that are about one meter in length, and it is assumed that the wire top heights (and wire lengths) were the same as the rocket heights. Rocket trajectories were determined by tracking either the engine plumes or rocket bodies in the highspeed video data. Luminosity at the wire tip from precursors was often
214 evident and was also used to aid in the trajectory measurements. The rockets do not always ascend purely vertically, and lack of tension or excess slack in a wire could cause wire cu rvature, especially if the wire were blown by the wind. The straightness and tilt of the wires were determined from the optical image data after the luminous wire explosion during the initial stage of the triggered lightning. None of the six wires studie d here exhibited a tilt angle of more than a few degrees or had a significant curvature. It is estimate d that the wire tops did not deviate horizontally from the launch tower more than 10 m. The rocket speeds were similar in all six launches. All height s discussed hereafter are relative to ground level. In Launches 1, 3, 4, and 5, the high speed video camera did not begin recording until the rockets were at heights of 23 m, 79 m, 40 m and 21 m, respectively. For t hese four launches, estimations were made for the rocket heights prior to the time when the highspeed video records began using a modeled trajectory created from the rocket height of Launch 2, which was tracked from 14 to 304 m. The modeled rocket height and wire extension rate (numerical t ime derivative of the height) versus time are shown in Figures 72A and 72 B respectively. Figure 7 2C shows the modeled wire extension rate versus the modeled wire height. The rocket in Launch 2 reached a maximum speed of about 160 m s1 when the rocke t was at a height of about 80 m. 7.2.2 GroundLevel Quasi Static Electric Field Measurements The groundlevel quasi static electric field measurements at 60 m and 350 m are co plotted with the rocket height on a 5s time scale in panels A B C D E and F in Figure 7 3 for Launches 1, 2, 3, 4, 5, and 6, respectively. The salient features in the groundlevel electric field change during the triggered lightning are identified in Launch 1 in Figure 7 3A and summarized in Table 71. These features are apparent to varying degree in all six launches. Table 7 2 summarizes the ground level field changes due to precursors for the six launches (Section 7.3.3). The precise time alignment of the field mill data to all other data was not straightforward
215 because the field mill data were not recorded with GPS timing. In order to perform the analysis presented in this chapter the times when the s ustained upward positive leader began in the high speed video images (recorded with GPS timing and precise to about 100 s) were assumed to correspond to the field mill data points at the onset of the relatively large and fast field change associated with the initiation of the sustained upward positive leader of triggered lightning (placed at time zero in the plots of Figure 7 3). For the data presented in Figure 7 3, the sustained upward positive leaders may have began any time between 0 s and 0.2 s, and it follows that there is 200 ms timing uncertainty in the analysis. The following describes the general changes, during the triggering of a lightning flash, in the groundlevel electric field within horizontal ranges that are similar to the total height of the triggering wire. Prior to launching the rocket, the ground level electric field magnitudes at 60 m and 350 m are about the same; they di ffer at most by 1.1 kV m1 in Launch 6. Further, the rate of change in the field magnitude before launch at both distances is about the same and relatively low. This fact is primarily a result of launching the wires at the ends of storms when the cloudrecharging rate is relatively slow and there is a low natural lightning flash rate. The maximum rate of ground level electric field change is 300 V m1 s1 in Launch 2 (at 60 m). The similarity in the field magnitudes and rates of change give an indication of the horizontal homogeneity of the electric field and space charge near ground between the two sensors, located 390 m apart. S hortly after the rocket launch, the groundlevel electric field magnitude at 60 m begins to decrease, but ap parently not significantly until the wire top has been lifted to a height between 50 and 75 m. T he field reduction shape due to the wire shielding at 60 m begins as convex and transitions to concave when the wire top has been lifted to a height of 150 m. This transition is not observed in Launch 4 because the sustained upward positive leader initiated at a height of
216 123 m. It is not clear if the extending wire causes significant ground level electric field reduction at 350 m, at least not until the wire reaches an altitude between 150 and 250 m. The field reduction at 350 m during the wire top ascent was at most 500 V m1 in Launch 1, but prior to launching the rocket the groundlevel electric field reduced at a rate of 200 V m1 s1. In all events, t he sustained upward positive leader and initial continuous current produced a large field change ( identified in panel A of F igure 7.3, henceforth referred to as the lightning field change) at both 60 m and 350 m. Table 73 presents, for the six triggere d lightning flashes, the initial stage (IS) duration, the time interval between the end of the IS and first return stroke (RS), the duration of the return strokes (the time from the first stroke to the end of the final strokes current), and total number of return strokes (these times were determined from channel base current measurement not shown here). The IS durations, as determined from the current records, were always longer than the lightning field change durations that were measured by the field mills, with the exception of Launch 1. The lightni ng field change was as large as 24.5 kV m1 at 350 m in Launch 4. The lightning field change was always larger at 350 m than at 60 m, and the sum of the field change during the wire ascent and the lightning field change at both distances were similar. After the flash ends, the electric field magnitude at ground recovers, i.e. begins changing in the positive direction, mainly due to negative space charge generation by corona at ground in response to the sudden onset of negative electric field of large magnitude [e.g., Standler and Winn, 1979; Chauzy and Soula, 1987; Chauzy and Soula, 1989]. Some of the field recovery possibly results from cloud recharging after the triggered lightning. Note that in Figure 7 3, the rate of field recovery is apparently higher when the maximum field excursion due to the lightning field change is higher.
217 Figure 7 4 presents the measured groundlevel electric field plotted versus wire top height for the six launches at distances from the launch tower of ( A ) 60 m and ( B ) 350 m The first data point in each curve corresponds to the electric field value just before the rocket was launched. The last data point represents the groundlevel electric field value and rocket height when the sustained UPL began. It is apparent in Figure 7 4 A that the rate of electric field change at 60 m was different in different launches, and the change began mostly after the wire top had reached a height of 50 m. As seen in Figure 7 4 B the ambient electric field change apparently dominates the total electric field at 350 m from the wire until the wire reached a height between 150 and 250 m perhaps with the exception of Launch 1. As show n in Section 7.3.3, some of the measured field change at ground during the wire ascent was due to precursors, particularly at 60 m. Precursor field changes will be acc ounted for in the modeling ( Section 7.4.3). 7.2.3 Precursor Current in the Wire and Corresponding Charge Transfer Each launch discussed here resulted in triggered lightning in electric fields of positive polarity (negative charge overhead), and thus, precursor charge deposited ahead of the wire tip wa s of positive polarity, and a current wave carrying an equal amount of negative charge wa s guided towards ground by the triggering wire. The propagation of the current wave on the wire radiates a damped oscillatory field signature, and a static field change at ground is produced from the overall lowering of negative charge from the wire tip to ground, as discussed in Chapter 6. Figure 7 5 presents examples of precursor current and electric field signatures on a 25 s time scale that transferred about 18 C of negative charge from a height of 152 m to ground, and produced a groundlevel electric field chan ge of about 10 V m1 at a distance of 60 m from the wire. In the comparisons between measured and modeled field changes during the wire ascents, the field changes from precursors are first removed from the measured groundlevel field change.
218 Based on t he modeling results in Section 6.4, i t is assumed here that precursor charge can be represented by a point source at the wire tip. Of the six launches analyzed here, both the wire base currents and fast electric field changes were adequately measured in L aunches 1 and 6. For these two launches, the field change of each precursor at 60 m and 350 m is inferred from the following approximation [ Uman 1969, Eq. 3.3]: 32 22 02QH E 4HR 71 wher 0 is the permittivity of free space, H is the wire tip altitude, R is the horizontal distance al charge transferred to ground. For a given precursor, the quantity w as determined b y computing the time integral from the beginning of the current to the time when the oscillations drop below the noise floor Additionally, Equation 71 was used to scale the precursor field changes measured by E2 at a range of 156 m to field change at ranges of 60 m (e.g., Figure 7 5A ) and 350 m. For Launches 2 through 5, the current measurement saturated at about 20 A, and the first current peaks of most precursors saturated, making it impossible to determine from integrating the precursor current at the wire bottom, so the measured field changes from E2 were used to determine via Equation 71. The placement of a plastic dome over the E2 sensor to shield it from rain introduced uncertainty to the sensors amplitude calibration, so the measured field changes from E2 were calibrated to the inf erred field change (using Equation 71) from accurate wire base current measurements for 96 precursors in four launches: Launches 1 (UF09 15) 6 (UF10 25) a nd two launches otherwise not analyzed here (different than Launches 1 through 6): UF09 12 and UF09 17 (the latter was in the same storm of Launch 1). According to this calibration, the E2 measurements were consistently too high in amplitude by 29%. Table 74 presents for the 96 precursor current pulses statistics on the total negative charge lowered to
219 ground and E2measured electric field change scaled to 60 m. There was no correlation between the amount of precursor charge deposited ahead of the wire tip and wire tip height. 7.3 Modeling This section begins with a description of the model construct and the assumed vertical profiles of space charge density, electric field intensity, and electric potential. Then, examples of possible model outputs are presented. The model parameters that yield electric field change predictions that best fit the measured electric field changes are determined for each launch, and thereby the vertical profiles of space charge density, electric field intensity, and electri c potential are inferred. Finally, the model predictions of the radial electric field along the wire as a function of height for Launch 1 are examined. 7.3.1 Model Description The electric field structure is assumed to have cylindrical symmetry centered o n the vertical wire, allowing the three dimensional field structure to be modeled in two dimensions. The triggering wire is infinitely thin in the model. The model domain is a square slice of the threedimensional space, with the left side being the ax is of symmetry. The following five conditions are imposed: (1) the total vertical and horizontal (radial) extent of the model space each is 3 km, (2) the vertical wire extension begins in the lower left corner at ground, and continues up along the left boundary, (3) the boundaries at ground (bottom side) and along the wire are at zero potential, (4) the horizontal (radial) derivative of the electric potential (the negative of the radial electric field) is zero on the right boundary and on the left boundary vertically above the wire top, and (5) the potential along the top boundary (at z = 3 km) is defined by Equation 74 (described below). The space charge densi ty profile versus altitude is assumed to decay exponentially This choice was based primarily on the rocket soundings of the electric field versus height with
220 relatively high spatial resolution that were presented in the work of Willett et al. , and an exponentially decaying space charge density profile is the simplest realistic profile with the minimum number of free parameters to test in the computationally intensive model. Prior to launching the rocket, the height profiles of the exponentially de caying space charge, the corresponding electric field as a function of z, and the electric potential as a function of z are described by the following three relations, respectively: 00 expzd z EE d 72 0EzEexpzdEE 73 0VzdEE1expzdEz 74 The equations for (z) and V(z) are consistent with the equation for E(z) via Gausss Law (z) = 0E( z) / z 0VzEz'dz' respectively. The two adjustable parameters of the model are: the rate of charge decrease with height (e folding length) d and the electric field magnitude far above the space charge layer E. The ground level electric field when the wire is first launched, E0, is a measured value. The electric potential is found first by numeri cally solving Poissons equation (or Laplaces equation for the zero space charge case) using the finiteelement method. The electric field is then found by taking the negative of the gradient of the electric potential. The initial finite element mesh was refined many times using higher order finite elements with the most grid points located near ground and along the left boundary where the wire was placed. Because of the computationally intensive nature of the Poisson solver, the model ing was done for on ly three values each of the two free parameters, E (20, 40 and 60 kV m1) and d (67, 100 and 200 m) as well as the zero space charge case (d is set to zero), for the six initial
221 measured groundlevel electric field values E0 (ranging from 3.2 to 7.6 kV m1). For example, Figure 7 6 presents (z), E(z), and V(z) for the nine combinations of E and d and E0 = 6 kV m1. For the zero space charge case, the electric field prior to launching the rocket is vertical and is equal to the measured field at the g round E0 for all z. The vertical profiles are inferred from t he solution that provided the best least squares fit to the time series of electric field measured at the 60 m range 7.3.2 Model Predictions Figure 7 7 presents the model predicted, groundleve l electric field change at ( A ) 60 m and ( B ) 350 m for the zero space charge case and for the nine cases of exponentially decaying space charge, all for E0 = 6 kV m1. The corresponding measurements for Launch 1 are also shown (although the E0 value at 35 0 m was about 6.1 kV m1 versus 6 kV m1 assumed in calculations). The model predicted groundlevel electric field change is lowest when zero space charge was assumed: about 1 kV m1 at 60 m and 100 V m1 at 350 m. The secondsmallest predicted ground level field change is for the lowest space charge density at ground (corresponding to highest d = 200 m and smallest E = 20 kV m1): about 1.4 kV m1 at 60 m and 0.1 kV m1 at 350 m. The largest model predicted field change is for the highest space charge density at ground (corresponding to smallest d = 67 m and highest E = 60 kV m1): about 4.9 kV m1 and 0.5 kV m1 at 60 m and 350 m, respectively. In all of the predicted ground level field changes at 60 m for zero space charge and the nine combinations of E and d, there is a point of inflection when the wire top reaches a height of about 130 m. An inflection poi nt is not evident in the modeled field change curves at 350 m, although presumably there would be one if the wire reached a height of 700 m.
222 7.3.3 Model Fit Figure 7 8, panels ( A ) th rough ( F ), present for Launches 1, 2, 3, 4, 5, and 6, respectively, the o riginal measured field change at 60 m, the measured field change with the precursor field changes removed (referred to as the precursor adjusted measurement), and also the model prediction that best matches the precursor adjusted measurement according to t he best least squares fit. The values of E0 (assumed to be equal to the measured value), E, and d corresponding to the best fitting model predictions, along with the space charge density at ground are given in each plot. For each of the plots in Figure 78, a vertical arrow points to the height at which the first precursor field change was removed from the measurement. Below these heights the original measured curves and the precursor adjusted measured curves are identical. In each launch, the overall field change from precursors, several hundred V m1, is small relative to the overall field change due to the wire shielding effect, several kV m1. The field adjustments for precursors appear as positive going steps, although the field change for many pr ecursors is too small to be evident in the plots of Figure 7 8. Accounting for precursor field changes has the effect of reducing the total field change. Table 75 summarizes the parameters that produced the best fitting model predictions for each launch as well as the model predictions of groundlevel space charge density, the ambient vertical electric field for the height at which the sustained UPL initiated (these heights are given in Table 7 1) and the electric potential traversed by the wire. The modeling results indicate that the ambient electric field at the wire tip height was lower and the electric potential traversed by the wire was larger when the sustained UPL initiated at higher altitudes. No attempt was made to fit modeled electric field changes to the measured electric field changes at 350 m since any wireshielding effect at this distance was not clearly observable.
223 7.3.4 Model Predicted Line Charge Density In addition to predicting the groundlevel electric field, the model yields the v ertical (z component) and radial electric field near the surface o f the wire. From these fields, the corresponding charge per unit length that must exist on the wire and/or corona sheath as a function of height can be inferred Figure 7 9 presents exampl es of the model predicted height profiles of the radial electric field along the wire at a radius of 5 m (bottom axis) and the approximate charge density (top axis) that must exist along the wire to produce the radial electric field according to Gausss La w when the input parameters were E = 40 kV m1 and d = 100 m, and E0 = 6 kV m1. Each of the four curves in Figure 79 is the model predicted radial electric field and corresponding charge per unit length from 0 m to 300 m at four different times, when t he wire top was at heights of: 60 m, 135 m, 210 m, and 285 m. The charge per unit length is calculated as follows. A Gaussian cylinder of a few meters height and a few meters radius has its axis co located with the wire, and 0E is integrated over the lateral surface of the cylinder to yield the charge inside the cylinder. For all locations of the Gaussian cylinder, except at the top of the wire, the electric flux out the top and bottom circular surfaces is negligible, leading to a charge per unit length 0rz2rEz (top axis of Figure 7 9) where Er is found to vary as r1 out to about 10 m. At the top of the wire, the electric flux out the top surface of the Gaussian cylinder is of the sam e order of magnitude as the flux out the cylindrical side surface, so the actual charge per unit length at the top of the wire is two or three times that plotted in Figure 7 9. The exact value determined depends on the grid size of the model calculations, which has a practical lower limit. The model predicts that the radial electric field magnitude and charge density at any given height are highest when the wire first reaches that height, thereafter decreasing slightly as the
224 wire continues ascending. The model predicted radial electric field (at r = 5 m) and charge density (underestimated near the wire tip) shown in Figure 7 9 reach maxima of about 210 kV m1 and 60 C m1, respectively, at a height of 270 m when the wire top is at 285 m. The model pre dicts that the radial electric field near the wire and corresponding charge per unit length increases with increasing values of E and decreasing values of d. Note that the nonsmooth nature of the curves is due to unevenly spaced finite element mesh poin ts. The model predicts that there is a total charge along the wire of about 6.5 mC when the wire top is at a height of 285 m. The current required to supply the charge (the rate of change of total charge on wire as the wire extends upward) increases steadily as the wire ascends to a height of 135 m, reaching a level of about 3 mA, and continues to increase for higher wire heights, although at a slower rate because the wire ex tension rate is decreasing ( Figure 7 2). The model predicts that the radial el ectric field magnitude is highest about 10 meters below the top of the wire. The predicted decrease of radial electric field in the upper 10 m or so of wire is due to the electric field becoming more vertical, and less radial, near the wire top. The radi al field does not drop to zero above the maximum wire top height because there is some radial component of electric field above the wire at a radial distance of 5 m (there should be radial electric field everywhere except directly along the wire axis), and to some extent because of insufficient mesh refinement. The model predicts that the vertical electric field at 5 m radius increases from small compared to the radial field some meters below the wire top to a maximum at the wire top, above which the z dir ected field decreases. 7.4 Discussion The measurements of the ground level electric field change during the vertical extension of a thin, grounded wire are similar to previous reports. W illett et al.  reported higher magnitude but similarly shaped field changes at a distance of about 30 m from their launcher, or
225 half the distance at which the measured field change presented here were made. For their flight 6 (as seen in their Figure 6), Willett et al.  reported that the electric field bega n at about 7 kV m1 and the field changed during the wire extension (up to 307 m) by a little over 7 kV m1, becoming slightly negative before the UPL initiated. For the launches analyzed in this Chapter the largest measured field change during a wire extension was 3.4 kV m1 for Launch 1. The lightning field change of flight 6 in Willett et al.  was about 7 kV m1, and the combined field change from the wire ascent and triggered lightning was about 14 kV m1. Liu et al.  reported a similar quasistatic electric field change signature measured 75 m from the launch er during a triggering attempt with positive charge overhead. The field change during the wire ascent was about 3.5 kV m1 ( as seen in their Figure 2). Figure 7 10 presents a scatter plot of the groundlevel electric field magnitude when the wire trailing rocket was launched versus the height at which the sustained UPL developed (triggering height). The two quantities show a strong linear relationship with a correlation c oef ficient of 0.85. Hubert et al.  reported a strong power law relationship (correlation coefficient of 0.82) between the triggering heights (from about 100 to 600 m) and groundlevel electric field magnitudes (between 4 and 13 kV m1) for 35 trigger ed flashes in Langmuir Laboratory in New Mexico. The power law relation of Hubert et al.  is also shown in Figure 7 10 (they did not report data points). The results in Figure 7 10 indicate that for the same electric field at ground lightning can be triggered at a lower triggering height at the ICLRT than at Langmuir Laboratory. In explanation of these observations, there may have been less space charge present in the vicinity of the triggering experiments at Langmuir than at the ICLRT, or the electric field magnitudes of Hubert et al  may have been enhanced by the mountainous local topography. It is worth noting that Horii and Nakano  reported for
226 winter triggered lightning studies at Kahokugata site in Japan that no clear correlatio n was observed between the triggering height and the initial ground level electric field for either positive or negative lightning polarity. As seen in Figure 7 8, there is good agreement between the model predicted and precursor adjusted measured groundlevel electric field at 60 m from the wire, when an exponentially decaying space charge profile is assumed, particularly in Launches 1, 4 and 5. There is nearly perfect agreement between measurement and model for Launch 5. Interestingly, there was a 1cm air gap in the ground lead for Launch 5, although it is unclear how the measurement would differ if the air gap were not present. The rate at which the measured electric field magnitude initially decreases is well modeled for Launches 1, 4 and 5. For Launches 2 and 3, the measured field change when the wire is at a higher altitude is larger than the model predicts. This discrepancy could well be due to the uncertain time alignment between the rocket trajectory and ground level field change. As noted in Section 7.3.2, it was assumed that the sustained upward positive leaders began when the lightning field changes in the field mill records began (time zero in the plots of Figure 7 3). However, the sustained upward positive leaders may have begun between 0 s and 0.2 s, introducing an uncertainty of 200 ms in the data time alignment. The timing uncertainty means that the wire may have been launched up to 200 ms later than was assumed in the present analysis and the computed field versus height curves may be shifted horizontally to lower wire top heights. For example, in Launch 2 the electric field increases ( as seen in Figures 74 and 7 8) for wire top heights from about 14 m to 60 m. The 200 ms timing uncertainty allows the wire launch to begin when the field maximum occurred, in which case there would probably be a better match of the model prediction to the measurement, although perhaps for a different space charge profile.
227 The radial electric field of the model predicted line charge along the wire is large enough to produce corona. T he wire has a diameter of 2 x 104 m, and if the minimum electric field strength necessary to produce corona is assumed to be 1 MV m1 [e.g., Kodali et al., 2005; Maslowski and Rakov 2006], then a line charge density as low as 11 nC m1 will produce corona. For a line charge density of 60 C m1 (the maximum modelprediction shown in Figure 79), the radial electric field drops below 200 kV m1 (the minimum electric field for corona propagation according to Griffiths and Phelps ) for a radius of about 5.4 m. The model indicates that for all wire launches, the induced charge on the wire expanded radially via corona on the order of five meters. However, the location of the wire/corona sheath charge does not affect t he model predictions as long as that corona sheath charge magnitude is essentially the same as would be found on the wire (or on a grounded wire of any radius) in the absence of corona. It is possible that wind advection or conduction current removes a pa rt of the charge created by corona from the vicinity of the wire, in which case corona resupplies the removed charge with additional charge. The removed charge would then be supplementary to the charge required to keep the wire at ground potential, and would enhance the overall electric field decrease measured at ground beyond what the model would predict (after accounting for precursor charge). The supplementary charge effect may explain some of the divergence of the model predictions and precursor adjus ted measurements of electric field change that typically begins around the wire heights when the first precursor begins ( Figure 7 8). Another possible source of supplementary charge is the rocket motor exhaust, as previously suggested by Fieux et al. . The rocket motors used in the experiments are specified to have a 1.2 s burn time, or about half the typical time the wire ascends before triggering lightning ( Figure 7 3). A ny potential charge deposition by the motor exhaust i s
228 thought to hav e negl igible effect on the measurements for the following reason: If charge deposition by the motor exhaust were significant, one would expect a discontinuity in the measured field reduction during the wire extension when the motor extinguishes at a time 1.2 s a fter launching the wire; such discontinuities are not observed. The choice to use an exponentially decaying space charge density, and the parameters E and d, was based on the rocket soundings of the vertical electric field versus altitude in the work of W illett et al. . The rocket soundings of Willett et al.  indicated that the electric field aloft increased exponentially with height up to heights of tens to hundreds of meters, above which it became more or less constant. All other reports of measurements of the electric field aloft found in the literature indicate it increases with height, although not necessarily exponentially. The true space charge profiles through which the wires ascended may not have varied with height exponentially, or even monotonically. Further, the model solutions are not unique to the space charge profiles that were assumed; other space charge density profiles versus height may yield similar or better model predictions. The nonunique nature of the model predictions is obvious in Figure 7 7, which shows that the model predict ed ground level electric field change with d = 100 m and E = 40 kV m1 is nearly the same as the model prediction with d = 200 m and E = 60 kV m1. In fact, for Launch 3, the model prediction with E = 60 kV m1 and d = 200 m fits the measurement only slightly better than the model prediction with E= 40 kV m1 and d = 100 m. Similarly, for Launch 6, the model prediction with E = 40 kV m1 and d = 100 m fits the measurement only slightly better than the model prediction with E = 60 kV m1 and d = 200 m The good agreement between the model predicted field change and precursor adjusted measured field change, especially for Launches 1, 4 and 5, indicates that the assumption made
229 here regarding the uncertainties in the inter measurement timing, supplementary charge creation along the wire, and the exponential ly decaying space charge profiles are not grossly inaccurate. The analysis at least shows that the triggering wires extended through space charge layers of significant density, such that the atmospheric electric field increased significantly with height. For example, for Launch 1, E0 was 6 kV m1, the wire reached a height of 230 m before the sustained upward positive leader began, and the wire caused a ground level electric field change of 3.2 kV m1. The model predicted groundlevel electric field change for the same E0 and wire height ( Figure 7 7) with zero space charge was only about 700 V m1, or a factor of four less than the measured field change.
230 Table 71. Salient values of the quasi static ground level electric fields and the upward positive leader (UPL) initiation height. Launch Flash ID Ground level field at launch (kV m 1 ) Ambient field change rate prior to launch (kV m 1 s 1 ) Total field reduction between launch and UPL initiation (kV m 1 ) Total lightning field reduction (kV m 1 ) UPL ini tiation height (m) 60 m 350 m 60 m 350 m 60 m 350 m 60 m 350 m 1 UF09 15 6.0 6.1 0.2 0.2 3.4 0.5 7.9 11.7 230 2 UF09 21 3.2 3.1 0.3 0.2 2.4 0.0 10.3 13.8 304 3 UF09 26 5.5 5.3 0.0 0.0 3.0 0.3 12.9 16.2 232 4 UF09 30 7.2 8.1 0.0 0.0 2.2 0. 0 22.7 24.5 123 5 UF09 42 7.6 7.2 0.0 0.0 2.5 0.1 13.7 15.9 161 6 UF10 25 5.1 4.0 0.0 0.0 2.9 0.2 8.8 10.2 233 Table 7 2. The number of precursors, the height at which they first occurred, and the total groundlevel field change they produced. Launch Number of precursors Height of first precursor (m) Total field reduction from precursors (kV m 1 ) a 60 m 350 m 1 12 153 0.25 0.03 2 36 229 0.28 0.07 3 24 168 0.67 0.13 4 10 79 0.17 0.10 5 37 83 0.32 0.02 6 22 147 0.15 0.03 a ) Distances s caled from E2 measurement at 156 m from wire
231 Table 73. The initial stage (IS) duration, the time interval between the end of the IS and the first return stroke, and the duration of the return stroke stage The duration of the return stroke stage is def ined as the time from the fast rise of the first return stroke current to the end of the final return stroke current, i ncluding any continuing current There were no return strokes in Launches 1, 2 and 6. Launch IS stage duration (ms) Time between IS and 1st return stroke (ms) Number of return strokes Return stroke stage duration (ms) 1 161 2 552 3 534 57.6 5 541 4 238 138 1 216 5 630 631 1 199 6 210 Table 74. Salient statistics of precursor charge and electric field change (sample size of 96). Value Charge Lowered to Ground (C) Field Reduction at 60 m (V m 1 ) a Arithmetic Mean 33.9 27.1 Standard Deviation 23.5 16.0 Geometric Mean 26.9 22.2 Median 27.8 24.0 Min 4.8 4.2 Max 151.7 86.9 a ) Distance s caled from E2 measurement at 156 m from wire. Table 75. Model parameters, the corresponding space charge density at ground, and the electric field and the electric potential at the triggering height. These values were calculated using Equa tions 72, 73 and 74 ( Section 7.4.1). Launch E 0 (kV m1)a E (kV m1) d (m) (z=0) (nC m3) E at triggering height (kV m1) V at triggering height (kV m1) 1 6.0 40 67 4.5 39 4.1 2 3.2 20 100 1.5 19 3.0 3 5.5 60 200 2.4 43 3.9 4 7.2 60 67 7.0 51 2.3 5 7.6 60 100 4.6 50 1.3 6 5.1 40 100 3.1 36 3.2 a) At a distance of 60 m from the launch tower, equal to the measured value
232 Figure 7 1. Schematic illustrations of the ambient electric field befo re and after the extension of a triggering wire. ( A ) An approximation of the electric field between negative thundercloud charge that is several kilometers above ground and ground surface The vertical electric field, shown with black arrows is a functio n of height in the space charge layer (red plus symbols). The horizontal equipotential lines (representing equipotential planes in 3D space) are further apart in the space charge layer than in the space charge free region. ( B ) The electric field with the grounded triggering wire present.
233 Figure 7 2. The model wire trajectory. (A) The modeled wire top height versus time (B) T he modeled wire extension rate versus time. (C) T he modeled wire extension rate versus the modeled wire top height. The minimum wire height is the top of the launch tubes, or a height of 14 m.
234 Figure 7 3. The ground level electric field changes and wiretop heights versus time for Launches 1 through 6. The groundlevel electric field changes at 60 m are shown with so lid blue line with circles ( left vertical scale) the 350 m are shown with solid red lines with x symbols ( left vertical scale) and the wire top heights are shown with dashed black lines (right vertical scale) Salient features in the electric field chan ge that are evident in all launches are identified in panel ( A ) for Launch 1. In each panel, time zero corresponds to the lightning field change and the last wire top height measurement.
235 Figure 7 4. Field change versus wire top height s for Launches 1 through 6. Panel A shows the field changes at 60 m and Panel B shows the field changes at 350 m. Note that the vertical scales of electric field in the two plots are different.
236 Figure 7 5. An example of a precursor that produced a static electric field change. Panel A shows the groundlevel electric field change measured at 156 m (by E2) but rangescaled by Equation 71 to a horizontal distance of 60 m from wire. Panel B shows the corresponding wire base current. The 18 C of negative charge transferred to ground during this precursor produced an overall field change at 60 m of about 10 V m1.
237 Figure 7 6. The vertical profiles of space charge density, electric field magnitude, and electric potential for the nine combinations of d and E values and E0 = 6 kV m1. Panel A shows the space charge density, Panel B shows the electric field, and Panel C shows the electric potential. A common legend is shown on the top panel.
238 Figure 7 7. The model predicted ground level field changes for no space charge and the nine cases of exponentially decaying space charge density for E0 = 6 kV m1. Panel A shows the field changes at 60 m and Panel B shows t he field changes at 350 m, with a common legend shown in panel B The measured field change for event 0604092 at both distances is shown for comparison. Note the different vertical scales of electric field in ( A ) and ( B ).
239 Figure 7 8. The model pr edictions that best fit the measured electric field changes for Launches 1 through 6. The measured field changes at 60 m are shown with solid black li nes the precursor adjusted measurement s are shown with dashed red line s and the model predict ed field change s are shown with dot dashed blue line s The values of E0 (assumed to be equal to the measured value), E density at ground) corresponding to the best model fit are shown in the bottom left of each plot. Note that the plots have different height and electric field scales. The vertical arrows point to the wire top height at which the first precursor is removed.
240 Figure 7 9. Examples of the model predicted height profiles of the radial e lectric field 5 m from the wire and equivalent approximat e line charge density The induced charge densities (top scale) are inferred from the radial electric field (bottom scale) using Gausss law: values of charge density near the wire top are underestimated because there is vertical component of electric field not taken into account in these calculations (Section 7.4.4). Each curve is a snapshot of the radial electric field and charge density along the wire when the wire top is at a certain height. The calculated radial electric field varies as 1/r from more than 10 m to the wires surface in the assumed absence of corona, except near the top of the wire. The radial field does not drop to zero above the maximum wire top height because there is some radial component of electric field above the wire at a radial distance of 5 m (one would expect a purely vertical field only along the wires longitudinal axis).
241 Figure 7 10. Triggering height versus initial groundlevel electric field magnitude.
242 CHAPTER 8 SUMMARY OF RESULTS AND RECOMMENDATIONS FOR FUTURE RESEARCH 8.1 Summary The work that has been presented was made possible by sever al key additions to the measurement infrastructure at the ICLRT. The relatively sensitive current sensor (II VLS) and electric field sensor (E2), both made possible by the use of an amplifier designed and constructed by the author, played an important rol e in resolving the low level current and electric field pulses that occurred during the times when the dart stepped leaders and upward positive connecting leaders were imaged ( Chapter 5 ) The II VLS and E2 sensor s allowed for the precursor signatures in c urrent and electric field to be recorded with high amplitude resolution. The precursor current signatures served as the basis for the modeling of transient current propagation on the triggering wire in Section 6.4. The precursor current and electric fiel d signatures measured using the II VLS and E2 sensors made possible important corrections to the measured ground level electric field changes in the analysis of Section 7.4. Additionally, new types of current pulse behavior w ere detected with the II VLS s ensor, namely the quasi periodic pulses that occur with regular intervals of hundreds of microseconds to several milliseconds, and have amplitudes that vary regularly in time (Section 6.2.2). The Positive Lightning Experiment (PLE) network of Digital Sto rage Oscilloscopes (D SO) played a key role in acquiring the data reported in this work In multiple instances, the PLE DSO network provided data for the wire ascent phase and initial phase in triggered lightning in which no return strokes occurred and the Multiple Station Experiment (MSE) DSO did not trigger. There were also some cases when the return stroke, and thus the MSE trigger time, occurred several seconds after the wire launch. For these cases, the MSE did not record the current and electric field data during the wire ascent
243 T he most important addition s to the ICLRT observational instruments w ere the high speed video cameras, which were essential to all of the work presented here. The high speed video cameras have made possible major advances i n the understanding of lightning leader propagation and attachment processes. The Photron SA1.1, operating at a framing speed of 300 kfps (3.3 s per frame) has provided the first images showing details of the stepped development of an upward positive lea der from a triggering wire (S ection 5.2) that is synchronized to wire base current The Photron has provided the first images in which the negative leader stepping mechanisms, namely the space stem and space leader, were both spatially and temporally reso lved (Section 5.3) These mechanisms have been observed in two downward negative dart stepped leaders (Section 5.3.1) in different classically triggered lightning flashes and for a downward stepped leader breaking down virgin air in an altitude triggered flash (Section 5.3.2). The observations of the stepping mechanisms show that negative lightning leaders and negative laboratory spark leaders propagate via the same mechanism, albeit on different scales of length, time, and voltage. The Photron has provided the first photographic images of the upward positive connecting leaders and the downward leaders in 15 return strokes in triggered lightning, including one for a return stroke in an altitude triggered flash (Section 5.4). The upward and downward lea ders were only a few meters to several tens of meters apart when they were imaged and, in one remarkable image recorded by a Photron (Figure 5. 4), the tip of a downward dart stepped leader could be seen about 40 m above ground, and about 15 m from an upwar d positive connecting leader the latter being about 1 6 m in length. In this image, the descendingleader streamer zone appears to be in contact with the upward connecting leader, and a space stem or space leader is evident directly between the two. The image pr esented in Figure 5.4 shows with great resolution
244 filamentary corona streamers emanating from several points along the leader, including the leader tip, and the bottom (cathode end) of the space stem/leader below the leader tip. The highspeed video cameras have made possible the direct observations of aborted leader channel s or precursors, as the wire ascends (Section 6.2.1) The Phantom camera was used in 2009 to track the rocket ascension in time, thereby providing a simple and accurate way to determine the wire length versus time (Section 7.3.1) The accurate measurement of the wire lengths via highspeed video made possible the research presented in Chapters 6 and 7. In Chapter 6, the current, electric field, and optical signatures associated with the sudden electrical breakdown processes (precursors) that occur red at the top of the copper wires used to artificially trigger lightning were examined The analysis was limited to data collected in 2009, since the II VLS and E2 sensors were not operational in 2008. Of the tens of thousands of pulses in current and electric field that were recorded, a total of 410 were analyzed in detail. Luminosity at the wire tip was observed for 339 of the 410 precursors and, in seven cases, discharge channe ls developed to lengths of 3 m to 8 m over times of several hundred microseconds. Precursors were found to occur at remarkably different rates and with behavior not previously observed. For example, in launch (UF0911), before the sustained upward posit ive leader initiated, it is estimated that between 5,000 and 10,000 precursors occurred (one every few hundred microseconds). The peak current amplitude was generall y one to about 100 amperes ( Figure 6 4), and the amplitudes formed an envelope that va ri ed with some periodicity. In the following launch (UF0912), which took place only 18 minutes later, there was a short period containing rapidly occurring precursors with amplitudes of about an ampere, followed by a 380 ms interval during which no precurs ors occurred, and then a 680ms interval during which 41
245 precursors occurred before the sustained upward positive leader was initiated ( Figure 6 5). It is not clear why precursors occur with different rates or why their amplitudes may vary periodically. Different wires may extend in different vertical profiles of electric field, or t he humidity in the air through which the wire travels may play a role. Corona process es require a higher electric field strength in air with high humidity than in air with lo wer humidity [ e.g., Griffiths and Phelps 1976; Gallimberti, 1977] Negative polarity precursor currents were observed in a single wire launched with predominately positive charge overhead. Unfortunately, no highspeed video was acquired for this launch, so the heights at which they occurred was not known, and no images of associated luminosity were acquired. Interestingly, t he currents of the observed negative polarity precursors did not appear much different in rate and shape from those of the positive polarity precursors. Considering that individual negative leader steps seem to develop only via the space stem and space leader mechanism, whereas individual positive leader steps seem t o extend incrementally [ Rakov and Uman, 2003, Section 5.3.2] one mig ht expect the current signatures for the two polarities to be different, at least in shape. The p recursor current pulse propagation speeds on the triggering wire were measured for 271 precursors The speed was about 10 to 20% less than the speed of light, and decreased with increasing wiretop height, from about 2.8 x 108 m s1 to about 2.3 x 108 m s1 for wire top heights from about 80 m to about 340 m ( Figure 6 8) The less than light speeds were attributed to an increased capacitance per unit length of the triggering wire system resulting from the presence of a corona sheath having a radius much larger than the wire radius, while the inductance per unit length is unchanged since the longitudinal current flows solely in the wire.
246 In Section 6.4, the trig gering wire and its grounding system we re modeled as uniform transmission lines in an attempt to reproduce the measured wirebase current signatures for three precursors occurring in the same launch at different wiretip heights. The model predictions mat ched the measured wirebase precursor current signatures very well, although the former seemed to lack the observed attenuation of high frequency signal components. For each precursor that was modeled, the current pulse was made to propagate in the model (by adjusting the capacitance per unit length) at the speed that was measured in Section 6.3.1. The good agreement between the signatures of the model predictions and the measurements validate s the method by which the speeds were measured. For each precu rsor that was modeled, t he incident input cur rent pulse used as model input was a unipolar pulse that was essentially the same as the first pulse of the measured signature, but with an assumed power law decay following the current peak. Since the first pu lse of the precursor signature measured at ground is the superposition of the incident wave and a reflected wave at ground, it is larger in amplitude than the current pulse arriving at ground (and could be potentially different from the input pulse in shap e) which itself is the input current attenuated from its initial value by propagating down the wire. It was found that the input current needed to be reduced in amplitude in order that the modeled current peaks match ed in amplitude the measured current pe aks. The corollary of this observation is that the measured current at ground is not the same as the current pulse created by the electrical breakdown at the wire tip. The modeling show ed that: (1) the triggering wire characteristic impedance is between 600 and 800 m groundrod grounding impedance for the peak precursor current is about 100 rounding resistance is 20 (3) the current pulses propagate in the low loss mode with an attenuation constant that is
247 approximately fr equen cy and height independent, and is 8.2 x 104 Neper m1, and (4) the current reflection coefficient at ground for peak precursor current is approximately 0.9. In Chapter 7, the ground l evel quasi static electric field at distances of 60 m and 350 m dur ing six wire launches that resulted in triggered lightning were examined in detail. For these six launches, the groundlevel electric fields ranged from 3.2 to 7.6 kV m1, and the triggering heights ranged from 123 to 304 m. From wire launch time to ligh tning initiation time, the ground level electric field reduction at 60 m ranged from 2.2 to 3.4 kV m1, with little ground level electricfield reduction being observed at 350 m. The precursors in these six launches were found to produce an appreciable fr action of the total field change measured at ground For example, in Launch 1, the total field change measured at 60 m was 3 kV m1, and the precursors that occurred during the wire launch were expected to have been responsible for about 670 V m1 (23%) o f this field change. In Section 7.4, the vertical profiles of space charge density and electric field intensity above ground were inferred by comparing modeling and measurements of the groundlevel electric field changes caused by elevating grounded lightn ing triggering wires. A Poisson equation solver simulated the groundlevel electric field changes as the zero radius grounded wires extend in assumed vertical profiles of space charge density and electric field intensity that var ied by an exponential relation and for the case when there was no space charge (i.e., the solution to Laplaces equation was also determined). As expected, the solution to Laplaces equation yielded field changes much smaller than those measured, ruling out the possibility that no space charge was present above ground. The model reproduced the measured ground level electric field changes when the assumed space charge density decayed exponentially with altitude, with groundlevel charge densities between 1. 5 and 7 nC m3, space ch arge exponential
248 decay height constants ranging from 67 to 200 m, and uniform electric field intensities far above the space charge layer ranging from 20 to 60 kV m1. However, the model generally predicted too much field change for low wire heights, and too little field change for greater wire heights. It is possible that a steady, low level current (glow corona) from the wire tip deposited charge continuously as the wire ascended, in a manner similar to the charge deposition by precursors, which caused the measured field to change more than would be expected without such a current. The addition of a milliampere scale current measurement at the wire base would be helpful in determining if this were the case. The line charge density along the triggering wire was inferred from the modeled radial electric field for the case when E0 = 6 kV m1, E = 40 kV m1, and d = 100 m. For this case, the radial electric field predicted by the model implies the existence of a corona sheath that increases in radius with increasing wire height, having a maximum radius of about 5 m at 285 m above ground. The l ine charge densit y on the wire or contained by the corona sheath would increas e steadily from less than 1 C m1 to about 60 C m1 at wire heights from 1 m to 285 m. Finally, for the six launches examined in Chapter 7, there was strong linear relationsh ip between the triggering height and the ground level electric field at launch time, with a correlation coefficient of 0.85. The triggering heights decreased from about 304 m to 123 m for ground level electric field values increasing from a bout 3.2 kV m1 to 8.1 kV m1, respectively. The triggering heights for a given field value were much lower than what would be expected from the relationship given in Hubert et al.  for lightning triggered at the su m mit of Mount South Baldy in the Magdalena Mount ains in c entral New Mexico at about 3 .23 km above sea level.
249 8.2 Recommendations for Future Resea r ch The various observations and modeling discussed in this work point to new paths of research to follow, some of which are discussed next Lightning leader s. A detailed study of laboratory spark leaders that develop step wise via the space leader mechanism (gaps greater than 2 m length and with long voltage rise times) using microsecond or sub microsecond highspeed video and synchronized x ray measurements might help to clarify the location and time of x ray production in lightning and long laboratory spark leaders. X ray film or other simple but sensitive xray sensors should be placed inside of the body and nose of the rockets. The detectors from launc hes in which only precursors occur, and in which precursors and an initial stage occur can be checked for x ray detection. This may prove to be a n inexpensive and simple way to determine if x rays are produced by precursors and/or the upward positive leader. T he rectangular shaped intercepting wire that was used in 2008 may have produced some kind of geometric field enhancement above the tower, and encouraged the development of upward positive connecting leaders. It would be interesting to erect a ground ed ring above or around the launch tube assembly and see if more upward positive connecting leaders are imaged. Steps and stepping mechanisms may develop over longer time scales in the downward negative stepped leader produced in altitude triggered lightning than in natural downward negative stepped leader from a cloud. This makes the downward negative leader in altitude triggered lightning well suited for the study of stepping mechanisms with high speed video cameras. Transient current pulse propagation on triggering wires. The modeling performed in Section 6.4 can be made more sophisticated by making the electrical parameters functions of height. Such a model would likely reproduce better the measured current signatures, and might render the frequency dependence of the grounding impedance unnecessary (Figure 6 13) The
250 modeling performed in Section 6.4 can also be extended to include the upward positive leader channel so as to infer the leaders electrical characteristics. One might expect that a coro na sheath will not form around the vertically extended triggering wire in fair weather electric fields. If a corona sheath were not present, then transient current pulses would be expected to propagate on the triggering wire at the speed of light. It wou ld be interesting to inject current pulses into the base of a wire launched in fair weather to test if this is true. An attempt should be made to predict wire lengths from the oscillatory current pulses at the beginnin g of the upward positive leader; t hat is, measure the peak to peak time, and multiply by the expected speed at that height. Electric field change during extension of triggering wires. The modeling in Chapter 7 can be constrained further with additional ground level electric field measurement s at different ranges and measurements of the wirebase current on milliampere and possibly microampere levels. Non zero radius upward extending conductors should be considered in future modeling of the wire shielding effects. The experiment should be pe rformed in fair weather electric fields, which is on the order of a 100 V m1 at ground, and is understood to decrease exponentially with height [ e.g., Gish 1944; Volland, 1984; MacGorman and Rust 1998; Rakov and Uman, 2003]. If the vertical electric field profile, E(z) does indeed decrease exponentially, then a comparison of the measured and modeled ground level field change may serve as an independent confirmation of the relations of E(z) given by Gish  and Volland , and as validation for the model presented in Chapter 7. Finally, a lternative methods of extending vertically grounded wires to heights of tens of meters such as using crossbows and using rockets propelled by pres surized gas, should be explored so that this experiment can be performed without triggering lightning.
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268 BIOGRAPHICAL SKETCH Christopher John Biagi was born in Tucson, Arizona in 1980. He received a Bachelor of Science degree in physics in 2003 from the University of Arizona. Shortly after wards he took a research assistant position at the Institute for Atmospheric Physi cs at the University of Arizona. Chris subsequently earned a Master of Science in a tmospheric s cience in 2006 from the University of Arizona Thereafter, he moved to Florida to join the Lightning Research Gr oup at the University of Florida, where he worked toward a Ph.D. at the International Center for Lightning Research and Testing from 2006 to 2009. He earned a second Master of Science degree in 2008 and a Ph.D. in 2011, both in e lectrical and c omputer e ngineering from the University of Florida. Chris has authored five peer reviewed journal publications, and been a co author on nine others. He has been author or coa uthor on 21 papers in conference proceedings, and on three technical reports.