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ANALYSIS OF PARAMETERS OF ROCKET-TRIGGERED LIGHTNING MEASURED DURING THE 1999 AND 2000 CAMP BLANDING EXPERIMENT AND MODELING OF ELECTRIC AND MAGNETIC FIELD DERIVATIVES USING THE TRANSMISSION LINE MODEL

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ANALYSIS OF PARAMETERS OF ROCKET-TRIGGERED LIGHTNING MEASURED DURING THE 1999 AND 2000 CAMP BLANDING EXPERIMENT AND MODELING OF ELECTRIC AND MAGNETIC FIELD DERIVATIVES USING THE TRANSMISSION LINE MODEL
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Antennas ( jstor )
Electric current ( jstor )
Electric fields ( jstor )
Electromagnetic fields ( jstor )
Geometry ( jstor )
Lightning ( jstor )
Magnetic fields ( jstor )
Modeling ( jstor )
Sine function ( jstor )
Waveforms ( jstor )
Camp Blanding ( local )

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ANALYSIS OF PARAMETERS OF ROCKET-TRIGGERED LIGHTNING MEASURED DURING THE 1999 AND 2000 CAMP BLANDING EXPERIMENT AND MODELING OF ELECTRIC AND MAGN ETIC FIELD DERIVATIVES USING THE TRANSMISSI ON LINE MODEL By JENS SCHOENE A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2002

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Copyright 2002 by Jens Schoene

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iii ACKNOWLEDGMENTS I would like to thank Dr. Martin Um an and Dr. Vladimir Rakov for their guidance, advice, and support. The research reported in this thesis wa s funded in part by the Federal Aviation Administration and the Na tional Science Foundation.

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iv TABLE OF CONTENTS page ACKNOWLEDGMENTS..........................................................................................iii ABSTRACT..............................................................................................................vii CHAPTER 1 INTRODUCTION....................................................................................................1 2 LITERATURE REVIEW.........................................................................................3 2.1 Introduction 3 2.1.1 Cloud Formation and Electrification..................................................................4 2.1.2 Formation of a Cumulonimbus...........................................................................5 2.1.3 Electrical Structure of a Cumulonimbus.............................................................7 2.1.4 Electrification of a Cumulonimbus.....................................................................9 2.2 Natural Lightning 11 2.2.1 Discharge Types associated with a Cumulonimbus......................................... 11 2.2.2 Lightning Discharges between Cloud and Ground.......................................... 12 2.3 Rocket Triggered Lightning 17 2.4 Return Stroke 20 2.4.1 Initial Bidirectional Return Stroke Wave.........................................................20 2.4.2 Return Stroke Current/Return Str oke Current Time Derivative.......................21 2.4.3 Return Stroke Speed.........................................................................................24 2.4.4 Electric Field/Electric Fi eld Time Derivative...................................................27 2.4.5 Magnetic Field/Magnetic Field Derivative.......................................................30 2.5 Return Stroke Models 32 2.5.1 “Engineering” Models......................................................................................34 2.5.2 Return Stroke Model Comparison and Validation............................................43 2.6 Measuring Lightning Produced Electric and Magnetic Fields and Field Derivatives47 2.6.1 Measuring Electric Field/El ectric Field Derivative..........................................47 2.6.2 Measuring Magnetic Field/Magne tic Field Derivative.....................................50 3 EXPERIMENT SETUP AND DATA REPRESENTATION................................53 3.1 Introduction 53 3.2 Setup of the FAA/NSF Experiment 53 3.2.1 Experimental System........................................................................................53

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v 3.2.2 Instrumentation.................................................................................................56 3.2.2.1 Data acquisition system 1999....................................................................56 3.2.2.2 Fiber optic system.....................................................................................61 3.2.2.3 Active integrator for magnetic field measurements..................................61 3.2.2.4 Optical equipment.....................................................................................63 3.2.2.5 Instrumentation for current/cu rrent derivative measurement....................63 3.2.2.6 Instrumentation for electric fiel d/field derivative measurement...............66 3.2.2.7 Instrumentation for magnetic field/magnetic field derivative measurement..................................................................................................67 3.2.2.8 2000 instrumentation.................................................................................68 3.3 Statistical Analysis of the 1999 and 2000 Data 69 3.3.1 Current..............................................................................................................73 3.3.1.1 1999 Experiment............................................................................................73 3.3.1.2 2000 Experiment........................................................................................... 79 3.3.1.3 1999 and 2000 Experiment........................................................................... 80 3.3.2 Current Derivative............................................................................................82 3.3.2.1 1999 Experiment............................................................................................82 3.3.2.2 2000 Experiment........................................................................................... 86 3.3.2.3 1999 and 2000 Experiment........................................................................... .86 3.3.3 Electric Field Change at 15 m and 30 m...........................................................89 3.3.3.1 1999 Experiment............................................................................................91 3.3.3.2 2000 Experiment........................................................................................... 92 3.3.3.3 1999 and 2000 Experiment........................................................................... .92 3.3.4 Electric Field Derivativ e at 15 m and 30 m......................................................96 3.3.4.1 1999 Experiment............................................................................................98 3.3.4.2 2000 Experiment........................................................................................... 99 3.3.4.3 1999 and 2000 Experiment........................................................................... .99 3.3.5 Magnetic Field at 15 m and 30 m.................................................................... 104 3.3.5.1 1999 Experiment.......................................................................................... 106 3.3.5.2 2000 Experiment.......................................................................................... 106 3.3.5.3 1999 and 2000 Experiment.......................................................................... 108 3.3.6 Magnetic Field Derivative at 15 m and 30 m.................................................. 112 3.3.6.1 1999 Experiment.......................................................................................... 114 3.3.6.2 2000 Experiment.......................................................................................... 114 3.3.6.3 1999 and 2000 Experiment..........................................................................115 4 MODELING OF ELECTROMAGNETIC FIELD DERIVATIVES...................119 4.1 Introduction 119 4.2 Return Stroke Electromagnetic Fields on Ground 120 4.2.1 Specification of Geomet rical Parameters........................................................ 120 4.2.2 Electric Field/Fiel d Derivative...................................................................... 123 4.2.3 Magnetic Field/Field Derivative................................................................... 127 4.3 Methodology of Field Calculations 129 4.4 Speed and Distance Dependence of Elect romagnetic Field Derivative Components ............................................................................................................................... ...........131

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vi 4.4.1 Speed Dependence of Electromagnetic Field Derivative Components at 15 m ............................................................................................................................... ......131 4.4.1.1 Electric field derivative...........................................................................131 4.4.1.2 Magnetic field derivative........................................................................135 4.4.2 Distance Dependence of dE/dt and dB/dt Components.................................. 137 4.4.2.1 Electric field derivative...........................................................................138 4.4.2.2 Magnetic field derivative........................................................................140 4.5 Comparison of Transmission Line Mode l Predictions with Measurements 142 4.5.1 Geometry of Event S9934............................................................................... 143 4.5.2 Overview of the Experimental Da ta for Strokes S9934-6 and S9934-7......... 147 4.5.3 Comparison of Measured and Mode l Predicted Electromagnetic Field Derivatives........................................................................................................ 152 4.5.3.1 Calculated and measured dE/dt...............................................................152 4.5.3.2 Calculated and measured dB/dt...............................................................160 4.5.4 Effect of Return Stroke Speed on Electromagnetic Field Derivatives of a Vertical and Slanted Lightning Channel........................................................... 168 4.5.4.1 Electromagnetic field derivative peaks...................................................168 4.5.4.2 Electromagnetic field derivative waveshape...........................................170 4.6 Summary and Discussion 172 4.6.1 Speed and Distance Dependence of Field Derivative s at 15 m....................... 172 4.6.2 Similarities of Waveshapes in Our Measured Field and Current Derivative Data................................................................................................................... 174 4.6.3 Modeling dE/dt and dB/dt Peaks using the TLM............................................ 175 4.6.4 Initial Fast Rise in Ou r dE/dt and dB/dt Data................................................. 177 5 RECOMMENDATIONS FOR FUTURE RESEARCH......................................179 LIST OF REFERENCES.........................................................................................180 BIOGRAPHICAL SKETCH...................................................................................184

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vii Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science ANALYSIS OF PARAMETERS OF ROCKET-TRIGGERED LIGHTNING MEASURED DURING THE 1999 AND 2000 CAMP BLANDING EXPERIMENT AND MODELING OF ELECTRIC AND MAGN ETIC FIELD DERIVATIVES USING THE TRANSMISSI ON LINE MODEL Jens Schoene May, 2002 Chairman: M. A. Uman, PhD. Major Department: Electrical and Computer Engineering We present statistical results on the sali ent characteristics of the electric and magnetic fields and their derivatives at distances of 15 m and 30 m from triggered lightning strokes. Return stroke current characteristics are also presented. The measurements were made in 1999 and 2000 at Camp Blanding, Florida. The experiment was designed to minimize the influence of th e strike object on the measured field and field derivative waveforms and to eliminate potential distortions of the field and field derivative waveforms both from ground arci ng and from propagati ng over imperfectly conducting ground. Measurements were made on about 108 return strokes or Mcomponents, although not all field variables were successfully record ed for each stroke. We present histograms of the following 28 wave form parameters, along with their means and standard deviations: current peak value, rise-time, a nd half peak width; current derivative peak value, rise-time, and width; electric fi eld peak value and width at 15 m

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viii and 30 m; electric field derivative peak valu e, rise-time, and wi dth at 15 m and 30 m; magnetic field peak value, rise time, and width at 15 m and 30 m; and magnetic field derivative peak value, rise-time and width at 15 m and 30 m. The current derivative from two return stro kes directly measured in 1999 is used as input to the transmission line model (TLM ) calculations. The el ectric and magnetic field components are calculated using the TLM for different distance s and velocities. The results are compared with the directly measur ed field derivatives at the same distance. It is shown that, if the transmission line model is applicable at early times in the triggered lightning return stroke process, the electric and magnetic radiation field components become the largest components be yond distances of a bout 15 m but are not dominant for distances less than 100 m. The experimental data pres ented indicate that measured dE/dt, dB/dt, and dI/dt waveshapes are very similar for the first 150 ns or so after the initiation of the return stroke. It is shown that, ba sed on transmission line modeling, the waveshapes of the dE/dt and dB /dt rising edges are relatively invariant for a return stroke speed v 2*108 m/s and, further, that the to tal waveshapes are exactly the same for v = c. Additionally, it is shown th at the dE/dt and dB/dt waveshapes do not depend much on channel inclination from the vertical, for inclinat ions less than 20 ° and return stroke speeds higher than 108 m/s. The TLM models the electric field derivatives well when the observed inclined channel with its base at the strike r od base or a slightly shifted channel origin is assumed.

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1 CHAPTER 1 INTRODUCTION Currents from direct or indi rect lightning strikes are th e cause of many deaths and injuries, and lightning currents and the electr ic and magnetic fields associated with lightning can have a deleterious effect on nearby electronic de vices. These hazards motivate the study of lightning currents and the close electromagnetic environment of lightning. Statistics on lightning cu rrents and nearby electric and magnetic fields, and an adequate understanding of the physics involve d in lightning processe s occurring near the strike point are needed for electromagnetic compatibility (EMC) studies. This thesis contributes to defining the cl ose electromagnetic environmen t by presenting a statistical analysis of currents and el ectromagnetic fields from rocket-triggered-lightning. Additionally, the validi ty of the transmission line model, a return stroke model that specifies the current distribution in the lightni ng channel, is tested. Return stroke models can be used to compute electromagnetic fi elds from specified currents–an important EMC application. A review of the pertinent lightning lite rature is presented in Chapter 2. An introduction to natural and ro cket-triggered lightning is give n with special focus on the return-stroke process. Various return stroke models are reviewed. The chapter concludes with a presentation of methods for measur ing lightning electric and magnetic fields. The analysis of salient tr iggered lightning parameters is presented in Chapter 3. Histograms of characteristics of the current and current derivative waveforms measured at the lightning channel base and of the el ectric and magnetic field waveforms and the

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2 associated time derivative waveforms 15 m a nd 30 m from triggered lightning strokes are presented. The data were obtained at the Inte rnational Center for Li ghtning Research and Testing (ICLRT) at Camp Blanding, Florid a, in 1999 and 2000. Strokes in triggered lightning flashes are thought to be equivalent to subsequent strokes (those after the first stroke) in natural cl oud-to-ground flashes. Chapter 4 is concerned with modeling th e electromagnetic field derivatives with the measured current derivatives as model i nputs. Equations are derived to calculate the electromagnetic fields and their derivativ es on ground produced by a vertical or a nonvertical lightning channel. These equations and the transmission line model are employed to investigate the speed and distance depe ndence of the electrostatic, induction, and radiation components of the el ectric fields and the induction and radiation components of the magnetic fields. Additionally, the validity of the transmission line model at early times in the lightning process is tested by cal culating the electromagnetic field derivatives at 15 m given the measured triggered lightni ng current derivatives and by comparing the results with the simultaneously measured electromagnetic field derivatives at 15 m. Recommendation for future research are given in Chapter 5.

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3 CHAPTER 2 LITERATURE REVIEW 2.1 Introduction Chapter 2 provides information about the physics of the development of clouds, the different lightning types, lightning parameters, and return stroke models. The processes that lead to the developmen t of thunderstorms, th e charge structure of a thundercloud, and the electrification processes that occur inside a cloud are explained. Information about the different discharge types associated with a thundercloud, specifically a bout the lightning discharge between cloud and ground, is given. One discharge type of great intere st is the cloud-to-ground downward lightning discharge that lowers negative charge to ground, since this type of cloud-to-ground lightning discharge occurs most frequently and is the cause for most injury and death to people and damage to structures and electr onics. The process of negative cloud-to-ground lightning is descri bed in detail. In order to conduct experiments on lightning, it is desirable to be able to control where and when lightning strikes. The concep t of artificial initiation of lightning using small rockets-so-called rocket tr iggered lightning-is described. A detailed description of lightning return stroke characteristic s including typical waveforms and statistics of some important parameters is given. An attempt is made in the literature to model the return st roke by specifying the current distribution as a functi on of the lightning channel heig ht. Four classes of return stroke models are discussed with special focu s on six “engineering” return stroke models.

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4 Figure 2-1: Cumulonimbus pr oducing cloud to ground lightning. 2.1.1 Cloud Formation and Electrification Regions of opposite electrical charge are a prerequisi te for the occurrence of lightning. Electrically charged clouds, so-calle d thunderclouds or cumulonimbi, are the energy source for most lightning occurring on Earth. The process of charge generation and separation is called electrification. Electri fication processes take place in a number of cloud types. The anvil shaped cumulonimbus (Figure 2-1; Moore) is the most common type. Lightning can also originat e from other sources that invo lve different electrification processes (e.g., clouds produced by forest fire , volcanic eruption, and atmospheric charge separation in nuclear blasts). The electri cal structure of a cu mulonimbus and the electrification process inside this cloud t ype are discussed in the following section.

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5 2.1.2 Formation of a Cumulonimbus A thundercloud is a lightning-producing deep convective cloud. Thunderstorms form in an unstable atmosphere. According to Henry, Portier, and Coin (1994), eight types of thunderstorms are known. The five thunderstorms common in Flor ida are Air-mass thunderstorms, sea/landbreeze thunderstorms, oceanic thunderstorms , squall line thunderstorms, and frontal thunderstorms. The first three thunderstorm t ypes are also known as convective or local thunderstorms. In Florida the mechanisms that lead to the development of cumulonimbi strongly depend on season. Air-mass and sea/land-breeze thunderstorms constitute the majority of Florida thunders torms and occur most frequent ly during the warm summer months. Frontal storms are a typical wint ertime phenomenon, alt hough they also occur less frequently during summertime. Air-ma ss thunderstorms develop if landmasses are heated by the sun. The landmasse s radiate heat to the mois t layers of air near ground, causing the air to rise. The air forms an updr aft if the air mass is sufficiently large. Sea/land-breezes are caused by the temp erature difference between water and land. Sea breezes occur typically during ear ly afternoon on sunny days; land breezes occur typically during nighttime (Figure 2-2; Encyclopaedia Britannica). Sea/land-breeze storms are primarily induced by the converg ence of air that accompanies sea breezes. Less common are sea/land-breeze storms due to land breezes.

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6 Figure 2-2: Formation of sea/land-breeze thunderstorms. Figure 2-3: Cold front moves under warm front resulting in the formation of cumulonimbus (frontal storm). Frontal storms are usually formed if a cold front advances toward warm air, forcing the warm air to rise (Figure 2-3; Kuehr, 1996). When parcels of warm, moist air rise in an updraft, which is caused by one of the mechanisms mentioned above, several other effects take place:

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7 The air pressure decreases with height causing the parc els of moist air to expand. The rising air cools and condenses on small particles in the atmosphere (condensation nuclei) once the relative humidity in the parcel exceeds saturation. The resulting small water particles form the visible cloud. The height of the condensation level, that is the bottom of the visi ble cloud, increases with decreasing relative humidity at ground. During the condensation process the heat of condensation (the energy absorbed as water changes from liquid to vapor) is rele ased. This heat supports the continued upward movement of the air ma sses and water particles. Some of the water particles freeze once th ey reach a height where the temperature is below 0 ° C. At -40 ° C or so all water particles freeze. The freezing process releases the heat of freezi ng (the energy absorbed as water changes from solid to liquid), which supports further the up ward movement of the particle. A cumulonimbus develops if th e decrease in atmospheric temp erature with height, the socalled lapse rate, exceeds a certain specific va lue which depends on the humidity of the air, the so-called moist-adiabatic lapse rate. 2.1.3 Electrical Structure of a Cumulonimbus Figure 2-4: Electrical structur e inside a cumulonimbus.

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8 The charge distribution inside a cu mulonimbus is complex and changes continuously as the cloud evolves. Most ch arge inside the cloud resides on hydrometeors (liquid or frozen water particles), but also so me free ions are present. Probably charged particles and ions of positive and negative pola rity coexist in the same regions inside the cloud, but in some areas particles of one polarity are dominant, forming regions of positive or negative net charge. Early ground based measurements (early 1930s) of the cloud charge revealed a vertical, positive (regions of positive net charge located above regions of negative net charge) dipole structure for the primary ch arge regions. Later in-cloud measurements [Simpson and Scrase, 1937] confirmed this resu lt and additionally identified a localized lower region of positive net charge. This pos itive charge region was not always present (or could not always be measured). Th e dipole and tripole model can describe approximately 60% of cloud charge distribut ion. Figure 2-4 [Simpson and Scrase, 1937] shows a typical electrical st ructure inside a thundercloud. The top two charge regions are usually re ferred to as main charge regions. In Florida the height of the main negative char ge center is typica lly 7–8 km above ground level, the main positive charge center is typically located 10–12 km above ground level, and the positive charge center at the bottom of the cloud is located 1–2 km above ground level [Rakov, 2001].

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9 2.1.4 Electrification of a Cumulonimbus The detailed physical processes that l ead to the generati on and separation of charge and the formation of the charged regions inside the thundercloud are poorly understood. Several hypotheses that try to e xplain this phenomenon have been proposed. They can be labeled either precipita tion theories or convection theories. Figure 2-5: Precipitation theory (lef t) and convection theory (right). In precipitation theories relatively heavy and large hydr ometeors (precipitation in the form of soft hail, so-called graupel) wi th a high fall speed (> 0.3 m/s) collide with lighter, smaller hydrometeors (cloud particles in the form of ice and water) carried upwards by updrafts (Figure 2-5; Williams, 1989). Charge is transferred during the interaction between the heavy and light partic les. In relatively cold regions (T < -15 ° C, or so) the heavy particles will become negatively charged and the lighter particles positively charged. In warmer regions (T > -15 ° C, or so) at the lower part of the cloud, the process

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10 reverses such that the heavy particles w ill become positively charged and the lighter particles negatively. Gravity and updrafts sepa rate the lighter particles from the more heavy ones and a main positive dipole with an additional separate localized positive region at the bottom of the cloud forms [Williams, 1989]. In convection theories electric charges are supplied by external sources–fairweather space charge, corona discharges on the ground and cosmic rays. The convection mechanism is illustrated in Figure 2-5 [W illiams, 1989]. Updrafts of warm air carry positive fair-weather space charge to the top of the developing cumulonimbus. Negative charges above the cloud produced by cosmic rays are attracted to the cloud’s surface by the positive charge within the cloud. Most of the negative charge resides on cloud particles. Cloud particles can carry more charge per uni t volume of cloudy air than precipitation. The negatively charged cloud particles are carried downward by downdrafts, causing corona at the surface. Th e corona generates positive charge below the cloud that is carried to the upper cloud by the updrafts. This hypothetical mechanism results in the formation of a positive dipole. Although it is possible that both precip itation and convection mechanisms are important for cloud electrificati on, the precipitation mechanism is viewed in the literature as the more significant.

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11 2.2 Natural Lightning 2.2.1 Discharge Types associated with a Cumulonimbus Figure 2-6: Discharge types for a cumul onimbus. Adapted from “Encyclopaedia Britannica”. The charges inside the cumulonimbus maybe partially neutralized by lightning discharges (Figure 2-6). Thes e discharges can be categorized in the following discharge types: Intracloud discharges (dis charge within the cloud) Cloud-to-ground discharges Intercloud discharges (dis charge from cloud to cloud) Cloud-to air-discharges Most research has been conducted on cloud-to-ground discharges since this discharge type is th e cause of most lightning damage, injury, and death. Intercloud and cloud-to-air discharges are t hough to be relatively rare comp ared to intracloud and cloudto-ground discharges.

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12 2.2.2 Lightning Discharges between Cloud and Ground Figure 2-7: Simplified draw ing of four discharges between cloud and ground. The various lightning discha rges between cloud and ground can be classified into four categories, based on the direction of pr opagation of the initial leader and the polarity of the charge transferred to Earth (Figure 2-7, Uman, 1987): Type 1 – Downward lightning discharge, lowering negative charge to Earth Type 2 – Upward lightning discharge, lowering negative charge to Earth Type 3 – Downward lightning discharge, lowering positive charge to Earth Type 4 – Upward lightning discharge, lowering positive charge to Earth Upward directed flashes (type 2 and 4) are typically initiate d from tall structures on flat ground or structures of moderate heights on mountains. The charge transferred and the current peak value is typically larger in downward lightning lowering positive charge than in downward lightning lowering nega tive charge. Downward lightning lowering

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13 positive charge contains typically one str oke, most downward lightning flashes lowering negative charge contain more than one st roke. Negative downward lightning (type 1) constitutes approximately 90% of all cloud to ground flashes. The remaining 10% of all cloud to ground flashes are covered by the other three categories; with positive downward lightning (type 3) being th e most frequent of the three. A rough outline of the physical proce sses involved in negative downward lightning is described and illustra ted in Figure 2-28 [Uman, 1987]. € Typical tripole struct ure of a lightning producing cumulonimbus–upper positive main charge region; lower negative main charge region; localized po sitive charge re gion at the cloud base. If the electric field at th e bottom of the negative charge region reaches a critical value, a preliminary breakdown starts. (t=0) € An in-cloud breakdown starts from the negative charge region toward ground carrying negative charge and neutralizing the positive charge region at the cloud base (1 ms). € A stepped leader, consisting of a thin, highl y ionized core surrounded by a wider corona shea th, leaves the cloud (1.1 ms). Figure 2-8: Drawings illustra ting some of the various pro cesses comprising a negative cloud to ground lightning flash.

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14 Figure 2-8: Continued € The stepped leader moves with a typical average speed of about 2*105 m/s toward ground. Negative charge from the cloud flows mo re or less continuously into the leader channel (1.15 ms–19 ms). Figure 2-8: Continued € When the stepped leader a pproaches ground, the electric fiel d strength at certain points on ground (notably at sharp and elevated object s) exceeds the breakdown value of air. At these points one or more positive upward-going leaders develop in the direction of the negative downward going leader from the cloud (20 ms). € An upward-going leader connects with a downward-going leader branch. A current wave with a current peak value of typical ly 30 kA, the first return stroke, starts propagating upward along the ionized channe l prepared by the leader (20.10 ms).

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15 Figure 2-8: Continued € The first return stroke neutralizes the nega tive charge deposited in the leader channel and in the process lowers negative charge to ground. The return stroke travels upward with a speed in the order of 108 m/s (20.10 ms–20.2 ms). € Following the first return stroke, the cloud region, where the leader has starte d, is near ground potential. Discharges between this re gion and negatively charged regions in the cloud can occur, so-called K and J processes (40 ms). Figure 2-8: Continued

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16 Figure 2-8: Continued € A dart leader may arise if the channel of the first return stroke has not yet dissipated. The dart leader usually follows the already ex isting channel prepared by the return stroke; therefore it is typically not branched. The speed of the dart leader is typically 107 m/s [Uman, 1987] and it lowers negative charge on to the defunct channel of the previous stroke (60 ms–62 ms). € Once the dart leader appr oaches ground, a second return stroke develops in similar manne r to the first return stroke (62.05 ms). Additional subsequent returns strokes can occur if this pro cess repeats itself. Figure 2-8: Continued

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17 2.3 Rocket Triggered Lightning Figure 2-9: Rocket triggere d lightning in Camp Bla nding, Florida (Flash U9910). The probability of a lightning strike to a structure, even in areas of high lightning activity, is very low. Thus experiments w ith close natural lightning are difficult to conduct. A more practical approach to conducti ng such experiments is to artificially initiate a lightning strike using the rocket and wire technique (Fi gure 2-9). The lightning type initiated by using this technique is te rmed rocket-triggered lightning. In rocket triggered lightning, a small rocket with an attached conducting wi re is used to artificially initiated lightning. Under favorable conditions , i.e., measured static electric field on ground < -5 kV/m, a rocket trailing a conducti ng wire is launched with a speed of 200 m/s towards a thundercloud.

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18 Figure 2-10: Sequence of events in classical rocket triggered. Two different rocket triggered lightning methods are currently in use [Rakov, 1999]: 1) In the classical rocket triggered lightning technique , illustrated in Figure 2-10 [Rakov, 1999], the triggering wire is a conti nuous conductor that is connected to ground. As the rocket ascends, the electric field at th e tip of the rocket is distorted. When the rocket reaches an altitude of about 200 m to 300 m, the field enhancement at the rocket tip can result into the development of a positiv e leader (provided that a sufficient ambient negative field is present) ascending with a speed of the order of 105 m/s from the rocket tip towards the thundercloud. The upward going positive leader vaporizes the wire and establishes an initial conti nuous current (ICC), which flows for typically some hundreds of milliseconds through the channe l. After the cessation of the ICC a no current interval having a typical duration of tens of milliseconds occurs, which may be followed by one or more downward leader/upward return stro ke sequences. These leader/return stroke sequences are believed to be ve ry similar to the subsequent leader/return stroke sequences in natural lightning.

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19 Figure 2-11: Sequence of events in a ltitude rocket triggered lightning. 2) Attempts have been made to reproduce some features of the first return stroke in natural lightning by using th e altitude lightning triggeri ng technique, illustrated in Figure 2-11 [Rakov, 1999]. In this technique th e triggering wire consists of 2, sometimes 3, sections–a 50 m long grounded conducting wire at the lower end (t his section is not always present), a 400 m long kevlar line in the middle, and a 150 m long ungrounded conducting wire attached to the rocket. An upward going positive leader and a downward going negative leader (bi-directi onal leader) start when the rock et is at a height of about 600 m. Once the downward leader connects to ground, an upward return stroke starts. The return stroke speed is two to three orders of magnitude greater than the speed of the upward going leader, and thus it catches up to the tip of the upward going leader. At this stage the process is similar to classical rocket triggered lightning, i.e., a continuous current flows through the channel possibly foll owed by one or more leader/return stroke sequences.

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20 2.4 Return Stroke In this section characteristics of the li ghtning return stroke that lowers negative charge to earth are discussed in detail. In the history of lightning research, most emphasis has been placed on understanding the return stroke, since it is the cause of most direct and indirect lightning effects. Furthermore, the fact that mo st return stroke parameters, i.e., luminosity, current, and time derivative of current, electromagne tic fields and their time derivatives, are of large magnitudes and thus can be easily identified experimentally has allowed more thorough analyses of return stroke features. 2.4.1 Initial Bidirectiona l Return Stroke Wave Weidman et al. [1986] and others hypot hesized the presen ce of an initial bidirectional return stroke wave. The a ttachment process between a downward going leader and a resulting upward connecting leader takes place some tens of meters above ground, resulting in a bidirectional return stroke wave. The upward traveling return stroke wave neutralizes the charge deposited by the downward leader and the downward traveling return stroke wave neutralizes the charge deposited by the upward connecting leader. The downward traveling wave is reflected at ground with unknown reflection coefficient. Upward and downward retu rn stroke waves both produce remote electromagnetic fields, while the current measur ed at the channel base is assumed to be associated with the downward going return stroke wave and its reflection at ground. It is believed that an upward connecti ng leader is always present in a stepped leader/first return stroke seque nce, implying the presence of an initial bidirectional first return stroke wave. Idone et al. [1984] presented indirect evidence of an upward connecting leader in rocket-triggered light ning. Therefore it seems that the initial

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21 bidirectional extension of the re turn stroke channel is also a feature of subsequent strokes. Wang et al. [1999] presented the first direct e xperimental evidence of the presence of an initial bidirection return str oke wave in rocket triggered lightning. They used a high speed optical imaging system (ALPS) with a spatial resolution of 3.6 m and a time resolution of 100 ns. The bidirectional return stroke wave c ould be detected in two events. The lengths of the upward going leaders were estimated to be 7-11 m and 4-7 m. The corresponding return stroke peak currents were 21 kA a nd 12 kA, and the corresponding leader electric field changes at 30 m from the strike point were 56 kV/m and 43 kV/m. 2.4.2 Return Stroke Current/Return Stroke Current Time Derivative Figure 2-12: Typical return stro ke current waveshape in tri ggered lightning measured at the channel base. The return stroke current measured at th e channel base is characterized by a sharp rising edge followed by a much slower decayi ng part. A typical return stroke current waveform is shown in Figure 2-12. The retu rn stroke current waveform contains 05101520253035404550 35 30 25 20 15 10 5 0 S9934 RS3 Attach Rod Base It [us]I [kA]

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22 information about possible direct damage (effect s of a direct lightning strike) and indirect damage (induced effects) caused by lightning. Berger et al. [1975] obtained the most complete statistics to date on lightning return stroke currents from measurements in Switzerland. For first retu rn strokes the 2 kA to peak rise-time had a median value of 5.5 µ s (89 events) and a median value of 1.1 µ s (118 events) for subsequent strokes. The slower rise-time of the first return stroke is probably due to the longer upw ard going leader that precedes the first return stroke [Uman, “Lightning Discharge”]. Berger found a median value for the current amplitude of first return strokes of 30 kA and 12 kA for subsequent strokes. Th e magnitude of the current amplitude (I) determines overvoltages (U) caused by a direct lightning strike (U=I*Z), where Z is the characteristic impedance of the struck object. The area under the current curve is the ch arge (Q) transferre d during the return stroke (= dt i Q). Berger found a median value for the charge transferred during first return strokes of 5.2 C and 1.4 C for subseque nt strokes. The transferred charge is responsible for the melting damage caused by lightning (W=U*Q). Another important current parameter is the so-called action integral, which is defined as the integral of the power dissipated by a 1 resistor (dt i2). Berger found a median value for the action integral of 5.5104 A2s for first return strokes and 6103 A2s for subsequent strokes. The action integral is a measure for the heating of conductors caused by a direct lightning strike.

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23 The time rate of current change ( t i ) is important for determining possible indirect damage caused by a lightning stri ke. The 10 – 90% rise-time contains some information about this parameter, although it represents the average value of current change during the 10 – 90% rise. More de tailed information can be obtained by differentiating measured current with respect to time, whic h usually results in a noisy waveform, or better, by directly m easuring the current time derivative. Figure 2-13: Typical return stroke current derivative waveshape in triggered lightning measured at the channel base. A typical current derivative waveform, illu strated in Figure 2-13, is characterized by a very fast rise-time and a slightly slower decay time. Theoretically the decaying part should always exhibit a positive overshoot, si nce the measured current always decays slowly to zero after peak. This overshoot is not always observed in our measurements, probably due to the insufficient low frequency response of the current derivative sensor, quantization errors, and noise level. 00.20.40.60.811.21.41.61.822.22.42.62.83 300 250 200 150 100 50 0 S9934 RS3 dI/dtt [us]dI/dt [kA/us]

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24 As previously mentioned, the maximum value of the current derivative is an important indicator for induced effects. Be rger found a median value for the current derivative amplitude of firs t return strokes of 12 kA/µs and 40 kA/µs for subsequent strokes. More than 5% of the measured curre nt derivatives of subsequent strokes had a value higher than 120 kA/µs. The largest directly measured current derivative peak value has been about 411 kA/µs for a triggered lightning stroke at the Kennedy Space Center [Depasse, 1994]. 2.4.3 Return Stroke Speed The average speed with which the return stroke current impulse is propagating along the channel is about 1/2 to 1/3 of the sp eed of light. In the li terature there is no consensus about the return stroke speed at the very bottom of the lightning channel. Experiments have been conducted to determine the return stroke speed at the very bottom of the channel using optical measuremen ts, although several problems have been encountered during these attempts: Optical measurements necessarily averag e the speed over a certain length of the channel. It is difficult to obtain optical data fr om very close to the bottom of the lightning channel. Often only the two-dimensional speed is measured. Early optical measurements conducted by Schonland et al. [1934, 1935] in South Africa using a Boys camera (a two-lens streak camera) revealed a first return stroke speed at the channel base near 1*108 m/s. The speed decreased abr uptly when the return stroke reached a branch point of the lightning channel.

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25 In later optical measuremen ts by Idone and Orville [1982] , the mean speed within about 1.3 km off ground was determined to be 9.6*107 m/s for first return strokes (17 values), and 1.2*108 m/s for subsequent strokes (46 values). The speed distribution derived in this experiment is illustrated in Figure 2-14. Figure 2-14: Distribution of measured return stroke twodimensional speed. Idone et al. [1984] measured a mean thre e-dimensional return stroke speed in artificially trigge red strokes of 1.2*108 m/s (56 values), with a minimum value at 6.7*107 m/s and maximum values at 1.7*108 m/s. Wang et al. [1999] measured the return stroke speed of triggered lightning strokes in Camp Blanding, Florida, using ALPS (Automatic Lightning Progressing Feature Observation System), a high-speed optical im aging system with 100 ns sampling interval. The measured return stroke speeds of two strokes occurring 530 m away from the ALPS, resulting in a spatial resolu tion of about 30 m, were 1.3*108 m/s and 1.5*108 m/s, respectively for the bottom 60 m or so of the channel. The speed of two different strokes

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26 250 m away from the ALPS, resulting in a spat ial resolution of about 3.6 m, were roughly estimated to be 2*108 m/s and 3*108 m/s, respectively for the very bottom of the channel. Baum [1990] argued on theoretical grounds th at the return stroke speed at the very bottom of the return channel might be near the speed of light (c=3*108 m/s). Leteinturier et al. [1990] us ed electric field derivati ve data measured at 50 m distance from the channel base and current deri vative data to calculated the return stroke speed of rocket triggered lightning in Fl orida and France by applying the Transmission Line model (TLM) and assuming that the elec tric field was pure radiation field. The average speed computed from 40 data sets was 2.9*108 m/s with a standard deviation of 0.4*108 m/s and a maximum value at 4.2*108 m/s. The unrealistic high speed values obtained, above the speed of light, is likely an indication that the field derivative is not pure radiation field, although other explanations of the speed derived are possible. Uman et al [2000] calculated return str oke speeds of rocket triggered lightning from current derivative data obtained by nu merically differentiating current waveforms and electric field derivative data measured at 10 m, 14 m, and 30 m distance from the strike point. The TLM for pure radiation field was used for the calculation. The average speed for the 10 m, 14 m, and 30 m data was, respectively, 1.7108 m/s (7 values, standard deviation: 4.6107 m/s, maximum speed: 2.3108 m/s), 3.1108 m/s (3 values, standard deviation: 1.1108 m/s, maximum speed: 4.7108 m/s), and 2.9108 m/s (7 values, standard deviation: 7107 m/s, maximum speed: 4.2108 m/s). Speeds for five events have been calculated from electric field derivativ e data simultaneously measured at 10 m and 30 m. The average speeds calculated from the 10 m and 30 m data is 1.7*108 m/s and 2.8*108 m/s, respectively.

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27 2.4.4 Electric Field/Electric Field Time Derivative Figure 2-15: Typical vertical electric field waveforms at different distances. The electric field produced by the lightning return stroke can be decom posed into three different components; each characterized by its distance dependence. The static fi eld component contribution dominates the electric field pe ak at close distances, the induction field component contri butes significantly to the total field at intermediate distances, and the radiation component dominates at fa r distances. The distance dependence of first stroke (s olid line) and subsequent stroke (dotted line) vertical electric fields of natural lightning measured at ground level is illustrated in Figure 2-15 [Lin et al., 1979]. The ini tial peak in the electric field waveshape can be attri buted to the radiation field component, implying a domina ting radiation field at early times. Distant electric field waveforms are bipolar and have the same waveshape as distant magnetic fields (see magnetic field for 200 km in Figure 2-18). Furthermore a slow ramp that follows the initial peak and is present for more than 100 µs is a typical feature of electric field measured within some tens of kilometers.

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28 The mean value of the initial electric fi eld peak normalized to 100 km is typically in the range of 6-8 V/m for first strokes a nd 4-6 V/m for subsequent strokes. The mean value of the zero to peak rise-time is typically in the range of 3-5 µs for first strokes and 1.5-3 µs for subsequent strokes [Uman, 1987]. Figure 2-16: Typical vertical el ectric field waveshape in tri ggered lightning measured at ground at 15 m distance from the strike point. The vertical electric field of a dart leader/return stroke sequence measured at close distances from the strike point is charact erized by its asymmetrical V-shape (Figure 2-16). The descending part of the waveform is associated with the negative downward going leader, the ascending part with the pos itive return stroke. The width of the V becomes larger with distance. The V-shap e is observed at distances well beyond 500 m [Uman et al., 1993]. 0102030405060708090100 250 200 150 100 50 0 S9934 RS3 E15t [us]Electric Field [kV/m]

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29 Figure 2-17: Typical time deriva tive of the vertical electric field waveshape in triggered lightning measured at ground at 15 m distance from the strike point. The waveshape of the time derivative of th e vertical electric field measured at ground at 15 m distance from the strike point is shown in Figure 2-17. The electric field time derivative typically exhibits a positive ex cursion, which is due to the leader, and a negative peak with a fast descending part a nd a slightly slower as cending part, which is due to the return stroke. Uman et al. [2000] measured electric field time derivativ es of rocket triggered lightning at 10 m, 14 m, and 30 m. For the 10 m data the mean peak electric field derivative was 209 kV/m/µs (7 values) with a standard deviation being 37.1 kV/m/µs, and the maximum value being 260 kV/m/µs. Four values saturated at 270 kV/m/µs were not included in the statistics. For the 14 m da ta the mean peak electric field derivative was 191 kV/m/µs (4 values) with a standa rd deviation being 76.8 kV/m/µs, and the maximum value being 299 kV/m/µs. For the 30 m data the mean peak electric field derivative was 144 kV/m/µs (7 values) with a standard deviation being 41 kV/m/µs, and the maximum value being 226 kV/m/µs. Three values saturated at 170 kV/m/µs were not included in the statistics. 00.511.522.533.544.555.56 500 400 300 200 100 0 100 200 S9932 RS2 dE15/dtt [us]dE/dt [kV/m/us]

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30 2.4.5 Magnetic Field/Magnetic Field Derivative Figure 2-18: Typical horizontal magnetic field waveforms at different distances. The magnetic field produced by the lightning return stroke can be deco mposed into two different components; each characterized by its distance dependence. The induction (m agnetostatic) contribution dominates the magnetic field peak at close distances and the radiation component domina tes at far distances. The distance dependence of first stroke (solid line) and subsequent stroke (dotted line) horizontal magnetic flux density of natural lightning measured at ground level is illustrated in Figure 2-18 [Lin et al., 1979]. The initial peak in the magnetic flux density waveshape can be attributed to the radiation field component, implying a dominating radiation field at early times. Distant magnetic flux density wavefo rms are bipolar and have the same waveshape as distant electric fields (see electric field for 200 km in Figure 2-15). A hump following the initial peak with a maximum occurring between 10 and 40 µs is a typical feature of magnetic fields measured within some tens of kilometers.

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31 Figure 2-19: Typical horizontal magnetic field waveshape in triggered lightning measured at ground at 15 m dist ance from the strike point. The horizontal magnetic field of a dart l eader/return stroke sequence measured at close distances from the strike point is char acterized by its fast descending front followed by a slow tail edge (Figure 2-19). Figure 2-20: Typical horizontal magnetic flux intensity time derivative waveshape in triggered lightning measured at 15 m distance from the strike point. The waveshape of the horizontal magnetic field time derivative measured at 15 m distance from the strike point is shown in Figure 2-20. The magnetic field time derivative waveshape resembles the waveshape of the current time derivative. This resemblance is discussed in chapter 4. 0102030405060708090100 500 450 400 350 300 250 200 150 100 50 0 S9934 RS3 B15t [us]Magnetic Flux [uW/m^2] 00.20.40.60.811.21.41.61.822.22.42.62.83 2000 1800 1600 1400 1200 1000 800 600 400 200 0 200 S9934 RS3 dB15/dtt [us]dB/dt [uW/(m^2*us)]

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32 2.5 Return Stroke Models Various approaches to modeling the li ghtning return stroke are found in the literature. Most published models can be categorized into one (or sometimes two) of four classes [Rakov and Uman, 1998]: 1) Gas dynamic models Gas dynamic models combine three gas dynamic (hydrodynamic) equations, which represent the conservation of mass, momentum, and energy with two equations of state. Input parameter is an assumed channel current versus time. Output parameters are usually temperature, pressure, and mass density as a function of time and space. Most gas dynamic models consider mainly the radial e volution of the lightning channel and neglect longitudinal evolution of the ch annel, electromagnetic skin e ffect, corona sheath, and any heating of the air surroundi ng the lightning channel. Maybe the most advanced and complete gas dynamic model to date has been presented by Paxton et al. [1986, 1990]. 2) Electromagnetic models In electromagnetic models the return stroke process is represented as a radiating lossy, thin-wire antenna. The current distributi on along the channel is determined by numerically solving MaxwellÂ’s equations. El ectromagnetic models have been proposed by e.g. Podgorski and Landt [1987], Bor ovsky [1995], and Moini et al. [1997]. 3) Distributed-circuit models In distributed-circuit models th e return stroke process is represented as a transient process on a vertical transmission line with a speci fied resistance (R), inductance (L), and capacitance (C), all per unit le ngth. Distributed-circuit models are also known as R-L-C transmission-line models. The re turn stroke current versus ti me and height of the channel

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33 can be determined with distributed-circuit m odels. Distributed-circuit models have been proposed by e.g. Oetzel [1968], Price and Pierce [1977], and Go rin [1985]. Sometimes distributed-circuit models are combined with gas dynamic models, e.g., [Strawe 1979]. 4) “Engineering” models “Engineering” models present a practical appr oach to model the return stroke process. The relatively easy to measure current at the channel base and its as sumed variation with height are used to specify th e current (or charge density) di stribution along the channel as a function of time and space. The quality of th e “engineering” model is determined by the capability to explain or reproduce observed light ning return stroke characteristics, such as channel luminosity and electromagnetic fields. “E ngineering” models can also be used to predict difficult to measure parameters, such as return stroke speeds and electromagnetic fields at a certain height above ground. Gas dynamic models can be used to dete rmine R(t), i.e., the lightning channel resistance per unit length as a function of tim e. R(t) is one of the input parameters of electromagnetic models and distributed circ uit models. An important electromagnetic compatibility (EMC) application of electrom agnetic models, distributed circuit models, and “engineering” models is the calculati on of remote electromagnetic fields to investigate coupling effects, such as induced voltages causing outages or destruction of electronic devices. The small number of input parameters is a characteristic feature of “engineering” models and predestine them fo r the calculation of channel currents from remote electromagnetic fields measuremen ts–an important application in lightning detection.

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34 2.5.1 “Engineering” Models “Engineering” models have been discussed in the literature by Bruce and Golede [1941], Willet et al. [ 1988], Willet et al. [1989], Diendorfe r and Uman [1990], Nucci et al. [1990], Thottappillil et al . [1991], Thottappillil and Um an [1993], Thottappillil and Uman [1994], Thottappillil et al. [1997], and Rakov and Uman [1998]. An “engineering” return stroke model (RSM) is defined as an equation, which relates the longitudinal return stroke cu rrent for every time and position along the lightning channel (I(z ,t)) with the current at the channe l base (I(0,t)). An equivalent expression specifying the line charge density al ong the channel can be obtained using the continuity equation [Thottappill il et al., 1997]. These equations can be used to calculate the electric and magnetic fields at a specified distance from th e channel to the current at the channel base. The “engineeri ng” return stroke models disc ussed in this section are (1) the transmission line model, TL, (2) the modified transmission line model with linear current decay with height, MTLL, (3) th e modified transmission line model with exponential current decay with height, MTLE, (4) the traveling cu rrent source model, TCS, (5) the Bruce-Golde model, BG, (6) the Diendorfer-Uman model, DU, and (7) the modified Diendorfer-Uman model, MDU. Rakov [1997] proposed a generalized cu rrent equation that represents many “engineering” models: ) / , 0 ( ) ( ) / ( ) , ( v z t I z P v z t u t z If Š Š = (2.1) where vf is the upward propagating front speed (r eturn stroke speed), v is the current wave propagation speed, z is the height of the channel section, u is the Heaviside unit

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35 step function (u(tz /vf) = 1 for t z /vf , otherwise u(tz /vf) = 0), and P( z ) is the height dependent current attenuation f actor introduced by Rakov and Dulzon [1991]. The “engineering” models discussed in this section can be grouped into two categories–A) Transmission line type models and B) Traveling current source models [Rakov, 2000]. A) Transmission line type models: TL, MTLL, MTLE In transmission line type models a current wave is injected at the channel origin and travels upward, therefore the lightning channe l behaves similar to ideal transmission line. Figure 2-21: Current versus time wave forms specified by TL model at ground ( z = 0) and at two heights 1z and 2z . t t t z' 0 z' z' z' /v v = v f f 2 2 1 0

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36 Figure 2-21 [Rakov, 1997]. illustrates the current distribution specified by the TL model. The current wave is shown for height z = 0, z = 1z , and z = 2z . The current wave travels upward without distortion or attenuation and with constant speed vf (symbolized by the dotted line). Current wave and current front propagate in the same direction with the same speed (v = vf). The current at for instance height 2z is the same as the current at ground (2z = 0) at time t = 2z /vf earlier. Therefore e quation (2.1) for the TL model is: ) / , 0 ( ) / ( ) , ' (f fv z t I v z t u t z I Š Š = (2.2) In the TL model no charge is deposited or removed from the channel. Therefore, the total net charge of th e channel remains unchanged. MTLL and MTLE model are similar to th e TL model except that the current decays with height. The current decay is linear for the MTLL model and exponential for the MTLE model. Therefore equation (2.1) becomes for the MTLL model ) / , 0 ( ) / 1 ( ) / ( ) , ' (f fv z t I H z v z t u t z I Š Š Š = (2.3) where H is the total height of the channel, and for the MTLE ) / , 0 ( ) / ( ) , ' (/ f z fv z t I e v z t u t z I Š Š = Š (2.4) where is the current decay constant.

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37 Figure 2-22: Current versus height z above ground at time t = t1 for the TL model. Figure 2-22 [ Rakov, 1997] shows the hei ght dependent current wave for the TL model at an arbitrary fixed moment in time (t = t1). The current wave moves from left to right, i.e., upward along the channel. The upw ard direction of propa gation of the current wave is a characteristic feature of transmission line type models. B) Traveling current source type models – BG, TCS, DU, MDU Traveling current source t ype models take the charge deposited by the preceding leader channel into account. In traveling current source type models the current wave originates at the upward moving return stroke front, due to the charge collection at this point. The generated current wave travels downward. 0 z' I(0,t ) { 1 I(z',t) v f f v t 1

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38 Figure 2-23: Current versus time wavefo rms specified by TCS model at ground ( z = 0) and at two heights 1z and 2z . Figure 2-23 [Rakov, 1997] illustrates the cu rrent distribution specified by the TCS model. The current wave is shown for height z = 0, z = 1z , and z = 2z . The shaded region under the curve indicates current that actually flows through th e channel; the blank portion of the waveform is shown for illustrative purposes only. The return stroke wavefront is assumed to propagate upward with constant velocity vf and without distortion or attenuation. Th e discharge current wave generated at the wavefront is assumed to propagate downward with the speed of light c. Therefore, the current at, for instance, height 2z is the same as the current at the channel bottom ( z = 0) at time t t t z' 0 z' z' z' /v v f f 2 2 1 0 v=-c z' /c 2

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39 t=2z /c later. The current wave at z > 0 exhibits a discontinuity at the return stroke front. This implies that charge on the channel is in stantaneously released by the return stroke front, which is physically unreasonable, but mi ght be a good approximation to the actual situation if the charge release takes place in a very short time. Equation (2.1) for the TCS model is: ) / , 0 ( ) / ( ) , ' ( c z t I v z t u t z If + Š = (2.5) Figure 2-24: Current versus height z above ground at time t = t1 for the TCS model. Figure 2-24 [Rakov, 1997] shows the height dependent current wave assumed in the TCS model at an arbitrary fixed moment in time (t = t1). The current front moves with vf from left to right, i.e., upward along the channel, while the current wave moves with the speed of light c from ri ght to left, i.e., downward. The downward direction of propagation of the current wave is a characteristic f eature of traveling current source type models. 0 z' I(0,t ) 1 I(z',t) c v f 1 f ct v t 1 {

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40 Figure 2-25: Current versus time wavefo rms specified by BG model at ground ( z = 0) and at two heights 1z and 2z . Figure 2-25 [Rakov, 1997] illustrates the cu rrent distribution specified by the BG model. The current wave is shown for height z = 0, z = 1z , and z = 2z . The return stroke wavefront is assumed to propaga te upward with constant velocity vf. The current carrying channel sections at every height ha ve the same current value as the channel current at the channel base at the same inst ant in time,i.e, the downward wave propagates at v = . Therefore, equation (2.1) for the BG model is: ) , 0 ( ) / ( ) , ' ( t I v z t u t z If Š = (2.6) t t t z' 0 z' z' z' /v v f f 2 2 1 0 v =

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41 The current wave velocity in the BG model is infinite; therefore the direction of propagation of the current wave is not determ ined, which makes the classification of the BG model as transmission line type or traveling current s ource type arbitrary. The BG model can be regarded as a special case of a transmission line type model (TL model with v replaced by infinity) or as a special cas e of a traveling current source model (TCS model with c replaced by ). Rakov and Uman [1998] incl uded the BG model into the traveling current source type category and so it is done in this section. The BG model is physically unreasonab le because 1) every channel section assumes the same current instantaneously, wh ich would mean that information transfer takes place with an infinite speed [Nucci et al ., 1990] and 2) there is a discontinuity at the channel front for z > 0 (also assumed in the TCS model). The DU model [Diendorfer and Uman, 1990] is physically more reasonable than the BG and TCS model. Similar to the TCS m odel the return stroke wavefront in the DU is assumed to propagate upward with constant velocity vf while the current wave propagates downward with the speed of light. The difference from the TCS model is that the charge is not released instantaneously into the channel, but gradually. This assumption is expressed mathematically by adding a second current component of opposite polarity to the current expression of the TCS. The additional component starts with the return stroke curren t value of the front and then decreases exponentially with a decay constant D, therefore disposing of the disc ontinuity at the channel front. Thottappillil and Uman [1993] and Thottappillil et al. [1997] assumed D to be 0.1 µ s. The current distribution in the DU model is:

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42 + Š + Š = Š ŠD fv z t f fe c z v z I c z t I v z t u t z I/) / / , 0 ( ) / , 0 ( ) / ( ) , ' ( (2.7) In the DU model, the current at the channel bottom is assumed to be composed of two different components with different decay constants. One component is due to the discharge of the channel core–t he so-called breakdown current IBD. The second current component is due to the neut ralization of the ch arge deposited in the corona sheath surrounding the channel–the so -called corona current IC. The charge stored in the channel core is relatively easy to re lease compared to the charge stored in the corona sheath; therefore it is assumed that IBD dominates the total base current for the first few µ s. The bulk of the charge is stored in the corona sheath, therefore IC is assumed to dominate the total base current after a few µ s. An analytical expression for IBD and IC can be found by approximating the sum of both current distributions to a measured cha nnel base current under consideration of the above mentioned properties of the current contributions. The MDU model [Thottappillil et al., 1991] is a generalized version of the DU model. In the MDU model the upward return stroke speed V and the downward discharge current speed U are specified as height dependent functions: = = = z z uz v z d z z t z z V0) ( ) ( ) ( (2.8) where tu( z ) is the time required for the return stroke front to reach height z .

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43 = = = z z dz v z d z z t z z U0) ( ) ( ) ( (2.9) where td( z ) is the time required for the cu rrent wave starting at height z to reach ground. Substituting (2.8) and (2.9) for vf and c, respectively in equation (2.7) yields the current distribution in the MDU: + Š + Š = Š ŠDz V z te z U z z V z I z U z t I z V z t u t z I) ( /)) ( / ) ( / , 0 ( )) ( / , 0 ( )) ( / ( ) , ' ( (2.10) 2.5.2 Return Stroke Model Comparison and Validation The treatment of the return stroke front as either a discontinuity (BG, TCS) or as a fast rising current wave (TL, MTLL, MTLE, DU, MDU) influences the peak value of the remote fields and field derivatives. The instan taneous charge removal from the leader via the discontinuity at the return stroke front in the BG and TCS model results in a relatively high peak value for the calculated electric and magnetic field deriva tives [Nucci et al., 1990]. As mentioned above, the TCS and the BG model are physically unreasonable because of the discontinuity at the return stroke wavefront and the BG model is physically unreasonable because of the infini te speed of the current wave. The TL model is not realistic for long time field calculati ons, since no charge is removed from the channel [Nucci et al., 1990].

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44 Jordan and Uman [1983] inferred from op tical measurements that the current amplitude decreases with height and the cu rrent rise-time increas es with height. All models discussed here except the TL model are able to simulate the decrease of the current amplitude with height. Only the DU and the MDU are capable of simulating an increase of the return stroke current rise -time with height. The decomposition of the return stroke current into breakdown component and corona component is needed to achieve a significant change of rise-time with height [Diendorfer and Uman, 1990]. Two approaches for return stroke va lidation are commonl y used [Rakov and Uman, 1998]. 1) “Typical return stroke” approach Using a typical base current waveform a nd return stroke sp eed to calculate electromagnetic fields at a specified distance and comparing the results with typical fields observed at the same distance. 2) “Specific return stroke” approach Using a measured waveform and return stroke speed for the calculation of electric/magnetic field at a specified di stance and comparing the results with the electric/magnetic field measured at the same distance. The second approach is clearl y preferred over the first appr oach, since it allows a more critical evaluation of the return stroke m odel under test. Base currents can only be directly measured for triggered lightning and for natural lightning strikes to high towers, restricting the sec ond approach to these lightning types. Nucci et al. [1990] used the “typical return stroke” appr oach to compare 5 return stroke models, i.e., the TL, MTLE, TCS, BG, and MULS model. The latter model is not

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45 discussed in this section. Nucci used the capability of the model to reproduce typical features of electric and magnetic fields at 1–100 km as evaluation criteria. The results can be summarized as follows: All models were capable of reprodu cing the sharp initial peaks observed on electric and magnetic fields that vary a pproximately proportional to the inverse of distance. All models except the TL model were capable of reproducing the slow ramp following the initial peak on electric field waveforms measured within some tens of kilometers. All models except the MTLE model we re capable of reproducing the hump following the initial peak on magnetic fiel ds waveforms measured within some tens of kilometers. No model except the MTLE model was cap able of reproducing the zero crossing observed in electric and magnetic fiel ds measured within 50–200 kilometers. Figure 2-26: Calculated electric fields 50 m from the lightning channel base for six return stroke models. Thottappillil et al . [1997] applied the TL, MTLL, MTLE, TCS, BG, and DU model to calculate electric fields from a typical current waveform. The results are displayed in Figure 2-26 [Thottappillil, 1997]. All models except the TL and MTLE model were capable of reproducing the characteristic flattening of the close electric fields.

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46 Figure 2-27: Comparison of calculated and meas ured electric fields of flash 8705_1 (left) and flash 8726_2 (right). Thottappillil and Uman [1993] used the “Specific return stroke” approach on 5 return stroke models, i.e., the TL, MTLL, TCS, DU, and MDU model. Base current, return stroke speed, and electric field at 5.16 km were simultaneously measured for 18 strokes. Willett et al. [1989] used the data previously for analysis of the TL model. Two examples for comparison between calculated and measured electric field are illustrated in Figure 2-27 [Thottappillil and Uman, 1993]. Th e calculated peak electric field value showed a mean absolute error of about 20% for the TL, MTLL, DU and MDU model and 40% for the TCS model. Tho ttappillil and Uman concluded that the TL model is the preferred model for estimating peak electric fi elds from peak curren ts. More sophisticated models such as the MDU are more able to produce an overall resemblance between the calculated and measured electric fields.

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47 2.6 Measuring Lightning Produced Elect ric and Magnetic Fields and Field Derivatives The theory needed for the design of ante nnas to measure the electric and magnetic field and field derivatives is presented in th is section. Bach [1996] and Crawford [1999] derive equations that relate the measured voltage to the parameter of interest. 2.6.1 Measuring Electric Field/El ectric Field Derivative The theory for the E-field and dE/dt antenna design is described in this chapter. The E-field produced by lightning can be meas ured by using a conducti ve plate (flat plate antenna). Protruding conducting objects in the presence of a previously uniform E-field distort (enhance) the E-field [Crawford, 1999]. Therefore th e plate has to be mounted flush with the ground in order to give a result undistorted by the pres ence of the flat plate antenna. It can be inferred from Maxwell’s eq uations that the charge Q(t) induced on the plate by the ambient electric field E is pr oportional to E and the surface area A of the plate–therefore: ) ( ) (0t AE t Q = (2.11) where 0 is the permittivity of free space. Taking the time derivative of (2.11) yields dt t dE A i dt t dQant) ( ) (0= = (2.12) where the antenna current to ground iant corresponds to the rate of change with respect to time of the total charge on the antenna surface and can be regarded as the short circuit current that flows if the top plate is grounded. The antenna ci rcuit can be represented by a Norton equivalent circuit cons isting of an ideal current s ource in parallel with the characteristic capacitance Cant of the flat plate antenna as shown in Figure 2-28. This configuration is an idealized circuit since it neglects th e capacitance of the system Csys

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48 and the load resistance Rin introduced by the measuring device (e.g., oscilloscope, fiber optic transmitter). Figure 2-28: Idealized Norton equivalent circuit of a flat plate antenna. The voltage vout across the antenna output terminals is: = dt i C vant ant out1 (2.13) Substituting (2.12) in (2.13) yields: E C A dt dt dE A C vant ant out 0 01 = = (2.14) Equation (2.14) shows that vout in the idealized circuit is propo rtional to the electric field. The electric field can be determined by meas uring the voltage acro ss the antenna output terminals. The Norton equivalent circuit for the antenna circuit with a connected measuring device is depicted in Figure 2-29. Rin is the input resistance of the measuring device, Cin is the input capacitance of the measuring device, Csys is the capacitance of the system, i.e., capacitance of the cables a nd connectors between the antenna output terminals and measuring device. It will be s hown later that a relatively large capacitance is sometimes needed to integrate the current adequately. For this purpose the capacitance Cint is added to the circuit as an additional passive integrator.

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49 Figure 2-29: Norton equivalent circuit of a flat plate ante nna and connected measuring device. vout for this circuit can be desc ribed by the following equation: t outEe C A vŠ=0 (2.15) with C = Cant + Csys + Cint + Cin and = Rin C. vout is no longer proportional to the electric field but decays with time. In order to measure the electric field adequately the time in terval of interest has to be much smaller than the system decay time constant (t << ). This can be accomplished by choosing a capacitance Cin such that becomes sufficiently large. The downside of increasing C is that vout becomes smaller since the denominator in equation (2.15) becomes larger. The measurement has to be designed such that a compromise between antenna gain and system time constant is found. For the measurement of dE/dt, the capacita nce of the system has to be as low as possible. The antenna systems for a very small capacitance can be approximated as a resistive circuit with vout found from Ohms law: in ant outR i v = (2.16) Substituting equation (2.12) in (2.16) yields: dt dE AR vin out0= (2.17)

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50 Rin has to be large enough to provide a suffici ently large antenna gain in order to avoid quantization errors in the measurement of vout. Furthermore the time constant has to be much shorter than the time interval of interest (t >> ), which can be accomplished by using a small Rin. Rin has to be picked such that a compromise between these two criteria is found. 2.6.2 Measuring Magnetic Field/ Magnetic Field Derivative The theory of the B-field and dB/dt antenna design is described in this chapter. According to FaradayÂ’s Law the change of magnetic flux density passing through an open circuited wire loop induces a voltage at the terminals of the wire. The induced voltage magnitude is dt dB A vn out= (2.18) where A is the area enclosed by the wire loop and Bn is the normal component of the magnetic flux density passing through the loop. The B-field and dB/dt produced by light ning are measured with loop antennas. The loop antenna are aligned such that th e total magnetic flux pa sses normal through the loop (Btotal=Bn) assuming the lightning channel to be vertical to the ground. The loop antenna circuit is represented in Figure 2-30 by a Norton equivalent ci rcuit with the short circuit current in the fre quency domain being [Bach, 1996]: L AB L j B Aj Z v iout= = = (2.19) where Z is the impedance of the circuit and is the angular frequency.

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51 Figure 2-30: Idealized Norton equiva lent circuit of a loop antenna. The impedance of the loop antenna circuit is inductive; therefore the impedance of the circuit is larger at higher frequencies. A suffi ciently large resistor R has to be connected in series with the antenna to achieve a lin ear relationship between the measured voltage and the signal. If the resistiv e impedance is much higher than the inductive impedance for the highest frequency of intere st, the antenna circuit becomes resistive and the signal can be recorded without distortion. For determining the B-field th e antenna output has to be integrated, which can be accomplished by using passive or active integrator. The antenna circuit with additional re sistance R and capacitance Cint as a passive integrator is displayed in Figure 2-31. Figure 2-31: Norton equivalent circuit of a loop antenna and passive integrator. The decay time constant for the circuit in Figure 2-31 will be = RCint as long as R is much smaller than the input resi stance of the recorder and Cint is much larger than the capacitance of the recorder. vout in the frequency domain is [Bach, 1996]:

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52 int int1 1 C j L j R C j B Aj vout + + = (2.20) If R>>j HL and R>> int1 C jL for the highest frequency ( H) and lowest frequency ( L) of interest then equation (2.20) reduces to: intRC AB vout= (2.21) Equation (2.21) allows to determine the B-field from the measured output voltage.

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53 CHAPTER 3 EXPERIMENT SETUP AND DATA REPRESENTATION 3.1 Introduction Chapter 3 contains detailed inform ation about the FAA/NSF experiment conducted during the summer of 1999. The experi ment setup, the instrumentation used in the experiment, an outline of th e course of the experiment, and a statistical analysis of the data collected during the 1999 experiment ar e presented. Additi onally, a statistical analysis of some of the da ta collected during the 2000 F AA/NSF experiment are also given, but in less detail. 3.2 Setup of the FAA/NSF Experiment This section describes the setup of the 1999 experimental system, the instrumentation used during the 1999 experiment, and the configuration of the instruments. Additionally, we discuss the major differences between the 1999 and 2000 instrumentation. 3.2.1 Experimental System The experiment was conducted at the Inte rnational Center for Lightning Research and Testing at Camp Blanding (ICLRT) duri ng Summer 1999 and 2000. A sketch of the experimental site is found in Figure 3-1. The rocket and wire technique was used to artificially initiate lightning from natural thunderclouds (Chapter 2). The rocket launcher consiste d of six vertically aligned metallic tubes mounted on insulating fiber glass legs. The launcher was placed

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54 underground in the center of a 4 m x 4 m pit with the top of the launcher flush with the ground surface. This setup was intended to minimize the e ffect of the launcher on the measured field. A galvanized-steel rod protruding one meter above the ground surface was used as the strike object for flas hes S9901–S9918. The rod length was changed to two meters for later flashes in 1999 in orde r to increase the proba bility of lightning attachment to the rod. The pit and launcher were located at the center of a 70 m x 70 m metal-mesh grid which was covered by up to 20 cm of sand. The mesh size of the grid was 5 cm x 10 cm. The grid was designed to simulate a perfectly conducting ground in order to minimize propagation effect a nd to avoid ground surface arcing. The low frequency, low current resistance of the grid was measured to be 6 . During 1999 the underground launcher was connected via four metal straps to th e grid and the base of the launcher was connected via two metal stra ps to a 16.5 m long ground rod whose low frequency, low current resistance was measured to be 40 . A pneumatic control system operated from the SATTLIF trailer was used to fire the rockets. Electric and magnetic fields and their time derivatives were m easured with antennas located 15 m and 30 m from the launcher. The locations of the an tennas are shown in Fi gure 3-2. Figure 3-3 shows a photograph of the experimental site and of trigge red lightning S9934.

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55 Figure 3-1: Sketch of the experiment al site at Camp Blanding, 1999-2000. Figure 3-2: Strike rod in the center of the buried metal grid with electric (E) and magnetic (B) field and field derivative antennas at 15 and 30 m.

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56 Figure 3-3: A photograph of th e experimental site and tr iggered lightning S9934. The photograph was taken from th e SATTLIF trailer. 3.2.2 Instrumentation The specifications and settings of th e data acquisition system and other instruments used in the 1999 experiment are given in this section. Additionally, some comments on the 2000 system are given. 3.2.2.1 Data acquisition system 1999 The SATTLIF digitizing system cons ists of 2 LeCroy model RM9400 digital storage oscilloscopes (DSO 2-3) and 3 LeCroy model RM9400A digital storage oscilloscope (DSO 1, 4, 5). Each of these oscilloscopes has two cha nnels that could store 25 kilosamples with a sampling rate of up to 125 MHz (RM9400) and 175 MHz (RM9400A), respectively, with 8-bit vertical resolution. Additionally two rented LeCroy digital oscilloscopes (LC 1 and LC2) were us ed for the experiment. The memory in the LeCroy oscilloscopes was segmented to allo w multiple triggers during a single lightning strike. Each channel consisted of 8 segmen ts with 2501 sample points each and therefore

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57 up to 8 strokes could be captured. Table 31 lists the measured parameter, vertical resolution, sampling rate, vertical scale, sweep rate, pre-/post-trigger, and trigger level for each oscilloscope and channel. The number in the parameter column indicates the distance in meters of the antenna from the stri ke point. The parameter labeled ‘Sh’ stands for shockwave and refers to the measured ac oustic signature of light ning. The results of the shockwave measurements are not discussed in this thesis. Table 3-1: Overview of oscilloscope settings Parameter Digitizer ID Ch. Vertical Res. [Bit] Sampling Rate [MHz] Vertical Scale [V/div] Record Length [ µ s] Pre/PostTrigger Trigger I rod DSO 11850 0.250 10%±.5V ext. I screen DSO 1 2 8 50 0.2 50 10% ±.5V ext. E 15 DSO 2 1 8 25 0.2 100 50% ±.5V ext. E 30 DSO 2 2 8 25 0.2 100 50% ±.5V ext. dB/dt 30 DSO 3 1 8 50 0.2 50 30% ±.5V ext. DSO 3 2 8 50 30% ±.5V ext. B 15 DSO 4 1 8 25 0.2 100 10% ±.5V ext. B 30 DSO 4 2 8 25 0.2 100 10% ±.5V ext. Sh 30 DSO 5 1 8 0.5 0.2 5000 + 89 ms ±.5V ext. DSO 5 2 8 ±.5V ext. dI/dt LC 1 1 8 250 0.2 10 50% ±.5V ext. dE/dt 15 LC 1 2 8 250 0.2 10 50% ±.5V ext. dB/dt 15 LC 1 3 8 250 0.2 10 50% ±.5V ext. dE/dt 30 LC 1 4 8 250 0.1 10 50% ±.5V ext. Sh 15 LC 2 1 8 0.05 0.2 50000 + 5 ms ±.5V ext. LC 2 2 8 ±.5V ext. In addition to being sampled by a digita l oscilloscope, some parameters were continuously recorded on analog magnetic tape . The low bandwidth tape data provide an overview of a total event and contain inform ation about the time between strokes and parameters that were not recorded by the dig ital system due to instrument failure or due to the limited number of sampled segments. Furthermore, some low amplitude, low

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58 frequency parameters that could not be reso lved by the digital recorders (such as the background current) and features that didn’t trigger the digital recorders (e.g., ICC, continuing current, small M-Components) we re captured on tape. The Ampex PR-2230 tape recorder was operated in FM mode w ith a bandwidth from DC to 500 kHz. An interconnect diagram for the SATTLIF data acqu isition system is shown in Figures 3-4 and 3-5. A TTL-level digital pulse trigger signal was generated when the magnetic field sensor placed 15 m from the ro cket launcher measured a magnetic field that corresponded to at least 5 kA (using Ampe re’s law of magnetostatics). The TTL signal was transmitted to the external trigger input of the SA TTLIF oscilloscopes to trigger the digitizing system. The oscilloscopes for the field and cu rrent measurement had a pre-trigger,i.e., a data display prior to the trigger pulse, which ranged from –10% to – 50% of the total time displayed. The two oscilloscopes for the s hockwave measurement had a post-trigger of 5 ms and 89 ms, i.e., they displayed data starting at those times after the trigger to account for the acoustic signal propagation at the speed of sound to the acoustic sensors.

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59 Figure 3-4: Interconnect diagram of 1999 SATTLIF data acquisition system , page 1 (Courtesy G. Schnetzer).

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60 Figure 3-5: Interconnect diagram of 1999 SATTLIF data acquisition system , page 2 (Courtesy G. Schnetzer).

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61 3.2.2.2 Fiber optic system Fiber optic transmitters (FOT) converted the analog electrical signals from the antennas to optical signals and transmitted those signals via fiber optic cables to fiber optic receivers (FOR). Meret and Nanofast fi ber optic links (FOL) were used in the experiment. The bandwidth of the Meret and Nanofast FOL is DC to 35 MHz and 5 Hz to 175 MHz, respectively. The FOT were powered with 12 V DC lead-a cid batteries. RG-58 or RG-223 coaxial cables (both 50 ) connected the FOT to the antennas, which were located in metal boxes near the antennas. The FOR in the SATTLIF trailer were powered with 120 V AC UPS power. RG-58 or RG-223 coaxial cables connected the FOT to the digitizing system. The optical fibers tran smitting the signal from the FOT to the FOR were 200 µm glass, KEVLAR-reinforced, duplex cables. 3.2.2.3 Active integrator for m agnetic field measurements Active integrators designed and built by Mr. George Schnetzer, formerly of Sandia National Laboratories, and described by Crawford [1999] were used for the Bfield measurement. The schematic of the integr ator is displayed in Figure 3-6. The units for the capacitors in this figure are nF unl ess noted otherwise. The active integrator GS012497 consists of two stages. The first stag e is the integrating circuit. The second stage is a high pass filter a nd amplifier with a gain of 5 7 R R Kf= and a 3-dB point at 10 5 1 C R =. The integrator time constant is 1 4intC R = . The integrator constant for the entire assembly is 1.7*105. The typical frequency response of the integrator is shown in Figure 3-7. The active integrator is pow ered from a 12 V DC battery supplying a ± 12 V DC-to-DC converter board.

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62 C10 -1.0 C7 -27 pf C8, C9 -0.01 C6 -27 pf C4 -.01 C3 -.01 C5 -68 pf R8 -1k 5% R9 -51 ohm 2% R6 -10k trimpot R4 -150k 5% R3 -1k 5% R5 -5.1k ohm 2% R7 -51k 2% C2 -27 pf U1, U1 -National Semiconductor LH0032CG C1 -.01 R2 -3k 5% R1 -51 ohm 5% Figure 3-6: Active integrator GS012497 circuit schematic (Courtesy G. Schnetzer). Figure 3-7: Typical frequency resp onse of active integrator GS012497. 103 102 101 10 0 10 1 10 2 10 1 10 2 10 3 10 4 10 5 10 6 Frequency [Hz] Gain

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63 3.2.2.4 Optical equipment Still Camera: A Pentax SG-10 automa tic 35-mm camera located inside the SATTLIF trailer was used to phot ograph the triggered flashes. The day of the month and the time was displayed on each photograph. A wide angle 19 mm lens was used with this camera. Framing Camera: A framing camera was employ ed for relatively high speed recording of the triggered lightning events. The framing came ra is operated with a 1 ms exposure time. The camera was operated at a rate of 200 fram es/second resulting in a time resolution of 5 ms. An LED timing index flashing at a 100 Hz rate provided 10 ms timing marks for accurate timing. Video Cameras: Three video cameras were used for recording each triggered lightning events. 3.2.2.5 Instrumentation for current/cu rrent derivative measurement Six P 110A current transformers (CT) w ith a lower frequency response of 1 Hz and an upper frequency response of 20 MHz we re used to measure the current at the channel base. The current range of each sens or is from a few amperes to approximately 20 kA, when terminated with a 50 resistor. Two CTs measured the current flow to the ground rod (Figure 3-8) and f our CTs measured the current flow to the ground screen (Figure 3-9). A passive comb iner summed the two signals from the ground rod CTs to a total ground rod current and another one summed the four signals from the ground screen CTs to a total screen current. The total gr ound rod current signal and the total screen current signal were then each transmitted vi a separate Meret FOL (35 MHz bandwidth) to the SATTLIF facility. Both signals were filtered with a 20 MHz, 3 dB anti-aliasing filter

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64 before they were digitized at 50 MHz and stored in separate data files. The total current at the channel base was obtained by numeri cal summing the ground rod and the ground screen current data. Additionally, the current was measured with a current shunt located under the dI/dt sensor but not recorded. The purpose of this measurement was to trigger the digitizing system as de scribed in Section 3.2.2. dI/dt was measured with an EG&G IMM5 I-Dot sensor with an upper frequency response of 300 MHz that was mounted at the bottom of the strike rod (Figure 3-10). The dI/dt signal was transmitted via a Nanofas t FOL (175 MHz bandwid th) to the SATTLIF facility where it was filtered with a 20 MHz, 3 dB anti-aliasing filter before it was digitized at 250 MHz. Figure 3-8: Two sensors measur ing ground rod current (1999).

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65 Figure 3-9: Four sensors meas uring screen current (1999). Figure 3-10: dI/dt sensor measuring the cu rrent derivative thr ough the strike object (1999).

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66 3.2.2.6 Instrumentation for electric fi eld/field derivative measurement Flat plate antennas (0.16 m2) were used for the electri c field and electric field derivative measurement. The antennas were connected to Meret fiber optic transmitters having an input impedance of about Rin = 1 M . For the dE/dt measurement, the antenna output was terminated in 50 . For the E-field measurement at 15 m/30 m, an integrating capacitor Cint = 105 nF/Cint = 55 nF was used. The housings of the flat plate antennas were grounded by electrically connecting them to the metallic grid. Hoffman boxes containing a fiber optic transmitter, a 12 V Battery, and an integrating capacitor (E-field measurement)/terminating resist or (dE/dt measurement) were covered with metallic screens. The screens were fastened to the antennas. The function of the screen was to minimize field distortion near the antenna. Figure 3-11 shows the flat plate antenna, Hoffman box, and metallic screen used to measure dE/dt at 15 m. Meret fiber optic links with a 35 MHz ba ndwidth transmitted the signal to the digitizer from the E-field antennas at 15 m, the E-field antennas at 30 m, and the dE/dt antenna at 15 m. A Nanofast FOL was used fo r the dE/dt antenna at 30 m. The E-field at 15 m was filtered with a 10 MHz, 3 dB low pass filter before the signal was digitized at 25 MHz; the E-field at 30 m was filtered with a 20 MHz, 3 dB low pass filter before it was digitized at 25 MHz; and dE/dt signals at 15 m and 30 m were filtered with a 20 MHz, 3 dB low pass filter before th ey were digitized at 250 MHz.

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67 Figure 3-11: Flat plate antenna for dE/dt measurement with Hoffmann box covered by metallic screen. 3.2.2.7 Instrumentation for magnetic field/m agnetic field deriva tive measurement The rectangular loop antennas (Figure 312) used for the magnetic field and magnetic field derivative meas urement had an area of 0.56 m2 and 0.12 m2, respectively. An active integrator with a decay time constant = 1.5 ms was used for measuring the Bfield. Meret fiber optic links with a 35 MHz bandwidth were used to transmit the signal from the magnetic field antennas at 15 m a nd 30 m, and the magnetic field derivative antenna at 15 m and 30 m to the digitizer. The magnetic fields at 15 m and 30 m were filtered with a 10 MHz, 3 dB anti-aliasing filter before the signals were digitized at 25 MHz, and dB/dt signals at 15m and 30 m were filtered with a 20 MHz, 3 dB anti-aliasing filter before they were digitized at 250 MHz and 50 MHz, respectively.

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68 Figure 3-12: Rectangular loop antenna fo r dB/dt measurement with Hoffmann box containing fiber optic transmitter and battery. In the background are the PVC channels for the fiber optic cables. 3.2.2.8 2000 instrumentation The 2000 instrumentation will be described in detail in the thesis of V. Kodali. The three major differences between the 1999 and the 2000 instrumentation are summarized below. 1) The 2000 current at the channel base was measured simultaneously by two different methods: (a) Single sensor: Th e current was measured through a single resistive shunt attached below the strike object. (b) Multiple sensors: The strike object had one connection to the ground rod and two connections to the grounding mesh. The current to the ground rod was m easured as in 1999 and the current in the two connections to the grounding mesh was measured with current viewing resistors (CVR) resistive shunts and the resu lts stored in separate data files. In 1999, the current was measured as described in Section 3.2.2.

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69 2) In 2000 the trigger signal was generated when the current viewing resistor (CVR) installed at the strike rod base measured a current that exceeded 3.2 kA. In 1999 the trigger signal was generated when a magnetic field that corresponded to at least 5 kA was measured. 3.3 Statistical Analysis of the 1999 and 2000 Data Data obtained during the 1999 and 2000 experime nts are discussed in this section. Table 3-2 lists each triggering attempt and its result. Duri ng the 1999 campaign a total of 40 attempts to trigger classical rocket-t riggered lightning were made. Thirty-nine attempts were made in an ambient electrosta tic field of negative polarity (according to atmospheric electricity sign convention, i. e., predominantly negative charge overhead results in an ambient electric field of nega tive polarity). One trigge ring attempt was made in an ambient electrostatic field of positive polarity. Twenty attempts resulted in no trigger, seven in wireburns (initial stage of rocket-triggered lightning only, no return strokes), including the triggering in a positive field one in an altitude trigger (bottom of wire not attached to ground), and 12 in classi cal triggers that lowe red negative charge to ground. The altitude triggered flash struck ground at azimuth 82 degrees, 82 m from the strike rod. A strike rod of 1 m height was used for triggering attempts S9901–S9920. For subsequent triggering attempts a st rike rod of 2 m height was used. Table 3-3 gives an overview of the data recorded from successfully triggered lightning events during the summer of 1999. Satu rated data are labeled ‘s’, not recorded data are labeled ‘nr’, useful data are labe led ‘x’, and excluded data are labeled ‘ed’. Useful data are data for which a rise-time, a half peak width, or a peak can be measured.

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70 Table 3-2: Record of 1999 trig gering attempts and results. Date Time (Launch or first RS) Event # E static field [kV/m] Results No. of RS Remarks 26-Jun-99 18:34 S9901 -7.5 Classical Trigger4 1 m strike rod 26-Jun-99 18:49:33.3 S9902 -10 Wireburn 0 26-Jun-99 18:59:04.9 S9903 -7.7 Classical Trigger4 28-Jun-99 19:05:55 S9904 -7.8 Wireburn 0 28-Jun-99 19:13:45 S9905 -6.2 Wireburn 0 01-Jul-99 20:17:00 S9906 -5.9 No Trigger 0 04-Jul-99 16:57:14 S9907 -7.2 Classical Trigger1 04-Jul-99 17:04:44 S9908 -6.3 Wireburn 0 04-Jul-99 17:09:46 S9909 -6.8 Wireburn 0 04-Jul-99 17:13:08 S9910 -6.1 No Trigger 0 04-Jul-99 20:17:41 S9911 -7 No Trigger 0 no field break during ascent (field went more positive) 04-Jul-99 20:25:11 S9912 -8.7 Altitude Trigger ? struck ground at azimuth 82 degrees true, range 82 m from strike rod 08-Jul-99 21:06:50 S9913 -5.2 No Trigger 0 10-Jul-99 22:25:46 S9914 NR No Trigger 0 14-Jul-99 21:11:20.491 S9915 -7.1 Classical Trigger6 possible 7 return stroke according to tape record 14-Jul-99 21:18:54 S9916 -5.7 No Trigger 0 14-Jul-99 21:38:18 S9917 -7.9 No Trigger 0 14-Jul-99 21:59:21.051 S9918 -6.4 Classical Trigger6 14-Jul-99 22:15:00 S9919 -6.5 Wireburn 0 14-Jul-99 22:28:39 S9920 -8.4 Wireburn 0 08-Aug-99 23:08 S9921 -6.8 No Trigger 0 2 m strike rod 08-Aug-99 23:24 S9922 -6.2 No Trigger 0 09-Aug-99 13:47 S9923 -6 No Trigger 0 09-Aug-99 NR S9924 -6.2 No Trigger 0 16-Aug-99 21:13:33.512 S9926 -7.5 Classica l Trigger1 no high-rate digitizer data 16-Aug-99 21:14:59 S9925 -7.5 Classical Trigger1 arcing observed around base of strike rod 16-Aug-99 21:17:27 S9927 -9.7 No Trigger 0 natural lightning preemption 16-Aug-99 21:34:00 S9929 -13.5 No Trigger 0 16-Aug-99 21:37:40 S9928 -9 No Trigger 0 17-Aug-99 22:21:44.173 S9930 -7.2 Classical Trigger2 17-Aug-99 22:30:12 S9931 -7.5 No Trigger 0 spool malfunction, rocket crashed shortly after launch 17-Aug-99 22:31:35.037 S9932 -7.5 Classical Trigger6 17-Aug-99 22:38:14.082 S9933 -7.5 Classical Trigger15 times and currents may not correspond correctly on stroke table for digitizer based current estimates 17-Aug-99 22:45:26.558 S9934 -6.8 Classical Trigger8 10-Sep-99 23:30:21 S9936 -5.5 No Trigger 0 10-Sep-99 23:32:38.531 S9935 -4.5 Classical Trigger8 previously mislabeled S9936. 10-Sep-99 23:36:23 S9937 0 No Trigger 0 natural lightning preemption 10-Sep-99 23:38:04 S9938 -7.5 No Trigger 0 10-Sep-99 23:43:29 S9939 -3 No Trigger 0 natural lightning preemption 27-Sep-99 22:13:38 S9940 +7.9 No Trigger 0

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71 Table 3-3: Overview of data recorded duri ng the 1999 experiment. Legend: RS = Return Stroke, MC = M-Component, x = successfully recorded “good” data, ed = excluded data nr = not recorded, s = saturated data. Flash Number Event dE15 dE30 E 15 E30 dB15 dB30 B15 B30 dI/dt I S9901 1 RS ed ed s s x x x ed nr x 2 RS s x s s x x s s nr x 3 RS x x x x x x x x nr x 4 RS x x s s x x s s nr x S9903 1 RS s nr s s x x s s nr x 2 RS x nr x x x x x x nr x 3 RS x nr x x x x x x nr x 4 RS s nr s x x x x x nr x S9907 1 RS nr nr x x nr s x x nr ed S9915 1 RS ed ed x x ed ed x x nr x 2 RS x x x x ed ed x x nr x 3 RS x x x x ed ed x x nr ed 4 RS x x x x ed ed x x nr ed 5 MC ed ed x x ed ed x x nr ed 6 RS ed x x x ed ed x x nr ed S9918 1 RS x x x x x x x x nr ed 2 RS x x x x x x x x nr ed 3 RS x x x x x x x x nr ed 4 RS x x x x x x x x nr ed 5 RS s x x s x x x x nr ed 6 RS x x x x x x x x nr ed S9925 1 RS x x x x x ed x x nr x S9930 1 RS nr nr x s nr nr x x nr x 2 RS nr nr x x nr nr x x nr x S9932 1 RS x x x x x nr x x ed x 2 RS x x x x x nr x x ed x 3 RS s s x x x nr x x x x 4 RS s x x x x nr x x x x 5 RS s x x x x nr x x x x 6 RS s s s s x nr x x x x S9933 1 MC ed nr x x ed nr x x ed x 2 RS x nr x x x nr x x ed x 3 RS x nr x x x nr x x ed ed 4 RS x nr x x x nr x x ed ed 5 RS x nr x x x nr x x ed ed 6 RS x nr x x x nr x x ed ed 7 RS x nr x x x nr x x ed ed 8 RS x nr x x x nr x x ed ed S9934 1 RS s nr x x x nr x x x x 2 RS s nr x x x nr x x x x 3 RS s nr x x x nr x x x x 4 RS s nr x x x nr x x x x 5 RS s nr x x x nr x x x x 6 RS x nr x x x nr x x x x 7 RS x nr x x x nr x x x x 8 RS s nr x x x nr x x x x S9935 1 RS x x x ed x nr x nr ed nr 2 RS x x x ed x nr x nr ed nr 3 RS x x x ed x nr x nr ed nr 4 RS x x x ed nr nr x nr ed nr 5 RS x x x ed x nr x nr ed nr 6 RS x x x ed x nr x nr ed nr 7 RS x x x ed x nr x nr ed nr Total stroke no. 53 53 53 53 53 53 53 53 53 53 No. of saturated data 14 2 6 7 0 1 3 3 0 0 No. of not recorded data 3 23 0 0 4 31 0 7 24 7 No. of excluded data 5 3 0 7 7 7 0 1 17 17 No. of "good" data 31 25 47 39 42 14 50 42 12 29

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72 05101520 200 150 100 50 0 S9901-1 Magnetic Field at 15 m B [ µ Wb/m2] t [ µ s] Figure 3-13: Magnetic field at 15 m of stroke S9901-1. The rise-time and width could be defined several ways, whereas the peak field can be unambiguously determined. Figure 3-13 shows the magnetic field of st roke S9901-1. Although this waveform is not a typical magnetic field waveform (compare with the typical magnetic field waveform shown in Figure 2-19), the waveform is still classified as useful data since the peak can be measured (the largest peak in the waveform). The rise-time and half peak width cannot be unambiguously defined. Excluded data are data that were not included in the statistical analysis because it was not possible to determine either a rise-time, a half peak width, or a peak from the recorded waveform. Examples of excluded data are saturated data and field and current derivativ es of M-components for which the record shows essentially a flat line.

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73 The following sections contain an analys is of the data ob tained during the 1999 experiment. The data obtained during the 2000 experiment are discussed to a lesser degree and are mainly included to point out trends in the statistical distributions or yearto-year variations of the disc ussed parameters. The histograms in the following sections contain the samples sizes (denoted by the letter n), arithmetic means (denoted by the letter µ ), and the standard deviat ions (denoted by the letter ) of the data obtained during the 1999 and 2000 experiments separately as well as for all data combined. The apparent bias in the 1999 data towards larger peaks can be attribut ed to the larger triggering threshold in the measurement and to the smaller sample sizes. 3.3.1 Current In this section a sta tistical analysis of the current parameters measured during the 1999 and 2000 FAA/NSF experiments is presented. Additionally, current peaks are determined from magnetic field data recorded in 1999 using Ampere’s law and current waveforms are calculated from integrating current de rivatives measured in 1999. Figure 3-14 shows a typical current waveform recorded during the 1999 experiment on an a) 25 µ s and b) 1 µ s time scale. 3.3.1.1 1999 Experiment Table 3-4 lists values and statistics of the current data obtained during the 1999 experiment. Current peaks for 27 return stro kes in 8 flashes and 30-90% rise-times and half peak width for 26 strokes in 8 flashes were determined from directly measured current data during the 1999 experiment.

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74 I [kA] I [kA] 0 -5 -10 -15 -20 a)tHPW 50 % 0 5 10 15 20 25 0 -5 -10 -15 -20 b)t30-90%30 % 90 % 3.4 3.6 3.8 4 4.2 4.4 t [ µ s] Figure 3-14: Current record of stroke S9930-2 on an a) 25 µs and b) 1 µs timescale. Halfpeak-width and 30-90% rise-time are illu strated in a) and b), respectively. To determine current peaks from magnetic field peaks we will approximate the lightning channel as a current -carrying vertical conductor above a perfectly conducting ground with a uniform time-varying current vs. height.

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75 Applying Ampere’s Law fo r magnetostatics yields: 02µ Peak PeakB r I = where r is the horizontal distance betw een lightning channel and observer, BPeak is the magnetic flux density peak measured at distance r, and IPeak is the current peak measured at the channel base. The current peaks obtained from directly measured currents, integrating measured dI/dt, and from magnetic field measurements at 15 m and 30 m are listed in Table 3-4. Forty-nine current peaks were determined from magnetic field peaks measured at r = 15 m during the 1999 experiment. The arithm etic mean of the current peaks is 16 kA, the geometric mean is 15 kA, and the standard deviation is 7 kA. Forty-one current peaks were determined from magnetic field peaks measured at r = 30 m during the 1999 experiment. The arithme tic mean of the current peaks is 18 kA, the geometric mean is 16 kA, and th e standard deviation is 7 kA.

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76 Table 3-4: Overview of current data recorded during the 1999 experiment. Flash Event # Return Stroke Current Peak Return Stroke Current 30-90% Rise Time Return Stroke Current Half Peak Width I Peak calculated from intergrating measured dI/dt I Peak calculated from B at 15 m using Amperes law I Peak calculated from B at 30 m using Amperes law [kA] [ns] [ µ s] [kA] [kA] [kA] S9901 1 10 12 S9901 2 26 152 22.3 S9901 3 11 263 9.3 14 14 S9903 1 35 127 22.7 S9903 2 10 119 2.6 6 7 S9903 3 13 89 9.5 9 11 S9903 4 21 114 6.7 14 17 S9907 1 6 7 S9915 1 12 1304 15.8 12 13 S9915 2 16 528 13.8 16 18 S9915 3 24 26 S9915 4 17 19 S9915 5 5 6 S9915 6 13 15 S9918 1 26 25 S9918 2 15 14 S9918 3 22 21 S9918 4 16 15 S9918 5 33 32 S9918 6 11 10 S9925 1 24 230 23.5 31 31 S9930 1 36 168 14.3 29 31 S9930 2 22 182 4.9 15 17 S9932 1 19 177 19.9 18 20 S9932 2 12 200 14.7 11 12 S9932 3 26 180 15.1 31 25 26 S9932 4 20 122 4.3 24 18 19 S9932 5 17 134 10.0 19 15 16 S9932 6 28 143 5.7 34 26 27 S9933 2 13 204 7. 7 16 18 S9933 3 7 7 S9933 4 12 13 S9933 5 11 12 S9933 6 12 14 S9933 7 14 16 S9933 8 9 10 S9934 1 30 138 20.7 38 32 34 S9934 2 23 157 4.9 27 21 22 S9934 3 18 118 12.9 22 18 18 S9934 4 19 118 7.8 21 17 18 S9934 5 24 124 12.6 28 23 24 S9934 6 9 126 3.0 9 7 7 S9934 7 11 113 7.5 12 10 11 S9934 8 23 248 4.4 29 22 23 S9935 1 21 S9935 2 26 S9935 3 13 S9935 4 7 S9935 5 11 S9935 6 15 S9935 7 9 n 27 26 26 12 49 41 Minimum 9 89 2.6 9 5 6 Maximum 36 1304 23.5 38 33 34 Arithmetic Mean 19 215 11.4 24 16 18 Geometric Mean 18 171 9.5 23 15 16 Standard Deviation 8 238 6.5 9 7 7

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77 01234 30 20 10 0 S9932-3 Current 01234 20 10 0 S9932-4 Current 01234 20 10 0 S9932-5 Current 01234 20 0 S9932-6 Current 01234 40 20 0 S9934-1 Current 01234 30 20 10 0 S9934-2 Current 01234 20 10 0 S9934-3 Current 01234 20 10 0 S9934-4 Current 01234 30 20 10 0 S9934-5 Current 01234 5 0 S9934-6 Current 01234 10 5 0 S9934-7 Current 01234 30 20 10 0 S9934-8 Current Time [ µ s] Time [ µ s] Current [kA], directly measured Current [kA], integrated dI/dt Figure 3-15: Comparison of dir ectly measured current and cu rrent obtained by integrating dI/dt of event S9932 Strokes 3-6 and S9934 Strokes 1-8.

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78 Twelve current peaks were determined from integrating directly measured dI/dt waveforms obtained during the 1999 experi ment. The following integration algorithm was used: t dt n dI n I n I dt dt nT dI t I + Š = =) ( ) 1 ( ) ( ) ( ) ( for the nth sample in the current record where t is the sampling interval. The arithmetic mean of the current peaks is 25 kA, the geometric mean is 23 kA, and the standard deviation is 9 kA. The waveforms of the dir ectly measured current and current obtained by integrating dI/dt of event S9932, strokes 36, and S9934, strokes 1-8, are compared in Figure 3-15. Figure 3-16: Ratio between current peaks obtai ned from integrating dI/dt and measured current peaks plotted with respect to measured current peaks (1999). I (measured directly) [kA] 8163264 I (from dI/dt) / I (measured directly) 1.00 1.05 1.10 1.15 1.20 1.25 1.30

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79 The initial rising parts of measured a nd calculated current waveforms are very similar. The current peaks obtained from inte grating dI/dt are larger than the measured current peak of the same event; the difference becomes relative larger for larger currents. A relation between the ratio of calculated a nd the logarithm of measured current peak, and the measured current peak is shown in Figure 3-16. 3.3.1.2 2000 Experiment The current was measured with (a) a single sensor and (b) multiple sensors (both methods being described in Section 3.2.2). Some current peaks and waveforms obtained from (a) differ considerably from current pe aks of the same event obtained from (b)-an observation that motivated the following comp arison of the directly measured current data with current data obtained from other sources. Comparing the current peaks obtained from magnetic field peaks at 15 and 30 m usi ng Ampere’s law with the measured current peaks shows that the current peaks obtained from (a) are between 20% higher and 300% lower than the current peaks obtained from Ampere’s law while the current peaks obtained from (b) deviate by roughly ±30%. The current waveforms measured with method (a) of all three stroke s in event S0022 and all three strokes in event S0023 exhibit atypical flat peaks. Both ev ents were the only two successf ul triggers on July 11, 2000. Differentiating the current waveforms obtaine d from (a) and (b) of strokes S0022 and S0023 and comparing the peaks w ith the directly measured cu rrent derivatives shows that the current derivative peaks from the current data obtained with method (a) are between 30% lower and 20% higher than the directly measured current derivative peaks while the current derivative peaks from the current da ta obtained with method (b) are up to 300% higher. The current peaks of strokes S0022 and S0023 obtained from (a) are up to three times smaller than current peaks obtained from measured magnetic field peaks at 15 m

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80 and 30 m using Amperes law while the current peaks of the two strokes from (b) are only about 20% smaller. A possible interpretation of these results is that flashovers to the Pockels sensor structure or over both the current 1-m shunt and current derivative sensor occurred, although no flashovers are disc ernible in the optical records. The current data of strokes S0022 and S0023 are not considered here due to 1) an atypical waveshape, 2) the inconsistency with current data obtai ned from (b), and 3) inconsistency with current data obtained from magne tic field peaks at 15 m and 30 m. Note that the current peaks obtained from (a) before event S0022 deviates between –20% and +40% from the current peaks obtained from (b) while the peaks obtained from (a) after event S0023 deviates only between –3% and +8%. Ther efore, the currents measured with both methods are consistent for all events except S0022 and S0023 and appear more accurate for events after event S0023. The arithmetic mean of 37 current peaks in 8 flashes obtained from (b) is 14 kA, the geometric mean is 12 kA, and the standard deviation is 7 kA. The arithmetic mean of 42 current peaks in 10 flashes obtained from (a) is 13 kA, the geometric mean is 11 kA, and the standard deviation is 6 kA. 3.3.1.3 1999 and 2000 Experiment Histograms and statistics of current peaks, current half peak widths, and current 30-90% rise times are found in Figure 3-17, Fi gure 3-18, and Figure 3-19, respectively. The parameters were obtained from current data directly measured during the 1999 and 2000 experiment. The current data in the 2000 experiment used in the histogram were obtained with method (b), as described above.

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81 Figure 3-17: Distribution of return stroke cu rrent peaks obtained from directly measured current during the 1999 experiment and 2000 experiment. Figure 3-18: Distribution of return stroke current 30-90% rise times obtained from directly measured current during the 1999 expe riment and 2000 experiment. Three values at 1300 ns, 1680 ns, and 1750 ns are not shown in the histogram. The measurements are included in the statistics. Current Peak [kA] 6121824303642 Number 0 5 10 15 20 25 1999 n = 27 µ = 19.5 kA = 7.7 kA 2000 n = 37 µ = 13.8 kA = 6.7 kA 1999 and 2000 n = 64 µ = 16.2 kA = 7.6 kA Current 30-90 % Rise Time [ns] 80160240320400480560640720 Number 0 3 6 9 12 15 18 21 24 27 1999 n = 26 µ = 215 ns = 238 ns 2000 n = 39 µ = 290 ns = 359 ns 1999 and 2000 n = 65 µ = 260 ns = 316 ns

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82 Figure 3-19: Distribution of return stroke curr ent half peak widths obtained from directly measured current during the 1999 experiment and 2000 experiment. 3.3.2 Current Derivative In this section a statistical analysis of the current derivative data measured during the 1999 and 2000 FAA/NSF experiment is presen ted. Additionally, current derivative waveforms are calculated from differenti ating currents measured in 1999. Figure 3-20 shows the current derivative waveform of str oke S9934-1 (the largest directly measured current derivative in 1999) on an a) 1 µs and b) 0.15 µs time scale. 3.3.2.1 1999 Experiment Table 3-5 lists values and statistics of the dI/dt peaks obtained during the 1999 experiment. dI/dt peak values for 12 return strokes in 2 flashes (S9932 and S9934) were determined from directly measured current derivative data obtained during the 1999 experiment. Current Half Peak Width [ µ s] 510152025303540 Number 0 3 6 9 12 15 18 1999 n = 26 µ = 11 µ s = 6 µ s 2000 n = 38 µ = 14 µ s = 10 µ s 1999 and 2000 n = 64 µ = 13 µ s = 9 µ s

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83 Table 3-5: Overview of dI/dt data recorded during the 1999 experiment. Flash Event # Return Stroke dI/dt Peak Return Stroke dI/dt 30-90% Rise Time Return Stroke dI/dt Half Peak Width dI/dt Peak calculated from differentiating I [kA/ µ s] [ns] [ns] [kA/ µ s] S9901 1 130 S9901 2 204 S9901 3 100 S9903 1 292 S9903 2 94 S9903 3 138 S9903 4 243 S9925 1 128 S9930 1 193 S9930 2 121 S9932 1 113 S9932 2 81 S9932 3 173 144 S9932 4 189 172 S9932 5 143 45 115 149 S9932 6 206 35 112 172 S9933 2 91 S9934 1 270 29 124 256 S9934 2 137 107 S9934 3 205 35 87 206 S9934 4 204 40 88 186 S9934 5 263 27 88 234 S9934 6 79 38 97 89 S9934 7 99 25 102 101 S9934 8 141 122 n 12 8 8 25 Minimum 79 25 87 81 Maximum 270 45 124 292 Arithmetic Mean 176 34 102 155 Geometric Mean 166 34 101 145 Standard Deviation 59 7 14 59

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84 Figure 3-20: dI/dt r ecord of stroke S9934-1 on an a) 1 µs and b) 0.15 µs timescale. Halfpeak-width and 30-90% rise-time are illu strated in a) and b), respectively. dI/dt [kA/ µ s] 0 -100 -200 -300 a)tHPW dI/dt [kA/ µ s] 50 % 0 0.2 0.4 0.6 0.8 1 0 -100 -200 -300 b)t30-90% 30 % 90 % 0.3 0.32 0.34 0.36 0.38 0.4 4.2 0.44 t [ µ s]

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85 00.20.40.60.81 200 100 0 S9932-3 dI/dt 00.20.40.60.81 200 100 0 S9932-4 dI/dt 00.20.40.60.81 150 100 50 0 50 S9932-5 dI/dt 00.20.40.60.81 200 100 0 S9932-6 dI/dt 00.20.40.60.81 300 200 100 0 S9934-1 dI/dt 00.20.40.60.81 150 100 50 0 S9934-2 dI/dt 00.20.40.60.81 200 100 0 S9934-3 dI/dt 00.20.40.60.81 200 100 0 S9934-4 dI/dt 00.20.40.60.81 300 200 100 0 S9934-5 dI/dt 00.20.40.60.81 100 50 0 S9934-6 dI/dt 00.20.40.60.81 100 50 0 50 S9934-7 dI/dt 00.20.40.60.81 100 0 S9934-8 dI/dt Time [ µ s] Time [ µ s] dI/dt [kA/µs], directly measured dI/dt [kA/µs], differentiated I Figure 3-21: Comparison of dir ectly measured dI/dt and dI/d t obtained by differentiating I of event S9932 Strokes 3-6 and S9934 Strokes 1-8.

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86 The arithmetic mean of the dI/dt peaks is 176 kA/µs, the geometric mean is 166 kA/µs, and the standard deviation is 59 kA/µs. The largest directly measured dI/dt value was 270 kA/µs. Twenty-five dI/dt peaks were determined from differentiating directly measured current waveforms obtained during the 1999 experiment. The differentiation of the current record was performed by cubic spline interpolating the data and using the build-in differentiation function in the Math cad 2001 software. No additional filtering was performed on the data, resu lting in a high noise level in the differentiated data. The arithmetic mean of the dI/dt peaks obtained from differentiating the current waveforms is 155 kA/µs, the geometric mean is 145 kA/µs, and the standard deviation is 59 kA/µs. The waveforms of the directly measured dI/dt a nd dI/dt obtained by diffe rentiating the current of event S9932, stroke 3-6, and S9934, str oke 1-8, are compared in Figure 3-21. 3.3.2.2 2000 Experiment The peaks from differentiated current m easured with a single resistive shunt (method (a) described in Section 3.3.1) are on average 10% larger (30 values) than the directly measured current derivative peak s while the peaks from differentiated current measured with multiple sensors (method (b) de scribed in Section 3.3.1) are on average 90% larger (24 values). dI/dt peak values for 39 return strokes were determined from directly measured current derivative da ta obtained during the 2000 experiment. The arithmetic mean of th e dI/dt peaks is 88 kA/µs, the geometric mean is 73 kA/µs, and the standard deviation is 50 kA/µs. The largest directly measured dI/dt value was 221 kA/µs. 3.3.2.3 1999 and 2000 Experiment Histograms and statistics of current derivative peaks, current derivative 30-90% rise times, and current derivative half peak widths are found in Figure 3-22, Figure 3-23,

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87 and Figure 3-24, respectively. The paramete rs from the 1999 experiment were obtained from directly measured current derivative data and differentiate d current data. The parameters from the 2000 experiment were obtained from directly measured current derivative data only using met hod (b), as described above. Figure 3-22: Distribution of dI/dt peaks from the 1999 and 2000 experiment. The dI/dt peaks from the 1999 experiment were obtai ned from directly measured current derivatives and differentiated current. The dI/dt peaks from the 2000 experiment were obtained from directly measur ed current derivatives only. dI/dt Peak [kA/ µ s] 4080120160200240280320 Number 0 3 6 9 12 15 18 1999 n = 25 µ = 148 kA/ µ s = 65 kA/ µ s 2000 n = 39 µ = 88 kA/ µ s = 50 kA/ µ s 1999 and 2000 n = 64 µ = 117 kA/ µ s = 65 kA/ µ s

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88 Figure 3-23: Distribution of dI/dt 30-90% rise times from the 1999 and 2000 experiment. Figure 3-24: Distribution of dI/dt half p eak widths from the 1999 and 2000 experiment dI/dt Half Peak Width [ns] 20406080100120140160 Number 0 2 4 6 8 10 12 1999 n = 8 µ = 102 ns = 14 ns 2000 n = 21 µ = 88 ns = 27 ns 1999 and 2000 n = 29 µ = 92 ns = 25 ns dI/dt 30-90 % Rise Time [ns] 10203040506070 Number 0 2 4 6 8 10 12 14 1999 n = 8 µ = 34 ns = 7 ns 2000 n = 21 µ = 32 ns = 15 ns 1999 and 2000 n = 29 µ = 32 ns = 13 ns

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89 3.3.3 Electric Field Change at 15 m and 30 m The electric field change E is defined as the difference between the E-field after and the E-field before the even t that causes the field change: initial finalE E E Š = The leader electric field change, EL, is the field change at ground level due to the descending leader. The leader lowers ne gative charge; therefore according to the atmospheric electricity sign convention the polarity of EL at close range is negative. The return stroke electric field change, ERS, is the field change at ground level due to the ascending return stroke. The retu rn stroke removes all or some of the negative charge previously deposited by the leader. The polarity of ERS is positive, according to the atmospheric electricity sign convention. EL and ERS are illustrated in Figure 3-25 a). The zero value was arbitrarily assigned to the first data point in a 50 µ s record with a 25 µ s pre-trigger. The leader E-field change wa s determined as the difference between the E-field value at the beginning of the record and peak; the return stroke E-field change is the difference between peak and the field valu e at which the E-field waveform flattens. Determining the latter value sometimes invol ves subjective judgment which therefore introduces some variation (error) in the measurement. This variation is usually very small compared to the field variation during the steep return stroke field change and can essentially always be neglected. The width of the electric field pulse, tHPW, was measured at 0.5*EL, as illustrated in Figure 3-25 b). Values and statistics of EL, ERS, and of tHPW at 15 m and 30 m are presented in this section. Both EL and ERS are included in the tables, while histograms are shown for ERS only since EL and ERS are usually similar.

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90 Figure 3-25: Electric field at 15 m of stroke S9925-1 on an a) 50 µs and b) 7 µs timescale. The electric field change due to the leader, ELeader, and electric field change due to the return stroke, EReturn Stroke, are illustrated in a). The width of the electric field pulse, tHPW, was measured at 0.5*ELeader, as illustrated in b). a) 0 -100 -200 -300 -400 E [kV/m] ELeader EReturn Stroke 0 10 20 30 40 50 b) 0 -100 -200 -300 -400 E [kV/m] tHPW 50 %20 21 22 23 24 25 26 27 t [ µ s]

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91 3.3.3.1 1999 Experiment Table 3-6 lists values and statistics of EL, ERS, and tHPW at two distances, 15 m and 30 m, studied during the 1999 experiment. EL was measured 15 m from the strike poi nt for 45 leaders in 11 flashes during the 1999 experiment. The arithmetic mean is 127 kV/m, the geometric mean is 117 kV/m, and the standard deviation is 52 kV/m. ERS values were measured 15 m from the strike point for 45 return str okes in 11 flashes during the 1999 experiment. The arithmetic mean is 115 kV/m, the geometric mean is 108 kV/m, and the standard deviation is 40 kV/m. Six values for EL at 15 m and ERS at 15 m that saturated between 100 and 190 kV/m are not included in the statistic. EL values were measured 30 m from the strike point for 38 leaders in 10 flashes during the 1999 experiment. The arithmetic mean is 65 kV/m, the geometric mean is 61 kV/m, and the standard deviation is 24 kV/m. ERS values measured 30 m from the strike point fo r 38 return strokes in 10 flashes during the 1999 experiment. The arithmetic mean is 64 kV/m, the geometric mean is 61 V/m, and the standard deviation is 21 kV/m. Six values for EL at 30 m and ERS at 30 m saturated between 50 and 100 kV/m are not included in the statistic. The mean ratio between EL at 15 m (30 m) and ERS at 15 m (30 m) is -1.1 (-1.01) with a standard deviation of 0.07 (0.07). Rubinstein et al. [199 5] measured the electric fiel d of two strokes at 30 m and found a leader field–return stroke field ratio of 1 and 0.8. The ratio between EL at 15 m (ERS at 15 m) and EL at 30 m (ERS at 30 m) is 1.95 (1.81) on average with a standard deviation of 0.17 (0.14); therefore EL and ERS for close fields are roughly inverse distance dependent. An inverse distance dependen ce of close leader field change was also

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92 generally observed by Crawford et al. [2001] and implies a uniform charge distribution on the lower leader channel. 3.3.3.2 2000 Experiment ERS was measured 15 m from the strike poi nt for 41 return strokes in 9 flashes during the 2000 experiment. The arithmetic m ean is 93 kV/m, the geometric mean is 84 kV/m, and the standard deviation is 40 kV/m. ERS was measured 30 m from the strike point for 48 return strokes in 11 flashes dur ing the 2000 experiment. The arithmetic mean is 57 kV/m, the geometric mean is 51 kV/m , and the standard deviation is 24 kV/m. 3.3.3.3 1999 and 2000 Experiment The combined distribution of ERS at 15 m and 30 m during the 1999 and 2000 experiment is displayed in Figure 3-26 and Figure 3-27, respectively. The overall distribution of the 15 m data resembles a l og normal distribution, the overall distribution of the 30 m data resembles a normal distribution. The distribution of the half peak widths of the leader-return stroke electric field pul se at 15 and 30 m is shown in Figure 3-28 and Figure 3-29, respectively. Both distributions resemble a chi-square distribution. The distribution of the ratio between ERS at 15 m and 30 m from the 1999 experiment and the distribution of the E-fiel d ratios obtained during the 2000 experiment shown in Figure 3-30 both resemble a normal distribution. Th e normal distribution for the 1999 data and the 2000 data are slightly shifted, which might indicate that the ca libration factors used for the 1999 and 2000 data were inconsistent. The mean ratio of the 1999 is 1.8 and the standard deviation is 0.14. The mean rati o of the 2000 data is 1.7 and the standard deviation is 0.13. A statistic al test assuming normal distribution and equal variances of the 1999 data and 2000 data sets shows that th e means are significantl y different at the p

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93 = 0.1% level. This result shows that th e calibration factors us ed in 1999 and 2000 are inconsistent. It is not clear which calibration factor is the most accurate. Table 3-6: Electric field data recorded dur ing the 1999 experiment. The negative signs for EL and EL/ERS are omitted. Flash Event # EL 15 m ERS 15 m tHPW 15 m EL 30 m ERS 30 m tHPW 30 m EL/ ERS 15m EL/ ERS 30m EL 15m / EL 30m ERS 15m / ERS 30m [kV/m][kV/m] [ µ s] [kV/m] [kV/m] [ µ s] S9901 3 107 108 1.83 60 63 3. 52 1.00 0.95 1.78 1.70 S9903 2 64 65 3.98 31 35 8. 23 0.98 0.89 2.07 1.87 S9903 3 86 80 1.32 45 45 2. 60 1.08 1.01 1.92 1.79 S9903 4 71 69 4.08 1.03 S9907 1 59 61 5.32 32 36 8. 51 0.96 0.88 1.84 1.69 S9915 1 58 61 8.19 39 44 10. 19 0.94 0.88 1.48 1.39 S9915 2 98 93 1.78 58 58 2. 80 1.05 1.01 1.69 1.62 S9915 3 164 139 1.26 85 78 2. 03 1.18 1.09 1.92 1.78 S9915 4 113 104 1.15 61 59 1. 98 1.09 1.03 1.87 1.76 S9915 6 74 74 2.28 48 49 3. 75 1.00 0.97 1.54 1.49 S9918 1 165 146 0.85 87 83 1. 43 1.13 1.06 1.90 1.77 S9918 2 102 99 1.15 56 56 1. 98 1.03 0.99 1.83 1.76 S9918 3 210 178 1.86 98 91 3. 62 1.18 1.08 2.14 1.97 S9918 4 154 140 1.76 69 67 3. 82 1.10 1.03 2.23 2.08 S9918 5 246 197 0.99 6.13 1.25 S9918 6 117 114 2.57 49 52 1. 47 1.02 0.95 2.39 2.21 S9925 1 191 164 0.87 103 94 1.17 1.09 1.86 1.74 S9930 1 238 196 3.29 1.21 S9930 2 127 120 3.92 62 65 8. 13 1.05 0.96 2.03 1.86 S9932 1 152 133 1.13 79 73 2. 17 1.14 1.08 1.92 1.81 S9932 2 90 88 1.49 48 49 3. 08 1.03 0.98 1.87 1.78 S9932 3 202 171 1.32 107 97 2. 53 1.18 1.10 1.90 1.77 S9932 4 174 156 3.07 85 83 6. 23 1.12 1.02 2.06 1.88 S9932 5 141 127 1.71 73 70 2. 98 1.11 1.05 1.93 1.82 S9933 2 104 97 1.27 56 57 2. 12 1.07 0.99 1.84 1.70 S9933 3 54 54 1.83 28 29 3. 50 1.00 0.96 1.92 1.84 S9933 4 98 92 1.26 47 48 2. 41 1.07 0.98 2.09 1.92 S9933 5 89 84 1.39 45 45 2. 60 1.06 1.01 1.97 1.87 S9933 6 94 87 1.16 50 49 2. 15 1.09 1.03 1.89 1.79 S9933 7 113 103 1.34 59 57 2. 47 1.10 1.03 1.91 1.79 S9933 8 80 79 2.95 40 42 5. 58 1.02 0.94 2.02 1.86 S9934 1 199 164 0.82 110 96 1. 36 1.22 1.14 1.82 1.70 S9934 2 190 170 3.48 88 90 7. 09 1.12 0.98 2.15 1.88 S9934 3 139 124 1.16 71 67 2. 21 1.12 1.06 1.96 1.85 S9934 4 146 132 1.37 71 69 2. 89 1.11 1.04 2.04 1.91 S9934 5 175 153 1.13 88 82 2. 15 1.14 1.07 1.98 1.87 S9934 6 63 65 2.47 31 34 4. 81 0.98 0.92 2.05 1.92 S9934 7 80 78 1.23 40 42 2. 39 1.02 0.95 2.00 1.86 S9934 8 202 184 5.28 92 100 10. 13 1.10 0.92 2.19 1.85 S9935 1 151 130 1.17 1.16 S9935 2 154 136 0.85 1.13 S9935 3 100 92 1.41 1.08 S9935 4 58 61 5.95 0.95 S9935 5 88 85 1.50 1.03 S9935 6 129 116 1.74 1.11 S9935 7 71 70 2.38 1.01 n 45 45 45 37 37 37 45 37 36 36 Minimum 54 54 0.82 28 29 1.36 0.94 0.88 1.48 1.39 Maximum 246 197 8.19 110 100 10.19 1.25 1.14 2.39 2.21 Arithmetic Mean 127 115 2.14 64 63 3.92 1.08 1.00 1.94 1.81 Geometric Mean 117 108 1.78 60 60 3.33 1.08 1.00 1.94 1.80 Standard Deviation 52 40 1. 55 23 20 2.48 0.07 0.06 0.17 0.14

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94 Figure 3-26: Distribution of return stroke el ectric field change peaks measured at 15 m during the 1999 experiment and 2000 experiment. Figure 3-27: Distribution of return stroke el ectric field change peaks measured at 30 m during the 1999 experiment and 2000 experiment. E at 15 m [kV/m] 0306090120150180210 Number 0 5 10 15 20 25 30 1999 n = 45 µ = 114.9 kV/m = 40.1 kV/m 2000 n = 41 µ = 93.3 kV/m = 39.5 kV/m 1999 and 2000 n = 86 µ = 104.6 kV/m = 41.0 kV/m E at 30 m [kV/m] 20406080100120 Number 0 5 10 15 20 25 30 35 1999 n = 38 µ = 63.8 kV/m = 20.6 kV/m 2000 n = 48 µ = 57.0 kV/m = 24.4 kV/m 1999 and 2000 n = 86 µ = 60.0 kV/m = 22.9 kV/m

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95 Figure 3-28: Distribution of the leader-return stroke electric field half peak widths measured at 15 m during the 1999 experiment and 2000 experiment. Figure 3-29: Distribution of the leader-return stroke electric field half peak widths measured at 30 m during the 1999 experiment and 2000 experiment. Electric Field Half Peak Width at 15 m [ µ s] 12345678910111213 Number 0 5 10 15 20 25 30 35 40 45 1999 n = 45 µ = 2.1 µ s = 1.6 µ s 2000 n = 42 µ = 2.6 µ s = 2.4 µ s 1999 and 2000 n = 87 µ = 2.3 µ s = 2.0 µ s Electric Field Half Peak Width at 30 m [ µ s] 1234567891011121314 Number 0 3 6 9 12 15 18 21 24 1999 n = 37 µ = 3.9 µ s = 2.5 µ s 2000 n = 47 µ = 4.4 µ s = 3.0 µ s 1999 and 2000 n = 84 µ = 4.2 µ s = 2.8 µ s

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96 Figure 3-30: Distribution of th e ratio between return stroke electric field change peaks measured at 15 m and 30 m dur ing the 1999 and 2000 experiment. 3.3.4 Electric Field Derivative at 15 m and 30 m The electric field derivative measured at close distance typically exhibits a negative excursion due to the descending lead er followed by a positive excursion due to the ascending return stroke. Figure 3-31 show s a typical dE/dt waveform measured in 1999 on an a) 4 µs time scale and b) 0.5 µs time scale. As shown in Figure 3-31 the time immediately following the sharp rise was chosen to determine t30-90% if the waveform was roughly flat when the actual peak value wa s obtained, since this approach provides physically more meaningful information about th e rise-time. In this section a statistical analysis of the dE/dt peak values meas ured at 15 m and 30 m during the 1999 and 2000 experiment is presented. Additionally, return stro ke 30-90% rise-times, t30-90%, and half E at 15 m / E at 30 m 1.41.51.61.71.81.92.02.12.22.3 Number 0 3 6 9 12 15 18 21 24 27 1999 n = 36 µ = 1.81 = 0.14 2000 n = 41 µ = 1.71 = 0.13 1999 and 2000 n = 77 µ = 1.76 = 0.15

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97 peak widths, thpw, of dE/dt measured at 15 m and 30 m during the 1999 experiment are shown in Table 3-7. Figure 3-31: dE/dt at 15 m of stroke S9932-1 on an a) 4 µs and b) 0.5 µs timescale. Halfpeak-width and 30-90% rise-time are illu strated in a) and b), respectively. dE/dt [kV/m/ µ s] t [ µ s] 1.9 2 2.1 2.2 2.3 2.4 t30-90% 0 % 30 % dE/dt [kV/m/ µ s] 90 % b) 300 200 100 0 -100 100 % 0 1 2 3 4 tHPW 0 % 50 % 100 %a) 300 200 100 0 -100

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98 3.3.4.1 1999 Experiment Return stroke dE/dt peaks were measured 15 m from the strike point for 32 return strokes in 9 flashes during the 1999 experime nt. The arithmetic mean is 303 kV/m/µs, the geometric mean is 276 kV/m/µs, and the standard deviation is 109 kV/m/µs. Return stroke dE/dt peaks were measured 30 m from the strike point for 25 return strokes in 6 flashes during 1999 experiment. The arithmetic mean is 100 kV/m/µs, the geometric mean is 87 kV/m/µs, and the standard deviation is 46 kV/m/µs. The arithmetic mean of the ratio between 21 return stroke dE/dt p eaks simultaneously measured at 15 m and 30 m is 3.05, the geometric mean is 3.02, and the standard deviation is 0.44. It can be inferred that the distance re lation between the dE/dt peak s at 15 m and at 30 m is r-1.6 on average. This observation is in contrast to th e result of similar analysis of data found in Uman et al. [2000]. The arithmetic mean of th e ratio between 5 return stroke dE/dt peaks simultaneously measured at 10 m and 30 m is 1. 77, resulting in a distance relation of r-0.5 on average. The difference between the dist ance relation calculated from the 1999 data and the distance relation calculated from data found in Uman et al. [2000] is likely due to irregularities in their 10 m dE/dt measuremen t, perhaps due to local ground arcing, the narrower system bandwidth used at that distan ce, a system calibration error, or the effects of the relatively high strike objec t [Uman 2001, private communication].

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99 3.3.4.2 2000 Experiment Return stroke dE/dt peaks were measured 15 m from the strike point for 48 return strokes in 12 flashes during 2000 experime nt. The arithmetic mean is 319 kV/m/µs, the geometric mean is 271 kV/m/µs, and the standard deviation is 158 kV/m/µs. Return stroke dE/dt peaks were measured 30 m from th e strike point for 39 re turn strokes in 10 flashes during the 2000 experiment. The arithmetic mean is 118 kV/m/µs, the geometric mean is 101 kV/m/µs, and the standard deviation is 57 kV/m/µs. The arithmetic mean of the ratio between 39 return stroke dE/dt p eaks simultaneously measured at 15 m and 30 m is 2.81, the geometric mean is 2.79, and the standard deviation is 0.3. It can be inferred that the distance relation between dE/dt peak s at 15 m and dE/dt peaks at 30 m is r-1.5 on average. This result is similar to the distance relation found in the 1999 dE/dt data (r-1.6), thus supporting the validity of 1999 data and further questioning the validity of the r-0.5 distance dependence of the 10 m and 30 m dE /dt data found in Uman et al. [2000] 3.3.4.3 1999 and 2000 Experiment Histograms and statistics of return stroke dE/dt peaks at 15 and 30 m, dE/dt 3090% rise times at 15 and 30 m, and dE/dt ha lf peak widths at 15 and 30 m are found in Figure 3-32, Figure 3-33, Figure 3-34, Figur e 3-35, Figure 3-36, and Figure 3-37, respectively. The parameters were obtained fr om dE/dt data directly measured during the 1999 and 2000 experiment. The distribution of the ratio between dE/dt peaks measured at 15 m and 30 m during the 1999 and 2000 expe riment is shown in Figure 3-38.

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100 Table 3-7: dE/dt data recorded at 15 m a nd 30 m during the 1999 e xperiment. Data and statistics for return stroke peaks, return str oke 30-90% rise-times, return stroke half peak widths, and the ratio between return stroke peaks at 15 m and 30 m are shown. Flash Event # Leader dE/dt Peak at 15 m Return Stroke dE/dt Peak at 15 m Return Stroke dE/dt 30/90 Rise Time at 15 m Return Stroke dE/dt HPW at 15 m Leader dE/dt Peak at 30 m Return Stroke dE/dt Peak at 30 m Return Stroke dE/dt 30/90 Rise Time at 30 m Return Stroke dE/dt HPW at 30 m [kV/m/ µ s] [kV/m/ µ s] [ns] [ns] [kV/m/ µ s] [kV/m/ µ s] [ns] [ns] S9901 2 422 27 248 28 150 31 215 S9901 3 35 169 26 322 57 36 354 S9901 4 67 291 482 95 S9903 2 22 343 30 155 S9903 3 62 414 41 151 S9903 4 77 S9915 2 21 68 209 876 4 30 237 899 S9915 3 53 156 10 63 S9915 4 32 196 42 207 6 75 52 253 S9915 6 250 749 3 24 247 883 S9918 1 451 278 32 141 293 S9918 2 78 235 19 303 12 80 21 352 S9918 3 83 498 291 10 143 82 356 S9918 4 68 436 104 227 6 121 121 261 S9918 5 37 178 47 346 S9918 6 34 370 72 209 3 97 81 215 S9925 1 170 291 348 27 98 44 361 S9932 1 422 76 333 24 113 79 401 S9932 2 78 308 43 290 8 82 57 349 S9932 3 27 S9932 4 76 185 S9932 5 109 11 158 330 260 S9932 6 97 9 S9933 2 90 270 337 S9933 3 28 183 20 255 S9933 4 75 378 25 198 S9933 5 65 332 35 214 S9933 6 93 374 18 207 S9933 7 101 357 26 270 S9933 8 38 308 54 232 S9934 2 60 S9934 3 123 S9934 4 90 S9934 5 170 S9934 6 26 307 29 170 S9934 7 63 355 24 192 S9934 8 67 S9935 1 128 321 330 23 104 358 S9935 2 183 385 19 275 36 152 39 249 S9935 3 71 284 63 249 13 92 66 257 S9935 4 60 23 S9935 5 56 238 68 270 9 77 72 283 S9935 6 74 321 49 271 15 104 45 282 S9935 7 32 144 374 6 50 441 n 37 32 24 31 23 25 18 21 Minimum 21 60 18 151 3 23 21 215 Maximum 183 498 250 876 37 185 330 899 Arithmetic Mean 76 303 57 300 16 100 94 365 Geometric Mean 66 276 42 276 12 87 70 336 Standard Deviation 40 108 58 154 11 46 87 185

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101 Figure 3-32: Distribution of return stroke electric field deriva tive peaks measured at 15 m during the 1999 experiment and 2000 experiment. Figure 3-33: Distribution of return stroke electric field deriva tive peaks measured at 30 m during the 1999 experiment and 2000 experiment. dE/dt Peak at 15 m [kV/m/ µ s] 125250375500625750 Number 0 5 10 15 20 25 30 35 1999 n = 32 µ = 303 kV/m/ µ s = 108 kV/m/ µ s 2000 n = 48 µ = 319 kV/m/ µ s = 158 kV/m/ µ s 1999 and 2000 n = 80 µ = 313 kV/m/ µ s = 140 kV/m/ µ s dE/dt Peak at 30 m [kV/m/ µ s] 4080120160200240 Number 0 5 10 15 20 25 1999 n = 25 µ = 100 kV/m/ µ s = 46 kV/m/ µ s 2000 n = 39 µ = 118 kV/m/ µ s = 57 kV/m/ µ s 1999 and 2000 n = 64 µ = 111 kV/m/ µ s = 53 kV/m/ µ s

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102 Figure 3-34: Distribution of return stroke el ectric field derivative 30-90% rise times measured at 15 m during the 1999 experiment and 2000 experiment. Figure 3-35: Distribution of return stroke el ectric field derivative 30-90% rise times measured at 30 m during the 1999 experiment and 2000 experiment. dE/dt 30-90 % Rise Time at 15 m [ns] 153045607590105120135150 Number 0 2 4 6 8 10 12 14 16 18 20 22 24 26 1999 n = 24 µ = 57 ns = 58 ns 2000 n = 33 µ = 38 ns = 30 ns 1999 and 2000 n = 57 µ = 46 ns = 44 ns dE/dt 30-90 % Rise Time at 30 m [ns] 20406080100120140160 Number 0 2 4 6 8 10 12 14 16 1999 n = 18 µ = 94 ns = 87 ns 2000 n = 21 µ = 50 ns = 57 ns 1999 and 2000 n = 39 µ = 70 ns = 75 ns

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103 Figure 3-36: Distribution of return stroke el ectric field derivative half peak widths measured at 15 m during the 1999 experiment and 2000 experiment. The data contain 2 values at 750 ns and 880 ns that are not in cluded in the histogram. The measurements are included in the statistics. Figure 3-37: Distribution of return stroke el ectric field derivative half peak widths measured at 30 m during the 1999 experiment and 2000 experiment. The data contain 2 values at 880 ns and 900 ns that are not in cluded in the histogram. The measurements are included in the statistics. dE/dt Half Peak Width at 15 m [ns] 60120180240300360420480540 Number 0 3 6 9 12 15 18 21 24 1999 n = 31 µ = 300 ns = 154 ns 2000 n = 42 µ = 216 ns = 80 ns 1999 and 2000 n = 73 µ = 252 ns = 124 ns dE/dt Half Peak Width at 30 m [ns] 120180240300360420480540 Number 0 2 4 6 8 10 12 14 16 18 20 1999 n = 21 µ = 365 ns = 185 ns 2000 n = 28 µ = 284 ns = 128 ns 1999 and 2000 n = 49 µ = 319 ns = 159 ns

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104 Figure 3-38: Distribution of the ratio between return stroke dE/dt peaks measured at 15 m and 30 m during the 1999 and 2000 experiment. 3.3.5 Magnetic Field at 15 m and 30 m Figure 3-39 shows a typical magnetic fiel d waveform measured at 15 m during the 1999 experiment on an a) 25 µs time scale and b) 1.5 µs time scale. A statistical analysis of the magnetic field peaks m easured at 15 m and 30 m during the 1999 and 2000 FAA/NSF experiment is presented in this section. Additionally, the 30-90% risetime, t30-90%, and half peak width tHPW of the magnetic field deri vatives measured at 15 m and 30 m during the 1999 experiment are shown in Table 3-8. dE/dt Peak at 15 m / dE/dt Peak at 30 m 1.92.22.52.83.13.43.74.0 Number 0 5 10 15 20 25 30 1999 n = 21 µ = 3.05 = 0.44 2000 n = 39 µ = 2.81 = 0.30 1999 and 2000 n = 60 µ = 2.90 = 0.37

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105 Figure 3-39: Magnetic field at 15 m of stroke S9918-3 on an a) 25 µs and b) 1.5 µs timescale. Half-peak-width and 30-90% rise-time are illustrated in a) and b), respectively. 0 -100 -200 -300 a)tHPW B [µWb/m2] 50 % 0 5 10 15 20 25 0 -100 -200 -300 b)t30-90% B [µWb/m2] 30 % 90 % 4.6 4.8 5 5.2 5.4 5.6 5.8 6 t [ µ s]

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106 3.3.5.1 1999 Experiment Table 3-8 lists values and st atistics of the B-field at two distances obtained during the 1999 experiment. B-fields measured 15 m fr om the strike point for 48 return strokes in 11 flashes were obtained during the 1999 experiment. The arithmetic mean of the peaks is 219 µWb/m2, the geometric mean is 199 µWb/m2, and the standard deviation is 94 µWb/m2. Peaks from three B-field waveforms saturated at 366 µWb/m2 are not included in the statistics. B-fields were meas ured 30 m from the strike point for 40 return strokes in 10 flashes during the 1999 experiment . The arithmetic mean of the peaks is 119 µWb/m2, the geometric mean is 109 µWb/m2, and the standard deviation is 48 µWb/m2. Peaks from three B-field waveforms saturated at 176 µWb/m2 are not included in the statistics. The mean ratio between 40 B-field peaks simultaneously measured at 15 m and 30 m is 1.87 with a standard deviation of 0.14. 3.3.5.2 2000 Experiment B-fields measured 15 m from the strike point for 45 return strokes in 11 flashes were obtained during the 2000 e xperiment. The arithmetic mean of the peaks is 186 µWb/m2, the geometric mean is 165 µWb/m2, and the standard deviation is 94 µWb/m2. Peaks from three B-field wave forms that saturated at 150 µWb/m2 and 1 B-field waveform saturated at 490 µWb/m2 are not included in the statistic. B-fields measured 30 m from the strike point for 48 return stroke s in 11 flashes were obtained during the 2000 experiment. The arithmetic mean of the peaks is 101 µWb/m2, the geometric mean is 89 µWb/m2, and the standard deviation is 51 µWb/m2. The mean ratio between 45 B-field peaks simultaneously measured at 15 m and 30 m is 1.93 with a st andard deviation of 0.15.

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107 Table 3-8: Magnetic field da ta recorded at 15 m and 30 m during the 1999 experiment. Data and statistics for return stroke peaks, re turn stroke 30-90% rise-times, return stroke half peak widths, and the ratio between retu rn stroke peaks at 15 m and 30 m are shown. Flash Event # B Peak at 15 m B 30/90 Rise Time at 15 m B HPW at 15 m B Peak at 30 m B 30/90 Rise Time at 30 m B HPW at 30 m Ratio: B at 15 m / B at 30 m [ µ Wb/m2] [ns] [ µ s] [ µ Wb/m2] [ns] [ µ s] S9901 1 163 S9901 2 S9901 3 185 346 11.64 93 334 9.27 2.00 S9901 4 S9903 1 S9903 2 74 212 8.52 47 209 5.48 1.57 S9903 3 117 269 23.25 76 275 13.58 1.54 S9903 4 190 267 24.73 116 237 9.23 1.64 S9907 1 80 683 20.29 48 659 17.54 1.65 S9915 1 154 1279 21.00 85 1319 17.57 1.82 S9915 2 213 533 21.22 120 611 18.28 1.78 S9915 3 317 437 20.66 176 439 17.03 1.80 S9915 4 224 291 21.33 126 296 15.46 1.77 S9915 5 S9915 6 173 511 17.04 97 530 13.66 1.79 S9918 1 347 370 36.80 170 376 31.25 2.04 S9918 2 201 446 24.5 97 394 21.52 2.08 S9918 3 290 264 10.0 138 268 7.66 2.09 S9918 4 209 260 8.12 100 268 7.06 2.09 S9918 5 436 316 24.90 216 388 18.89 2.02 S9918 6 141 241 5.67 65 249 5.14 2.17 S9925 1 411 367 30.84 203 389 26.54 2.02 S9930 1 390 337 17.83 210 358 15.81 1.86 S9930 2 205 282 8.80 110 318 8.27 1.86 S9932 1 245 334 22.84 133 326 18.62 1.84 S9932 2 152 340 15.10 80 359 13.14 1.91 S9932 3 330 331 19.23 176 375 17.16 1.87 S9932 4 238 276 6.84 125 269 6.03 1.90 S9932 5 205 268 12.77 109 258 10.75 1.88 S9932 6 340 300 6.97 182 329 6.25 1.87 S9933 1 S9933 2 214 418 26.36 117 375 25.60 1.82 S9933 3 88 300 14.59 50 314 12.39 1.76 S9933 4 163 273 15.76 88 322 14.66 1.85 S9933 5 145 288 16.76 80 342 15.47 1.80 S9933 6 166 351 22.68 91 346 18.75 1.82 S9933 7 193 314 18.23 109 371 15.96 1.77 S9933 8 116 268 6.44 66 299 4.93 1.76 S9934 1 425 284 43.44 227 321 30.04 1.88 S9934 2 283 247 6.29 147 274 5.69 1.92 S9934 3 237 277 16.14 123 294 13.69 1.93 S9934 4 231 259 12.69 121 263 9.88 1.91 S9934 5 303 246 16.67 160 265 14.42 1.89 S9934 6 95 251 6.95 49 267 5.15 1.93 S9934 7 135 273 11.87 73 285 8.94 1.86 S9934 8 287 346 5.79 152 331 5.25 1.89 S9935 1 281 342 29.29 S9935 2 344 323 37.81 S9935 3 178 313 21.03 S9935 4 99 608 10.97 S9935 5 149 334 16.00 S9935 6 204 316 14.45 S9935 7 125 451 13.55 n 48 47 47 40 40 40 40 Minimum 74 212 5.67 47 209 4.93 1.54 Maximum 436 1279 43.44 227 1319 31.25 2.17 Arithmetic Mean 219 354 17.54 119 363 13.80 1.87 Geometric Mean 199 333 15.45 109 339 12.13 1.86 Standard Deviation 94 168 8.77 48 180 6.88 0.14

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108 3.3.5.3 1999 and 2000 Experiment Histograms and statistics of magnetic field peaks at 15 and 30 m, magnetic field 30-90% rise times at 15 and 30 m, and magnetic field half peak widt hs at 15 and 30 m are found in Figure 3-40, Figure 3-41, Figure 342, Figure 3-43, Figur e 3-44, and Figure 3-45, respectively. The parameters were obtai ned from magnetic fields directly measured during the 1999 and 2000 experiment. The dist ribution of the ratio between magnetic field peaks measured at 15 m and 30 m duri ng the 1999 and 2000 experiment is shown in Figure 3-46. Figure 3-40: Distribution of magnetic flux density peaks measured at 15 m during the 1999 experiment and 2000 experiment. Magnetic Flux Density Peak at 15 m [ µ Wb/m2] 70140210280350420490 Number 0 5 10 15 20 25 30 35 1999 n = 48 µ = 219 µ Wb/m2 = 94 µ Wb/m2 2000 n = 45 µ = 186 µ Wb/m2 = 94 µ Wb/m2 1999 and 2000 n = 93 µ = 203 µ Wb/m2 = 95 µ Wb/m2

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109 Figure 3-41: Distribution of magnetic flux density peaks measured at 30 m during the 1999 experiment and 2000 experiment. Figure 3-42: Distribution of ma gnetic flux density 30-90% rise times measured at 15 m during the 1999 experiment and 2000 experiment. Magnetic Flux Density Peak at 30 m [ µ Wb/m2] 306090120150180210240 Number 0 5 10 15 20 25 30 1999 n = 40 µ = 119 µ Wb/m2 = 48 µ Wb/m2 2000 n = 48 µ = 101 µ Wb/m2 = 51 µ Wb/m2 1999 and 2000 n = 88 µ = 109 µ Wb/m2 = 50 µ Wb/m2 Magnetic Flux Density 30-90 % Rise Time at 15 m [ns] 160240320400480560640720 Number 0 3 6 9 12 15 18 21 24 27 30 33 1999 n = 47 µ = 355 ns = 168 ns 2000 n = 45 µ = 383 ns = 301 ns 1999 and 2000 n = 92 µ = 369 ns = 242 ns

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110 Figure 3-43: Distribution of ma gnetic flux density 30-90% rise times measured at 30 m during the 1999 experiment and 2000 experiment. Figure 3-44: Distribution of ma gnetic flux density half peak widths measured at 15 m during the 1999 experiment and 2000 experiment. Magnetic Flux Density 30-90 % Rise Time at 30 m [ns] 160240320400480560640720 Number 0 3 6 9 12 15 18 21 24 27 30 33 1999 n = 40 µ = 361 ns = 180 ns 2000 n = 48 µ = 409 ns = 249 ns 1999 and 2000 n = 88 µ = 387 ns = 220 ns Magnetic Flux Density Half Peak Width at 15 m [ µ s] 612182430364248 Number 0 3 6 9 12 15 18 21 24 1999 n = 47 µ = 18 µ s = 9 µ s 2000 n = 45 µ = 17 µ s = 9 µ s 1999 and 2000 n = 92 µ = 17 µ s = 9 µ s

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111 Figure 3-45: Distribution of ma gnetic flux density half peak widths measured at 30 m during the 1999 experiment and 2000 experiment. Figure 3-46: Distribution of th e ratio between magnetic flux density peaks measured at 15 m and 30 m during the 1999 and 2000 experiment. B Peak at 15 m / B Peak at 30 m 1.61.71.81.92.02.12.22.3 Number 0 5 10 15 20 25 30 1999 n = 40 µ = 1.87 = 0.14 2000 n = 45 µ = 1.93 = 0.15 1999 and 2000 n = 85 µ = 1.90 = 0.14 Magnetic Flux Density Half Peak Width at 30 m [ µ s] 6121824303642 Number 0 3 6 9 12 15 18 21 24 1999 n = 40 µ = 14 µ s = 7 µ s 2000 n = 48 µ = 15 µ s = 9 µ s 1999 and 2000 n = 88 µ = 15 µ s = 8 µ s

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112 3.3.6 Magnetic Field Derivative at 15 m and 30 m In this section a statistical analysis of the magnetic field derivative peaks measured at 15 m and 30 m during the 1999 a nd 2000 FAA/NSF experiment is presented. Additionally, the 30-90% rise-time, t30-90%, and half peak width, tHPW, of the magnetic field derivative measured at 15 m and 30 m during the 1999 experiment is shown in Table 3-9. Figure 3-47 shows a typical magnetic field derivative wa veform measured at 15 m during the 1999 experiment on an a) 1 µs time scale and b) 0.15 µs time scale. Figure 3-47: dB/dt at 15 m of stroke S9933-6 on an a) 1 µs and b) 0.15 µs timescale. Half-peak-width and 30-90% rise-time are illustrated in a) and b), respectively. a) 0 -200 -400 -600 -800 -1000 tHPW dB/dt [ µ Wb/m2/ µ s] 50 % 0 0.2 0.4 0.6 0.8 1 b) 0 -200 -400 -600 -800 -1000 dB/dt [ µ Wb/m2/ µ s] t30-90% 30 % 90 % 0.3 0.32 0.34 0.36 0.38 0.4 4.2 0.44 t [ µ s]

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113 Table 3-9: dB/dt data recorded at 15 m a nd 30 m during the 1999 e xperiment. Data and statistics for dB/dt peaks, 30-90% rise-tim es, half peak widths, and the ratio between dB/dt peaks at 15 m and 30 m are shown. Flash Event # dB/dt Peak at 15 m dB/dt 30/90 Rise Time at 15 m dB/dt HPW at 15 m dB/dt Peak at 30 m dB/dt 30/90 Rise Time at 30 m dB/dt HPW at 30 m [ µ Wb/m2/ µ s] [ns] [ns] [ µ Wb/m2/ µ s] [ns] [ns] S9901 1 620 240 S9901 2 1466 37 129 679 27 127 S9901 3 441 49 221 233 36 176 S9901 4 685 151 325 S9903 1 2190 40 137 921 38 133 S9903 2 786 24 90 394 28 70 S9903 3 993 51 93 431 47 91 S9903 4 1798 35 78 799 30 70 S9907 1 113 S9918 1 1108 87 187 481 92 190 S9918 2 730 23 133 312 22 154 S9918 3 1098 74 224 483 85 237 S9918 4 854 127 192 382 126 200 S9918 5 1932 43 163 732 60 186 S9918 6 747 79 109 323 84 136 S9925 1 1024 54 203 S9932 1 857 75 261 S9932 2 632 60 182 S9932 3 1437 S9932 4 1509 121 130 S9932 5 1275 35 131 S9932 6 1617 86 197 S9933 2 563 69 252 S9933 3 396 26 132 S9933 4 826 33 113 S9933 5 671 48 120 S9933 6 911 26 77 S9933 7 807 41 158 S9933 8 539 68 142 S9934 1 1922 38 119 S9934 2 1094 S9934 3 1529 33 85 S9934 4 1591 34 80 S9934 5 1958 36 90 S9934 6 672 27 91 S9934 7 777 21 106 S9934 8 1086 64 117 S9935 1 673 67 283 S9935 2 1357 48 S9935 3 583 62 171 S9935 5 494 72 171 S9935 6 702 53 167 S9935 7 269 317 n 42 38 37 15 12 12 Minimum 269 21 77 113 22 70 Maximum 2190 151 317 921 126 237 Arithmetic Mean 1029 56 153 456 56 148 Geometric Mean 921 49 142 401 48 138 Standard Deviation 488 30 61 230 33 53

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114 3.3.6.1 1999 Experiment Table 3-9 lists values and st atistics of peak dB/dt at two distances, 15 m and 30 m, obtained during the 1999 experiment. dB/dt was measured 15 m from the strike point for 42 return strokes in 8 flashes during the 1999 experiment. The arithmetic mean of the peaks is 1029 µWb/m2/µs, the geometric mean is 921 µWb/m2/µs, and the standard deviation is 488 µWb/m2/µs. dB/dt was measured 30 m from the strike point for 15 return strokes in 4 flashes during the 1999 experiment . The arithmetic mean of the peaks is 456 µWb/m2/µs, the geometric mean is 401 µWb/m2/µs, and the standard deviation is 230 µWb/m2/µs. The mean ratio between 14 dB/dt peaks simultaneously measured at 15 m and 30 m is 2.27 on average with a standard deviation of 0.2. 3.3.6.2 2000 Experiment dB/dt was measured 15 m from the strike poi nt for 48 return strokes in 12 flashes during the 2000 experiment. The arit hmetic mean of the peaks is 831 µWb/m2/µs, the geometric mean is 713 µWb/m2/µs, and the standard deviation is 417 µWb/m2/µs. dB/dt values measured 30 m from the strike point for 48 return strokes in 12 flashes were obtained during the 2000 experiment. The arithmetic mean of the peaks is 405 µWb/m2/µs, the geometric mean is 349 µWb/m2/µs, and the standard deviation is 199 µWb/m2/µs. The mean ratio between 48 dB/dt peaks simultaneously measured at 15 m and 30 m is 2.05 with a standard deviation of 0.14. The distribution of dB/dt peaks measur ed at 15 m and 30 m during the 1999 and 2000 experiment and the distri bution of the ratio between the 15 m and 30 m data is

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115 displayed in Figure 3-48. The ove rall distribution of the disp layed parameters resembles a log normal distribution. 3.3.6.3 1999 and 2000 Experiment Histograms and statistics of dB/dt peaks at 15 and 30 m, dB/dt 30-90% rise-times at 15 and 30 m, and dB/dt half peak widt hs at 15 and 30 m are found in Figure 3-48, Figure 3-49, Figure 3-50, Figure 3-51, , and Figure 3-53, respectivel y. The parameters were obtained from dB/dt directly meas ured during the 1999 and 2000 experiment. The distribution of the ratio between dB/dt peak s measured at 15 m and 30 m during the 1999 and 2000 experiment is shown in Figure 3-54. Figure 3-48: Distribution of dB/dt peaks measured at 15 m during the 1999 and 2000 experiment. dB/dt Peak at 15 m [µWb/m2/µs] 04008001200160020002400 Number 0 5 10 15 20 25 30 35 40 1999 n = 42 µ = 1030 µ Wb/m2/ µ s = 488 µ Wb/m2/ µ s 2000 n = 48 µ = 831 µ Wb/m2/ µ s = 417 µ Wb/m2/ µ s 1999 and 2000 n = 90 µ = 923 µ Wb/m2/ µ s = 460 µ Wb/m2/ µ s

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116 Figure 3-49: Distribution of dB/dt peaks measured at 30 m during the 1999 and 2000 experiment. Figure 3-50: Distribution of dB/dt 30-90% ri se times measured at 15 m during the 1999 and 2000 experiment. dB/dt Peak at 30 m [µWb/m2/µs] 1503004506007509001050 Number 0 3 6 9 12 15 18 21 24 1999 n = 15 µ = 456 µ Wb/m2/ µ s = 230 µ Wb/m2/ µ s 2000 n = 48 µ = 405 µ Wb/m2/ µ s = 199 µ Wb/m2/ µ s 1999 and 2000 n = 63 µ = 417 µ Wb/m2/ µ s = 206 µ Wb/m2/ µ s dB/dt 30-90 % Rise Time at 15 m [ns] 20406080100120140160 Number 0 3 6 9 12 15 18 21 24 27 30 1999 n = 38 µ = 56 ns = 30 ns 2000 n = 29 µ = 33 ns = 18 ns 1999 and 2000 n = 67 µ = 46 ns = 27 ns

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117 Figure 3-51: Distribution of dB/dt 30-90% ri se times measured at 30 m during the 1999 and 2000 experiment. Figure 3-52: Distribution of dB/dt half peak widths measured at 15 m during the 1999 and 2000 experiment. dB/dt 30-90 % Rise Time at 30 m [ns] 153045607590105120135 Number 0 2 4 6 8 10 12 14 16 1999 n = 12 µ = 56 ns = 33 ns 2000 n = 30 µ = 34 ns = 16 ns 1999 and 2000 n = 42 µ = 40 ns = 24 ns dB/dt Half Peak Width at 15 m [ns] 306090120150180210240270300330 Number 0 3 6 9 12 15 18 21 1999 n = 37 µ = 153 ns = 61 ns 2000 n = 34 µ = 114 ns = 42 ns 1999 and 2000 n = 71 µ = 134 ns = 56 ns

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118 Figure 3-53: Distribution of dB/dt half p eak widths measured at 30 m during the 1999 and 2000 experiment. Figure 3-54: Distribution of the ratio between dB/dt peaks measured at 15 m and 30 m during the 1999 and 2000 experiment. dB/dt Half Peak Width at 30 m [ns] 306090120150180210240270 Number 0 2 4 6 8 10 12 14 16 1999 n = 12 µ = 148 ns = 53 ns 2000 n = 36 µ = 120 ns = 51 ns 1999 and 2000 n = 48 µ = 127 ns = 52 ns dB/dt Peak at 15 m / dB/dt Peak at 30 m 1.852.002.152.302.452.602.75 Number 0 3 6 9 12 15 18 21 24 1999 n = 14 µ = 2.27 = 0.20 2000 n = 48 µ = 2.05 = 0.14 1999 and 2000 n = 62 µ = 2.10 = 0.18

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119 CHAPTER 4 MODELING OF ELECTROMAG NETIC FIELD DERIVATIVES 4.1 Introduction Uman et al. [2000] have presented electri c field derivatives measured 10 to 30 m from triggered lightning return strokes dur ing the 1998 Camp Blanding campaign. They found that the electric field derivative wavesh apes at both distances were very similar. Additionally they reported that the observ ed electric field and current derivative waveforms were similar well past the time of peak value although their current derivative data were obtained by numerically differe ntiating the measured current and were therefore noisy and bandwidth limited. They suggested that the observed waveshape similarities between electric field and curre nt derivatives and be tween electric field derivatives measured at different distances could possibly be indicative of a dominant radiation field (Chapter 2). These observations have, in part, motivated the measurement and theory presented in this thesis. The current derivative from return stroke s of rocket-trigger ed lightning was directly measured in 1999 and is used as input to the transmission line model (TLM) calculations. The electric and magnetic fiel d components are calculated using the TLM for different distances and velocities to inve stigate the hypothesis of a dominant radiation field during the initial 100 ns or so of the dE/dt waveforms at close distances (15 and 30 m). Additionally, the TLM is used to calculate the electri c and magnetic field derivatives at 15 m. The results are compared with directly measured field derivatives at

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120 the same distance for two strokes to test the validity of the TLM and to make inferences about the return stroke speed at early times. In the first part of this chapter, equati ons are derived from which to calculate the electromagnetic fields on a perfectly conduc ting ground from the current as a function of spatial position and time in the lightning channel. In the second part of the chapter, the derived equations and the TLM are employed to calculate the electromagnetic field derivatives and their components. The dependenc e on distance and retu rn stroke speed of the electric field derivative and its three components (radiation, induction, and electrostatic) and the magnetic field deri vative and its two com ponents (radiation and induction) is investigated. The la st part of this chapter is c oncerned with investigating the applicability of the TLM to reproduce meas ured field derivative s and the correlation between measured field and current derivatives. 4.2 Return Stroke Electromagnetic Fields on Ground A general expression for the electromagne tic fields produced on a perfectly conducting ground will be derived using the elec tric dipole approach, i.e., deriving the electric and magnetic field equa tions resulting from a differen tial electric dipole carrying uniform current i(t) and then integrating thos e expressions over the length of the channel. The effect of a perfectly conducting ground w ill be included by applying the method of images. 4.2.1 Specification of Ge ometrical Parameters The geometry of the problem is illustra ted in Figure 4-1 and Figure 4-2. The source is a straight line fr om the origin at an angle from the vertical. A dipole of length d oriented from the channel origin towards its position on the channel carrying uniform

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121 current i(t) produces an electromagnetic field at field point P. An image dipole of length * d (the star (*) denotes the image parameters ) oriented from its location on the channel towards the channel origin is assumed in order to satisfy the boundary conditions on a perfectly conducting ground. Th e image current i*(t) provide s a complete simulation of the re-radiation by the ground plane of the prim ary radiation from th e source current. The unit vectors ˆ and * ˆ (unit vectors are denoted with caps ) are pointing in the direction of the current and image current flow. With the field point on the ground plane, the geometrical parameters can be specified as follows: € r is a vector pointing from the origin to field point P: x r rˆ= (1) € * /r r is a vector pointing from the origin to the dipole/image dipole: z r y r x r rˆ cos ˆ sin sin ˆ cos sin + + = (2a) z r y r x r rˆ cos ˆ sin sin ˆ cos sin * Š + = (2b) € * ˆ / ˆ is a unit vector pointing in the direct ion of the current/image current flow: r =ˆ ˆ (3a) * ˆ * ˆr Š = (3b) € * / R R is a vector pointing from the dipo le/image dipole to the field point P: ()z r y r x r r R ˆ cos ˆ sin sin ˆ cos sin Š Š Š = (4a) ()z r y r x r r R ˆ cos ˆ sin sin ˆ cos sin * + Š Š = (4b) ()()() 2 2 2cos sin sin cos sin * r r r r R R + + Š = = (5) R R R R = =ˆ (6a) R R R R * * * ˆ = = (6b)

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122 The return stroke channel with a current distribution specified by the return stroke model used produces an electr omagnetic field at P at time t. The observer at P ‘sees’ a retarded current, i.e., the return stroke front is delayed due to the finite propagation speed (speed of light c) of electromagnetic waves. The retarded current/image current can be expressed as a function of time and space (not e that the arguments of the current and image current are identical if P is a point on the ground due to symmetry): ) ) ( , ( * ) ) ( , ( c r R t r i c r R t r i Š = Š (7) Figure 4-1: Current ca rrying dipole of length d and image dipole of length *d producing electromagnetic fields at P.

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123 Figure 4-2: Geometry used in deriving electric and magnetic field equations. 4.2.2 Electric Field/Field Derivative Le Vine and Meneghini [ 1983] derived the following general equation for the electric field produced by an electric dipole d t i R c R R i R c R R d i R R R E dc R v t dipole Š + Š + Š Š =Š Š 2 2 / / 0 3 0) ˆ ( ˆ ) ˆ ( 3 ˆ ) ˆ ( 3 ˆ 4 1 (8) The electric field due to the im age current-carrying element is * * * * *) * ˆ ( * ˆ * * * *) * ˆ ( 3 * ˆ * * * *) * ˆ ( 3 * ˆ 4 12 2 / * / * 0 3 0 d t i R c R R i R c R R d i R R R E dc R v t dipole image Š + Š + Š Š =Š Š (9)

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124 where 0 is the permittivity of air: m F / 10 * 8.85412 0 Š= and c is the speed of light: s m c / 10 * 38= . Evaluating R R Š ) ˆ ( 3 ˆ and R R Š ) ˆ ( ˆ in (8) using (1) (6) we find that ()() () () () Š + + Š + + + Š + + = Š2 2 2 2 2 2 2 2 2cos sin 3 1 cos ˆ cos sin 3 1 sin sin ˆ cos sin cos sin 1 3 cos sin ˆ ) ˆ ( 3 ˆ r r r R z r r r R y r r r r R x R R (10) ()() () () () Š + + Š + + + Š + + = Š2 2 2 2 2 2 2 2 2cos sin 1 1 cos ˆ cos sin 1 1 sin sin ˆ cos sin cos sin 1 1 cos sin ˆ ) ˆ ( ˆ r r r R z r r r R y r r r r R x R R (11) Evaluating * *) * ˆ ( 3 * ˆ R R Š and * *) * ˆ ( * ˆ R R Š in (9) using (1) (6) we find ()() () () () Š + + Š + Š + Š + + Š = Š2 2 2 2 2 2 2 2 2'* cos sin '* * 3 1 cos ˆ '* cos sin '* * 3 1 sin sin ˆ cos sin '* cos sin 1 '* * 3 cos sin ˆ * *) * ˆ ( 3 * ˆ r r r R z r r r R y r r r r R x R R (12)

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125 ()() () () () Š + + Š + Š + Š + + Š = Š2 2 2 2 2 2 2 2 2* cos sin * * 1 1 cos ˆ * cos sin * * 1 1 sin sin ˆ cos sin * cos sin 1 * * 1 cos sin ˆ * *) * ˆ ( * ˆ r r r R z r r r R y r r r r R x R R (13) The total electric field at P can be calculate d by summing the electric field contributions due to the dipole and image dipole: Š Š+ = Š = + =) ( 0 ) ( 0 ) ( 0 ) ( 0 ) ( 0 0 ) (t Lt Lt Lt L dipole image dipole dipole image dipole t L t L dipole image dipoleE d E d E d E d E d E d E ()+ =) ( 0 t L dipole image dipoleE d E d E (14) Substituting (7) (13) in (14) we obtain () () () z d t c r R t i r R c r r r r R d c r R t i r cR r r r r R d d i r R r r r r R t r Et L t L t L c R v tˆ ) / ) ( ( ) ( cos sin ) ( 1 1 cos 2 1 ) / ) ( ( ) ( cos sin ) ( 3 1 cos 2 1 ) ( ) ( cos sin ) ( 3 1 cos 2 1 ) , () ( 0 2 2 2 0 ) ( 0 2 2 2 0 ) ( 0 / / 0 3 2 2 0 Š Š + Š Š Š + Š Š + Š = Š Š (15) Note that the x and y com ponents of the dipole and image dipole field on ground cancel (as required by the boundary condition at the surface that the tangential electric field be zero) and the z component doubles.

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126 The time derivative of the electric field is () () () z d t c r R t i r R c r r r r R d t c r R t i r cR r r r r R d c r R t i r R r r r r R dt t r E dt L t L t Lˆ ) / ) ( ( ) ( cos sin ) ( 1 1 cos 2 1 ) / ) ( ( ) ( cos sin ) ( 3 1 cos 2 1 ) / ) ( ( ) ( cos sin ) ( 3 1 cos 2 1 ) , () ( 0 2 2 2 2 2 0 ) ( 0 2 2 2 0 ) ( 0 3 2 2 0 Š Š + Š Š Š + Š Š Š + Š = (16) For the special case of a vert ical return stroke channel ( = 0 ° ), equations (15) and (16) become z d t c r R t i r R c r d c r R t i r cR r r d d i r R r r t r Et L t L t L c R v t channel verticalˆ ) / ) ( ( ) ( 2 1 ) / ) ( ( ) ( 2 2 1 ) ( ) ( 2 2 1 ) , () ( 0 3 2 2 0 ) ( 0 4 2 2 0 ) ( 0 / / 0 5 2 2 0 Š Š Š Š + Š = Š Š (17) z d t c r R t i r R c r d t c r R t i r cR r r d c r R t i r R r r dt t r E dt L t L t L channel verticalˆ ) / ) ( ( ) ( 2 1 ) / ) ( ( ) ( 2 2 1 ) / ) ( ( ) ( 2 2 1 ) , () ( 0 2 2 3 2 2 0 ) ( 0 4 2 2 0 ) ( 0 5 2 2 0 Š Š Š Š + Š Š = (18)

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127 The classical equation (17) is commonly found in the literature (e.g., Uman et al. 1975). The first term in (17) is referred to as the electrostatic fiel d component, the second term as the induction electric field component, and the third term as the radiation electric field component. If the distance r between obs erver and source is large compared to the dimension of the source then the following distance dependences of the electric field components apply. The electrostatic field is pr oportional to the cube of the inverse of r (~1/r3). The induction electric field is proportional to the square of the inverse of r (~1/r2). The radiation electric field is proportional to the i nverse of r (~1/r). The radiation electric field dominates the total electric field for large distances. 4.2.3 Magnetic Field/Field Derivative A general equation for the magnetic field produced by a current-carrying electric dipole is [Le Vine and Meneghini, 1983] d t i R c R i R R B ddipole × + × = ˆ ˆ 42 0 µ (19) The magnetic field due to the image dipole is * * * * * ˆ * * * * ˆ 42 0 d t i R c R i R R B ddipole image × + × = µ (20) where 0 µ is the permeability of air ( m H / 10 47 0Š = µ), c is the speed of light ( s m c / 10 38 = ), and v is the speed of the current impulse propagating along the channel. Evaluating R × ˆ and * * ˆ R × using (1) (6), we find z R r y R r R ˆ sin sin ˆ cos ˆ Š = × (21)

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128 z R r y R r R ˆ sin sin ˆ cos * * ˆ + = × (22) The total magnetic field at P can be calculated by summing the magnetic field contribution due to the dipole and image dipole and integrating over th e length L(t) of the channel and image channel, respectively: + = Š = + =Š Š) ( 0 ) ( 0 ) ( 0 ) ( 0 ) ( 0 0 ) ( t Lt L dipole image dipole t Lt L dipole image dipole t L t L dipole image dipoleB d B d B d B d B d B d B ()+ =) ( 0 t L dipole image dipoleB d B d B (23) Substituting equations (7) and (19)-(22) in (23), we obtain y d t c R t i R c r d c R t i R r t r Bt L t Lˆ ) / ( cos 2 ) / ( cos 2 ) , () ( 0 2 0 ) ( 0 3 0 Š + Š = µ µ (24) Note that the z components cancel (as required by the boundary condition at the surface that the vertical magnetic field be zero) and the y components double. The time derivative of the B-field is: y d t c R t i R c r d t c R t i R r dt t r B dt L t Lˆ ) / ( cos 2 ) / ( cos 2 ) , () ( 0 2 2 2 0 ) ( 0 3 0 Š + Š = µ µ (25) Note that (23) and (24) are valid eq uations for any channel orientation. For a vertical channel, is 0 ° and cos is unity. Equation (23) for th e special case of a vertical channel is commonly found in th e literature (e.g., Uman et al. 1975). The first term in

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129 (23) is referred to as th e induction or magnetostatic ma gnetic field component, and the second term as the radiation magnetic field component. If the distance r between observer and source is large compared to the dimension of the source then the following distance de pendences of the electric field components apply. The induction magnetic field is proportion al to the square of the inverse of the distance r (~1/r2). The radiation magnetic field is pr oportional to the inverse of r (~1/r). The radiation magnetic field dominates the total magnetic field for large distance. 4.3 Methodology of Field Calculations The following assumptions were made for th e calculation of el ectric and magnetic fields and their time derivatives: straight channel perfectly conducting ground return stroke current traveling with constant speed without distortion or attenuation (transmission line model) Measured value of dI/dt as a function of time were cubic spline or linearly interpolated and used as input s to equations (16) and (25). The second current derivative needed for the calculation of the radiati on components of dE/dt and dB/dt was obtained by differentiating the interpolated dI/dt. The current derivative was filtered using Matlab 5.3 to achieve relatively low noise results for th e radiation terms of th e field derivatives. A 3rd order lowpass elliptic filter with a cuto ff frequency of 20 MHz, 0.5 dB of ripple in the passband, and 12 dB of attenuation in the stopband was used. Figure 4-3 shows the unfiltered and filtered dI/dt waveform of triggered lightning event S9934, return stroke 6 (S9934-6) a nd return stroke 7 (S9934-7). The dI/dt

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130 00.10.20.30.40.5 100 50 0 a)S9934-6 Current Derivative dI/dt [kA/ µ s] dI/dt (unfiltered) dI/dt (filtered) t [ µ s] 00.10.20.30.40.5 100 50 0 b)S9934-7 Current Derivative dI/dt [kA/ µ s] dI/dt (unfiltered) dI/dt (filtered) t [ µ s] waveforms of strokes S9934-6 a nd S9934-7 are used as a model input for the calculations found in this chapter. The electromagnetic fields were calcul ated using Mathcad 2001. The tolerance setting (TOL), which gives the precision to which integrals are evaluated, was set between 0.1 and 0.5. The relatively high TOL (= low precision) was necessary for the integration to converge to a solution. Figure 4-3: Unfiltered and filtered dI/dt wave form of triggered flash S9934, a) return stroke 6 and b) return stroke 7.

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131 4.4 Speed and Distance Dependence of Electromagnetic Field Derivative Components Electromagnetic field deriva tives and their components are calculated using the transmission line model (TLM) in order to examine the return stroke speed and field distance dependence. The methodology descri bed in Section 4.3 was used for the calculations. The TLM specifies the return stro ke current along the channel as a current wave that travels upward with a constant speed and without dist ortion or attenuation (Chapter 2). The field derivatives presente d in this section are calculated using the measured dI/dt of stroke S9934-6 as input to the TLM for a vertical channel. 4.4.1 Speed Dependence of Electromagnetic Field Derivative Components at 15 m With measured dI/dt of str oke S9934-6 as an input to the model, as noted earlier, field derivatives are calculated at close distance (r = 15 m) for three velocities, i.e., v = 1*108 m/s, v = 2*108 m/s, and v = c. The dependence of 30-90% rise-time, half peak width, radiation, induction, and, for dE/dt, el ectrostatic components on return stroke speed is examined. 4.4.1.1 Electric field derivative Figure 4-4 shows calculated dE/dt wave forms at 15 m and their radiation, induction, and electrostatic components usi ng the transmission line model for three different speeds. Looking at the total dE/dt waveforms calculated for v = 1*108 m/s, v = 2*108 m/s, and v = c, we observe that peak values are larger for larger speeds, waveforms are narrower for larger speeds, rise-times are smaller for larger speed.

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132 The above correlations will be examined in more detail in Section 4.5. The radiation component exhibits a ze ro crossing that occurs sligh tly earlier for larger speeds and the peak is larger for larger speeds. The induction component exhibits zero crossing that occurs much earlier for larger speeds, and the peak is essentially unchanged for all three speeds. The electrostatic component doe s not exhibit a zero crossing within the displayed time, and the peak is smaller fo r larger speeds. Note that the radiation component is dominant for the first 50 ns or so. Figure 4-5 illustrates the relative contributions of radiation, induction, and electrostatic components to th e dE/dt peaks of the waveform s shown in Figure 4-4. For v = 1*108 m/s the electrostatic component is the la rgest component of the peak field, for v = 2*108 m/s all components are roughly equal, a nd for v = c the radiation component is the largest component. The relative cont ribution of the induction component is approximately the same for all three speeds. In summary, the relative contribution of radiation, induction, and electrostatic components to the dE/dt peak at 15 m depe nds strongly on the assumed return stroke speed if the return stroke speed is assumed to be < 2*108 m/s. The relative contribution of the three components does not chan ge much for speeds between 2*108 m/s and 3*108 m/s.

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133 Figure 4-4: Calculated dE/dt and radiation, induction, and el ectrostatic component at 15 m distance of stroke S9934-6 for a) v = 1*108 m/s, b) v = 2*108 m/s, and c) v = c using measured dI/dt of stroke S9934-6 as input to the transmission line model. 100 0 100 200 300 a) v = 1*108 m/s dE/dt [kV/m/ µ s] 100 0 100 200 300 b) v = 2*108 m/s 00.050.10.150.20.250.30.350.40.450.5 100 0 100 200 300 Total dE/dt Radiation Field Induction Field Electrostatic Field c) v = ct [ µ s]

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134 Figure 4-5: Contribution of ra diation, induction, and electr ostatic component to dE/dt peak at 15 m of for v = 1*108 m/s, v = 2*108 m/s, and v = c using measured dI/dt of stroke S9934-6 as input to the transmission line model. Contribution of Components to dE/dt P eak, r = 15 mVelocity [m/s] 1e+82e+83e+8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Percentage of Radiation Component Percentage of Induction Component Percentage of Electrostatic Component

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135 4.4.1.2 Magnetic field derivative Figure 4-6 shows calculated dB/dt wavefo rms at 15 m and their radiation and induction components using the transmission line model for three different speeds. Looking at the total dB/dt wa veforms calculated for v = 1*108 m/s, v = 2*108 m/s, and v = c, we observe that peak values are larger for larger speeds, waveforms are narrower for larger speeds, rise-times are smaller for larger speeds. The above correlations will be examined in more detail in Section 4.5. The radiation component exhibits a ze ro crossing that occurs sligh tly earlier for larger speeds, and the peak is larger for larger speeds. The induction component doe s not exhibit a zero crossing within the displayed range, and the peak is larger for larger speeds. Note that the radiation component is dominant for the first 50 ns or so. Figure 4-7 illustrates th e relative contribution of radiation and induction components to the dB/dt peak s of the waveforms shown in Figure 4-6. For v = c the contribution of radiation and induction compone nts to the peak valu e is roughly equal. For smaller speeds the induction component becomes slightly larger than the radiation component. In summary, the relative contribution of radiation and induction components to the dB/dt peak at 15 m for a speed between 1*108 m/s and c does not depend much on the assumed return stroke speed.

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136 Figure 4-6: Calculated dB/dt, radiation, and induction com ponent at 15 m distance for a) v = 1*108 m/s, b) v = 2*108 m/s, and c) v = c using measur ed dI/dt of stroke S9934-6 as input to the transmission line model. 1000 500 0 a) v = 1*108 m/s 1000 500 0 dB/dt [ µ Wb/m2/ µ s] b) v = 2*108 m/s 00.050.10.150.20.250.30.350.40.450.5 1000 500 0 c) v = c Total dB/dt Radiation Field Induction Field t [ µ s]

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137 Figure 4-7: Contribution of ra diation and induction component to dB/dt peak at 15 m for v = 1*108 m/s, v = 2*108 m/s, and v = c using measured dI/dt of stroke S9934-6 as input to the transmission line model. 4.4.2 Distance Dependence of dE/dt and dB/dt Components The measured dI/dt of stroke S9934-6 will be used as an input to the model. Field derivatives are calculated at 3 distances (r = 1 m, r = 10 m, and r = 100 m) using the transmission line model. Reviewing the literature for subsequent na tural return stroke speeds and triggered stroke speeds, both at early times, we find typi cal return stroke speeds between 1.3*108 m/s and near c, based on optical measur ements and theoretical considerations (Chapter 2). Additionally, the re lative contribution of the elec tromagnetic field derivative components for v > 2*108 m/s changes very little as shown previously. With these Contribution of Components to dB/dt Peak, r = 15 mVelocity [m/s] 1e+82e+83e+8 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Percentage of Radiation Component Percentage of Induction Component

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138 considerations in mind, a return stroke speed of v = c is chos en to investigate the distance dependence of the electromagnetic field derivative components. 4.4.2.1 Electric field derivative Figure 4-8 shows calculated dE/dt wavefo rms at 1 m, 10 m, and 100 m and their radiation, induction, and electr ostatic components for the special case v = c. The waveshape of the total dE/dt waveform at every distance is exactly the same (small deviations seen in Figure 4-8 are due to calculation errors) and the field derivative decays as 1/r. The radiation compone nt is bipolar and becomes wi der with increasing distance. The induction component is primarily nega tive for very close distances and becomes bipolar and wider with increas ing distance. The electrostati c component is positive and becomes wider with increasing distances. Figure 4-9 illustrates the relative contribution of radiation, induction, and electrostatic components to the dE/dt peaks of the waveforms shown in Figure 4-8. For r = 1 m the electrostatic component is do minant, and the radiation component is essentially zero, for r = 10 m all compone nts are roughly equal, and for r = 100 m the radiation component is domina nt and the electrostatic com ponent is essentially zero.

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139 Figure 4-8: Calculated dE/dt, radiation, and induction, and elect rostatic component at a) r = 1 m, b) r = 10 m, and c) r = 100 m using v = c and measured dI/dt of stroke S9934-6 as input to the transmission line model. 2000 0 2000 4000 6000 a) r = 1 m dE/dt [kV/m/ µ s] 200 0 200 400 600 b) r = 10 m 00.050.10.150.20.250.30.350.40.450.5 20 0 20 40 60 Total dE/dt Radiation Field Induction Field Electrostatic Field c) r = 100 mt [ µ s]

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140 Figure 4-9: Contribution of ra diation, induction, and electr ostatic component to dE/dt peak at 1 m, 10 m, and 100 m using v = c and measured dI/dt of stroke S9934-6 as input to the transmission line model. 4.4.2.2 Magnetic field derivative Figure 4-10 shows calculated dB/dt waveforms at 1 m, 10 m, and 100 m and their radiation and induction components. The similari ty of waveshapes for different distances and the inverse distance dependence for the sp ecial case v = c observed for dE/dt is also observed for dB/dt. The radiation component is bipolar and becomes wider a nd relatively larger with increasing distance. The inducti on component is essentially un ipolar and becomes, wider, and relatively smaller with increasing distance. Contribution of Components to dE/dt Peak, v = cDistance [m] 110100 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Percentage of Radiation Component Percentage of Induction Component Percentage of Electrostatic Component

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141 Figure 4-11 illustrates the relative cont ribution of radiation and induction component to the dB/dt peaks of the wa veforms shown in Figure 4-10. For r = 1 m essentially only the induction component contributes to the peak. For r = 10 m the induction component is the la rgest component and the radi ation component contributes considerably (about 40%) to th e peak. For r = 100 m the radi ation component is dominant although some induction field (a bout 10%) is st ill present. Figure 4-10: Calculated dB/dt, radiation, and induction component at a) r = 1 m, b) r = 10 m, and c) r = 100 m using v = c and measured dI/dt of stroke S9934-6 as input to the transmission line model. 1.5.104 1.104 5000 0 a) r = 1 m 1500 1000 500 0 dB/dt [ µ Wb/m2/ µ s] b) r = 10 m 00.050.10.150.20.250.30.350.40.450.5 150 100 50 0 c) r = 100 m Total dB/dt Radiation Field Induction Field t [ µ s]

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142 Figure 4-11: Contribution of ra diation and induction component to dB/dt peak at 1 m, 10 m, and 100 m using v = c and measured dI/d t of stroke S99346 as input to the transmission line model. 4.5 Comparison of Transmission Line Model Predictions with Measurements In this section the transmission line model (TLM) is employed to model the measured electric and magnetic field derivativ es at a distance of 15 m distance from lightning strokes S9934-6 and S9934-7 with th e current derivative measured at the lightning channel base as a model input. Th e effect of the channel geometry on the calculated and measured electromagnetic fiel d derivatives is inve stigated. Additionally, the correlation between the measured fiel d derivatives and the measured current derivative is investig ated. Comparison of measured and model predicted electromagnetic field derivatives allows some inferences on the return stroke speed at early times, Contribution of Components to dB/dt Peak, v = cDistance [m] 110100 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Percentage of Radiation Component Percentage of Induction Component

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143 assuming that the model gives a reasonable representation of the physical processes during the return stroke. 4.5.1 Geometry of Event S9934 Experimental data for event S9934 are used in the modeling attempts presented in this chapter. It is important to examine the geometrical characteristics of this event to determine and reduce, if possi ble, sources of error in th e model related to channel geometry. A still camera located approximately 50 m west of the strike point in SATTLIF and a video camera located on the road appr oximately 70 m north of the strike point recorded event S9934. The locations of the cam eras are illustrated in Figure 4-12. The channel as seen from SATTLIF (Figure 4-13) is approximate ly straight and vertical. Video frames of event S9934 are shown in Figure 4-14. The first frame from the left shows one of the 11 frames of the initial stag e of the flash. The other ten frames of the initial stage are not shown since they show e ssentially the same picture. The next five frames show return strokes, continuing cu rrent, and/or M-compone nts. The total number of strokes and the time between strokes fo r event S9934 was not determined from the continuous record due to an equipment failure . However, the total number of strokes in this flash is at least eight, so that some of the channel images seen in Figure 4-14 correspond to multiple strokes. It is not po ssible to determine with 100% certainty the channel image that shows stroke S99346 or stroke S9934-7 due to the missing information about the time between strokes. However, it can be argued that it is very likely that strokes six and seven are disp layed in frame 15, 19, or 23, since frame 24 likely shows the 8th or 9th stroke. Frames 15, 19, and 23 all display channels with essentially the same geometry. Therefore, the geometry of strokes S9934-6 and S9934-7

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144 can be determined with a reasonable degree of certainty. The bottom section of the lightning channel (approximately 5 m) in fram e 15, 19, and 23 is leaning with an angle of 40 ° from the vertical to the right, i.e., to wards SATTLIF. The top section of the channel is leaning with an angle of 20 ° from the vertical to the left (away from SATTLIF). In order to simplify our calculations we extrapol ate the top section of the channel to ground and ignore the effect of the leaning of the bo ttom section of the cha nnel and the effect of the 2-m strike rod. The point where the ex trapolated channel section hits ground is referred to as the “virtual” channel origin (the actual channel origin is the top of the strike rod). For the calculations in th e rest of this section we assume three different channel geometries: Geometry I The channel is straight and vert ical. The distance between the electric and magnetic field derivative antennas an d the channel orig in is 15 m. Geometry II The channel is straight and leaning at an angle = 20 ° from the vertical at a defined azimuthal angle = 0 ° (away from SATTLIF) with the “virtual” channel origin located at the bottom of the strike rod. The distance between electric and magne tic field derivative antenna and “virtual” channel origin is 15 m. The electric field derivative antenna is located at = 135 ° and the magnetic field derivative antenna at = 120 ° . Geometry III The channel is stra ight and leaning at an angle = 20 ° from the vertical at a defined azimuthal angle = 0 ° (away from SATTLIF) with the “virtual” channel origin located 4 m west and 0.2 m north of the strike

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145 rod1. The distance between electric and magnetic field derivative antenna and “virtual” channel origin is 12.2 m and 13.5 m, respectively. The electric field derivative antenna is located at = 120 ° and the magnetic field derivative antenna at = 105 ° . Figure 4-12: Location of photo and video cameras. Note that from the three geometries used for the calculations, geometry III is the most accurate representation of the actual channel geometry. Geometry I ignores the effect of the leaning channel and geometry II ignores the fact that the “virtual” channel origin is located west of the strike rod. 1 The extrapolated top section of the channel or iginates west of the strike rod resulting in a shorter distance between “vir tual” channel origin and fi eld derivative antennas. The new distances were estimated from optical records.

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146 Geometries II and III are used in Sect ion 4.5.3 to compare the measured field derivatives with the results from TLM modeli ng. Geometries I and II are used in Section 4.5.4 to investigate the effects of channel le aning on calculated fiel d derivative peaks and waveshapes. Figure 4-13: Photo of event S9934 taken from SATTLIF. Figure 4-14: Video frames of event S9934 take n from the road. The first frame from the left shows one of the 11 frames of the initia l stage of the flash. The frame number of the following frames is denoted at the top of each frame. 1-11 12 15 19 23 24

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147 4.5.2 Overview of the Experimental Data for Strokes S9934-6 and S9934-7 Figures 4-15 and 4-16 show a complete set of measurements (I, dI/dt, E, dE/dt, B, dB/dt), the latter four measur ements being taken at 15 m for strokes S9934-6 and S99347, respectively. These strokes were the sixt h and seventh in flash S9934. Both strokes lowered negative charge to ground, and the curren t is arbitrarily plotted as negative. The atmospheric electricity sign convention (downward-directed electric field vector is defined as positive) is used in plotting E and dE/dt. In Figure 4-17 and Figure 4-18 the current derivative, magnetic field derivative, an d electric field deriva tive are overlaid for strokes S9934-6 and S9934-7 on two time scales, showing a similarity in the waveshapes of these signals for the first 150 ns or so. Note that the electric fiel d derivative waveform exhibits an initial negative field change due to the downward propagating leader, clearly evident in Figure 4-18, prior to the positive derivative pulse from the upward propagating return stroke, as discussed by Uman et al. [2000]. The portion of the overall dE/dt waveform produced by the return stroke is of primary interest here. After about 150 ns, about 50 ns after the return-s troke derivative peak, the el ectric field derivative decays more slowly than the current and magnetic field derivative wavefo rms, the latter two being very similar for their total duration. Peak value, 3090% rise-time (RT), and half peak width (HPW) of the field derivatives at 15 m and current derivatives of stroke S9934-6 and S9934-7 are summarized in Table 4-1. Table 4-1: Parameters of dI/dt, dE/dt at 15 m, and dB/dt at 15 m of strokes S9934-6 and S9934-7. Event ID dI/dt Peak [kA/µs] dE/dt Peak [kV/m/µs] dB/dt Peak [µWb/m2/µs] dI/dt 30-90% RT [ns] dE/dt 30-90% RT [ns] dB/dt 30-90% RT [ns] dI/dt HPW [ns] dE/dt HPW [ns] dB/dt HPW [ns] S9934-6 80 310 800 40 30 30 100 170 90 S9934-7 100 360 1100 20 30 20 100 190 110

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148 Figure 4-15: For stroke S9934-6, a complete set of measurements (E, B, I, dE/dt, dB/dt, dI/dt), the latter four at 15 m.

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149 Figure 4-16: For stroke S9934-7, a complete set of measurements (E, B, I, dE/dt, dB/dt, dI/dt), the latter four at 15 m.

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150 Figure 4-17: Measured current derivative, magnetic field deri vative, and negative of the electric field derivative for S9934-6 on a (a) 3 µ s time scale and (b) 0.5 µ s time scale. 00.511.522.53 700 600 500 400 300 200 100 0 100 a) 8.5*dI/dt [kA/ µ s] dB/dt [ µ Wb/m2/ µ s] 00.050.10.150.20.250.30.350.40.45 700 600 500 400 300 200 100 0 100 b) 2.2*dE/dt [kV/m/ µ s] dE/dt dB/dt dI/dt t [ µ s]

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151 Figure 4-18: Measured current derivative, magnetic field deri vative, and negative of the electric field derivative for S9934-7 on a (a) 3 µ s time scale and (b) 0.5 µ s time scale. 00.511.522.53 800 700 600 500 400 300 200 100 0 100 200 a) 7.8*dI/dt [kA/ µ s] dB/dt [ µ Wb/m2/ µ s] 00.050.10.150.20.250.30.350.40.45 800 700 600 500 400 300 200 100 0 100 200 b) 2.2*dE/dt [kV/m/ µ s] dE/dt dB/dt dI/dt t [ µ s]

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152 4.5.3 Comparison of Measured and Mode l Predicted Electromagnetic Field Derivatives Electric and magnetic field derivatives at 15 m were calculated for three velocities, v = 1*108 m/s, v = 2*108 m/s, and v = 3*108 m/s (essentially the speed of light c), with the measured current derivatives of stroke S9934-6 and stroke S9934-7 used as inputs to Equations (15) and (24). Geometry II and geometry III described in Section 4.5.1 were used for the calculations. The result s are compared with the measured electric and magnetic field derivatives and an attempt is made to infer the return stroke speed at early times based on this comparison. 4.5.3.1 Calculated and measured dE/dt Model predicted electric field derivati ves for r = 15 m were overlaid with measured electric field derivatives at 15 m. In Figure 4-19 and Figure 4-21 the model predicted electric field derivatives were calc ulated assuming a shifted leaning channel so that the channel origin is at the bottom of the strike rod (geometry II) for strokes S9934-6 and S9934-7, respectively. In Figure 4-20 and Figure 4-22 the model predicted electric field derivatives were calculated assuming a leaning cha nnel in its original position and the channel origin shifte d towards SATTLIF (geometry III) for stroke S9934-6 and S9934-7, respectively. The waveforms at the top of each figure are not normalized. The measured dE/dt is aligned such that the wave form crosses zero at t = 0. The waveforms at the bottom of each figure are normalized and sh ifted in time for easy comparison between the calculated and measured waveshapes. The peaks of the calculated dE/dt wavefo rms in Figure 4-19 a) and Figure 4-21 a) (shifted slanted channel) are about 20% to 40% lower than the measured peaks. The peaks of the calculated dE/dt waveforms in Figure 4-20 a) (slanted channel, shifted

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153 origin) for v = 1*108 m/s, v = 2*108 m/s, and v = c are about 12%, 7%, and 3%, respectively, lower than the measured p eaks. The peaks of the calculated dE/dt waveforms in Figure 4-22 a) (slanted channel, shifted origin) for all speeds are essentially identical to the measured peaks. The normalized waveforms of the same flash calculated using the same speed for different channel geometries are essentially id entical as seen in Figure 4-19 Figure 4-22 for Geometry II and III for v = 1*108 m/s, v = 2*108 m/s, and v = c and illustrated in Figure 4-23 for Geometry I, II, and III for v = 2*108 m/s. Therefore, the dE/dt waveshapes calculated for different speeds can be compared regardless of channel geometry. The rising edges of all calculated waveforms for stroke S9934-6 in Figure 4-19 b) and Figure 4-20 b) are slower than the ri sing edge of the measured waveform before the times of the half peak value and are very similar for times after the half peak value for speeds > 2*108 m/s. The waveform for v = 2*108 m/s in Figure 4-19 b) is slightly slower than the measured waveform at times from about 20 ns to the time of peak value, has a wider peak, follows the measured field deriva tive at times from about 60 ns past peak value to 100 ns past peak value, and decays to zero faster 100 ns past peak value. The waveforms for v = c in Figure 4-19 b) and Figur e 4-20 b) are very similar to the measured waveform at times from about 30 ns before to 20 ns after peak value and decays to zero faster 20 ns past peak value. The calculat ed waveforms for stroke S9934-7 in Figure 4-21 b) and Figure 4-22 b) show reasonably good agreement with the rising edge of the measured waveform and for times earlier th an about 70 ns after peak value if speeds between 2*108 m/s and c are used for the calculation. The rising edge of the waveform for v = 2*108 m/s in Figure 4-21 b) is slightly sl ower than the measured waveform. The

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154 waveform for v = 2*108 m/s peaks about 20 ns later th an the measured waveform and decays faster after peak value. The wavefo rm for v = c shows very good agreement with the measured waveform for the first 100 ns a nd decays to zero faster for later times. Note that the waveforms for v = 1*108 m/s in all figures are much slower than the corresponding measured waveform. The generally good match between the meas ured and calculated waveshapes for times before about 70 ns–100 ns past the peak value for the higher return stoke speeds is in support of the hypothesis that the return st roke propagates with a speed close to the speed of light at early times of the return stroke process. The dE/dt waveshapes of strokes S9934-6 and S9934-7 suggest a return stroke spee d close to the speed of light for the first 100 ns of the return stroke process. After 100 ns the measured waveform decays slower than the calculated waveforms for v = 2*108 and for v = c which might be indicative of a return stroke speed < 2*108 m/s after 100 ns. An interesting fe ature is the very fast rise of the initial 50 ns in the measured wave form of stroke S9934-6. The TLM fails to reproduce this very fast rise and gives much sl ower slopes, even if v = c is used. The very fast rise might be indicative of (1 ) a bi-directional return stroke (Cha pter 2) for the first 50 ns and/or (2) the fact that the channel shape just above the strike rod was poorly modeled. The very fast rise at the beginning of the return stroke is also discernible in the dE/dt waveshape of stroke S9934-7, although it is necessary to examine the waveform on an expanded time scale to make that observati on. Figure 4-24 shows the first 80 ns of the measured dE/dt and the normalized calcula ted dE/dt for v = c for S9934-7. A 500 ns window of the same waveforms is displaye d in Figure 4-22 b). Clearly, the measured dE/dt is faster than the calculated dE/dt for the first 12 ns or so.

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155 Figure 4-19: Measured and model predicted el ectric field derivatives for three return stroke speeds for stroke S9934-6 (a) not normalized and (b) normalized. The model predicted waveform was calculated for a lean ing channel assuming the channel origin is at the bottom of the strike rod (Geometry II). 50 0 50 100 150 200 250 300 350 400 a) dE/dt, measured dE/dt, v = 1*108 m/s dE/dt, v = 2*108 m/s dE/dt, v = c dE/dt [kV/m/ µ s] 00.050.10.150.20.250.30.350.40.45 0 0.2 0.4 0.6 0.8 1 b)t [ µ s]

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156 Figure 4-20: Measured and model predicted el ectric field derivatives for three return stroke speeds for stroke S9934-6 (a) not normalized and (b) normalized. The model predicted waveform was calculated for a lean ing channel assuming the channel origin is shifted towards SATTLIF (Geometry III). 50 0 50 100 150 200 250 300 350 400 a) dE/dt, measured dE/dt, v = 1*108 m/s dE/dt, v = 2*108 m/s dE/dt, v = c dE/dt [kV/m/ µ s] 00.050.10.150.20.250.30.350.40.45 0 0.2 0.4 0.6 0.8 1 b)t [ µ s]

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157 Figure 4-21: Measured and model predicted el ectric field derivatives for three return stroke speeds for stroke S9934-7 (a) not normalized and (b) normalized. The model predicted waveform was calculated for a lean ing channel assuming the channel origin is at the bottom of the strike rod (Geometry II). 00.050.10.150.20.250.30.350.40.45 0 0.2 0.4 0.6 0.8 1 50 0 50 100 150 200 250 300 350 400 a) dE/dt, measured dE/dt, v = 1*108 m/s dE/dt, v = 2*108 m/s dE/dt, v = c dE/dt [kV/m/ µ s] b)t [ µ s]

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158 Figure 4-22: Measured and model predicted el ectric field derivatives for three return stroke speeds for stroke S9934-7 (a) not normalized and (b) normalized. The model predicted waveform was calculated for a lean ing channel assuming the channel origin is shifted towards SATTLIF (Geometry III). 00.050.10.150.20.250.30.350.40.45 0 0.2 0.4 0.6 0.8 1 50 0 50 100 150 200 250 300 350 400 a) dE/dt, measured dE/dt, v = 1*108 m/s dE/dt, v = 2*108 m/s dE/dt, v = c dE/dt [kV/m/ µ s] b)t [ µ s]

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159 Figure 4-23: Model predicted el ectric field derivatives for stroke S9934-6 for channel geometry I, II, and III and v = 2*108 m/s (a) not normalized and (b) normalized. 50 0 50 100 150 200 250 300 350 400 a) dE/dt, Geometry I dE/dt, Geometry II dE/dt, Geometry III dE/dt [kV/m/ µ s] 00.050.10.150.20.250.30.350.40.45 0 0.2 0.4 0.6 0.8 1 b)t [ µ s]

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160 Figure 4-24: Measured and model predicted electric field derivatives for v = c for stroke S9934-7 on an 80 ns time scale. Geometry III was assumed for the calculation. The circles indicate the sampling/calcu lated points of the waveforms. 4.5.3.2 Calculated and measured dB/dt Model predicted magnetic field derivativ es for r = 15 m were overlaid with measured magnetic field derivatives at 15 m. In Figure 4-25 and Figure 4-27 the model predicted electric field derivatives were ca lculated assuming a shifted leaning channel and the channel origin being at the bottom of the strike rod (geometry II described in Section 4.5.1) for stroke S9934-6 and S99347, respectively. In Figure 4-26 and Figure 4-28 the model predicted magnetic field deriva tives were calculated assuming a leaning channel in its original po sition with the channel origin shifted towards SATTLIF (geometry III described in Section 4.5.1) for stroke S9934-6 and S9934-7, respectively. The waveforms at the top of each figure are not normalized. The waveforms at the 01020304050607080 0 50 100 150 200 250 300 350 400 dE/dt [kV/m/ µ s] dE/dt, measured dE/dt, v = c t [ns]

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161 bottom of each figure are normalized and shifted in time for a comparison between the calculated and measured waveshapes. The peaks of the calculated and measured dB/dt waveforms in Figure 4-25 a) and Figure 4-27 a) (shifted slante d channel) give a reasonable match for a speed near 2*108 m/s and a speed between 1*108 and 2*108 m/s, respectively. The peaks of the calculated and measured dB/dt waveforms in Figure 4-26 a) and Figure 4-28 a) (slanted channel, shifted origin) give a reasonable match for speeds near 1*108 m/s. The normalized waveforms of the same flash calculated using the same speed for different channel geometries are essentially id entical as seen in Figure 4-25 Figure 4-28 for Geometry II and III for v = 1*108 m/s, v = 2*108 m/s, and v = c and illustrated in Figure 4-29 for Geometry I, II, and II for v = 2*108 m/s. Therefore, the dB/dt waveshapes calculated for different speeds can be compare regardless of channel geometry. The measured and calculated dB/dt waveshapes for v 2*108 m/s for stroke S9934-6 in Figure 4-25 b) and Figure 4-27 b) are similar for times 70 ns after the beginning of the dB/dt waveform. The measured waveshape ex hibits a sharp peak while the calculated peaks for all speeds are wider and more curved. The calculated waveforms for v = c in Figure 4-25 b) and Figure 4-26 b) provide the best overall fit to the measured waveform although the rising edge and the tail for times past half peak value for the calculated waveform using v = 2*108 m/s also gives a good match to the measured waveform. The measured and calculated dB/dt waveshapes for v 2*108 m/s in Figure 4-27 b) are very similar for all times. The calculated waveform for v = c peaks earlier than the measured waveform and the calculated waveform for v = 2*108 m/s peaks later. The measured peaks in Figure 4-25 b) and Figure 4-26 b) are narrower than any of th e calculated peaks.

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162 Note that the waveforms for v = 1*108 m/s in all figures are much slower than the corresponding measured waveform as seen be fore for measured and calculated dE/dt in Section 4.5.3. The best match in waveshape between m easured and calculated dB/dt waveforms in stroke S9934-6 and S9934-7 was achieved for v = c, although the calculated waveforms with v = 2*108 m/s also give a reasonable match. The TLM fails to reproduce the very fast rise in the measured dB/dt wa veform in Figure 4-25 at times in the rising signal before half peak and gives slower waveshapes a feature of the dE/dt waveform discussed in the previous sect ion and attributed to (1) a possible bi-direc tional return stroke at early times and/or (2) the poorly modeled lower channel geometry. Estimating the duration of the initial bi-directional return stroke is somewhat di fficult, since the very beginning of the magnetic field derivative due to the return stroke is obscured by the magnetic field derivative due to the upward going leader, which is of the same polarity. Based on the trend of the dB/dt waveform, the dur ation of the fast rise can be estimated to be between 30 and 60 ns. The duration of the bi -directional return stroke was estimated to be 50 ns based on the dE/dt waveform in the pr evious chapter, which is within the range of the estimation based on the dB/dt waveform. Th e very fast rise is not discernible in the dB/dt record of stroke S9934-7, possibly because it is hidden in the dB/dt signature of the downward directed leader.

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163 Figure 4-25: Measured and model predicted ma gnetic field derivatives for three return stroke speeds for stroke S9934-6 (a) not normalized and (b) normalized. The model predicted waveform was calculated for a lean ing channel assuming the channel origin is at the bottom of the strike rod (Geometry II). 1000 800 600 400 200 0 a) dB/dt [ µ Wb/m2/ µ s] dB/dt, measured dB/dt, v = 1*108 m/s dB/dt, v = 2*108 m/s dB/dt, v = c 00.050.10.150.20.250.30.350.40.45 1 0.8 0.6 0.4 0.2 0 b)t [ µ s]

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164 Figure 4-26: Measured and model predicted ma gnetic field derivatives for three return stroke speeds for stroke S9934-6 (a) not normalized and (b) normalized. The model predicted waveform was calculated for a lean ing channel assuming the channel origin is shifted towards SATTLIF (Geometry III). 1000 800 600 400 200 0 a) dB/dt [ µ Wb/m2/ µ s] dB/dt, measured dB/dt, v = 1*108 m/s dB/dt, v = 2*108 m/s dB/dt, v = c 00.050.10.150.20.250.30.350.40.45 1 0.8 0.6 0.4 0.2 0 b)t [ µ s]

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165 Figure 4-27: Measured and model predicted ma gnetic field derivatives for three return stroke speeds for stroke S9934-7 (a) not normalized and (b) normalized. The model predicted waveform was calculated for a lean ing channel assuming the channel origin is at the bottom of the strike rod (Geometry II). 1200 1000 800 600 400 200 0 a) dB/dt [ µ Wb/m2/ µ s] dB/dt, measured dB/dt, v = 1*108 m/s dB/dt, v = 2*108 m/s dB/dt, v = c 00.050.10.150.20.250.30.350.40.45 1 0.8 0.6 0.4 0.2 0 b)t [ µ s]

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166 Figure 4-28: Measured and model predicted ma gnetic field derivatives for three return stroke speeds for stroke S9934-7 (a) not normalized and (b) normalized. The model predicted waveform was calculated for a lean ing channel assuming the channel origin is shifted toward SATTLIF (Geometry III). 1200 1000 800 600 400 200 0 a) dB/dt [ µ Wb/m2/ µ s] dB/dt, measured dB/dt, v = 1*108 m/s dB/dt, v = 2*108 m/s dB/dt, v = c 00.050.10.150.20.250.30.350.40.45 1 0.8 0.6 0.4 0.2 0 b)t [ µ s]

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167 Figure 4-29: Model predicted magnetic field de rivatives for stroke S9934-6 for channel geometry I, II, and III and v = 2*108 m/s (a) not normalized and (b) normalized. 1000 800 600 400 200 0 a) dB/dt [ µ Wb/m2/ µ s] dB/dt, Geometry I dB/dt, Geometry II dB/dt, Geometry III 00.050.10.150.20.250.30.350.40.45 1 0.8 0.6 0.4 0.2 0 b)t [ µ s]

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168 4.5.4 Effect of Return Stroke Speed on Electromagnetic Field Derivatives of a Vertical and Slanted Lightning Channel The effect on return stroke speed on th e electromagnetic field derivative peaks and the field waveshape (characterized by 3090% rise-time and half peak width) is investigated in this section. Return stroke fi eld derivatives at 15 m are calculated for 12 speeds ranging from 8*107 to the speed of light c using the measured dI/dt of stroke S9934-6 as input to the transmission line model. The calculations were made for a vertical channel and for a slan ted channel with the channel origin being the bottom of the strike (geometry I and geometry II, respectively, described in Section 4.5.1)). Peaks, risetimes, and half peak widths of the calculat ed waveforms are plotted against the return stroke speeds used in the calculation. 4.5.4.1 Electromagnetic Fi eld Derivative Peaks Figure 4-30 shows electric and magnetic fiel d derivative peaks at 15 m calculated from measured dI/dt of stroke S9934-6 plotted against the sp eed used for the calculation. Geometry I (vertical channel) and geometry II (slanted channel with origin at the bottom of the strike rod) describe d in Section 4.5.1 were used for the calculations. The field derivative peaks gradually increase with increas ing speed (the dE/dt peak of the vertical calculated for 108 m/s being the exception). The dB/d t peak doubles (vertical and slanted channel) if the speed is changed from 8*107 m/s to c. The dE/dt peak increases by 15% (vertical channel) and 20% (slanted cha nnel) if the speed is changed from 8*107 m/s to c. The dB/dt peaks for the slanted channel are between 15% (v = 8*107 m/s) and 20% (v = c) lower than the corresponding dB/dt peaks for the vertical channel. The dE/dt peaks for the slanted channel and for all speeds are about 26% lower than the corresponding dE/dt peaks for the vertical channel.

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169 Figure 4-30: Calculated el ectromagnetic field derivative peaks at 15 m for a slanted/vertical channel using transmission line model and measured dI/dt of stroke S9934-6 vs. corresponding return stroke speed. dB/dt Peak [ µ Wb/m2/ µ s] 400 500 600 700 800 900 1000 1100 dB/dt, Slanted Channel dB/dt, Vertical Channel velocity [m/s] 1e+82e+83e+8 dE/dt Peak [kV/m/ µ s] 180 200 220 240 260 280 300 320 dE/dt, Slanted Channel dE/dt, Vertical Channel

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170 This observation suggests that dE/dt peaks are more sensitive to channel lean than dB/dt peaks, in particular if low speeds are assumed. Note that the field derivative peaks for the slanted channel are lower than the peaks for the vertical channel because the channel is inclined away from the antennas. They would be larger if the channel were inclined towards the antennas. 4.5.4.2 Electromagnetic Fiel d Derivative Waveshape Figure 4-31 shows 30-90% rise-times and half peak widths of electric and magnetic fields derivatives at 15 m, calculate d from the measured dI/dt of stroke S99346, plotted against the speed used for the calcu lation. Geometry I (vertical channel) and geometry II (slanted channel with origin at the bottom of the strike rod) described in Section 4.5.1 were used for the calculations. The half peak widths of the electric a nd magnetic field derivatives for the slanted channel are very similar to the half peak wi dth of the same parameter calculated using the same speed for a vertical channel. The 30-90% rise-time of dE/dt for a slanted channel is appreciably lower (about 25%) th an the rise-time for a verti cal channel if a speed of 8*107 m/s is used for the calculations. The rise -time for dE/dt for a slanted channel using v > 108 m/s and dB/dt for a slanted channel using v > 8*107 m/s are very similar to the corresponding rise-time of the same parameter and same sp eed for a vertical channel the slight difference getting even smaller for highe r speeds. It can be seen that, based on the above results from TLM calculations, a channel inclination of < 20º does not considerably affect the waveshape of the electromagnetic field de rivative if speeds > 108 m/s are used for the calculation.

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171 Figure 4-31: Calculated electromagnetic field derivative ri se-time and half peak width at 15 m for a slanted/vertical channel using tran smission line model and measured dI/dt of stroke S9934-6 vs corresponding return stroke speed. 30 90 % Rise Time [ns] 30 40 50 60 70 80 90 dB/dt, Slanted Channel dE/dt, Slanted Channel dB/dt, Vertical Channel dE/dt, Vertical Channel velocity [m/s] 1e+82e+83e+8 Half Peak Width [ns] 50 100 150 200 250 300 350 400

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172 The following correlations can be observed in Figure 4-31: 1) Half peak width and 30-90% rise-tim e for dB/dt and dE/dt become smaller for larger speeds. 2) Half peak width and 30-90% rise-time for dE/dt are more sensitive to speed variation than for dB/dt. 3) 30-90% rise-times for dE/dt and dB/d t are essentially the same if speeds 2*108 m/s are used for the calculations. 4) Half peak widths for dE/dt and dB/dt (sla nted and vertical channel) are exactly the same if v = c is used for the calculations. 5) 30-90% rise-times for dE/dt and dB/dt (s lanted and vertical channel) are exactly the same if v = c is used for the calculations. Observation 3) shows that the wavehapes of the modeled dE/dt and dB/dt rising edges are very similar for large speeds (v 2*108), which implies that actual dE/dt and dB/dt rising edges are also very sim ilar if the return stroke speed is large and if the TLM is valid. Observations 4) and 5) are as expected since the wave shape dE/dt and dB/dt are the same if the transmission line model with v = c is used, as discussed by Thotapillil et al. [2001]. 4.6 Summary and Discussion 4.6.1 Speed and Distance Dependence of Field Derivatives at 15 m In Section 4.4.1 electromagnetic field deri vatives were calculated at 15 m using the TLM for speeds between 1*108 m/s and the speed of light c. The following dependencies of the calculated electromagnetic field deriva tives on speed within the examined speed range were observed: For dE/dt and dB/dt the peak s are larger and the waveform faster and narrower if a larger speed is used in the calculation. For dE/dt the relative co ntribution of radiation, in duction, and electrostatic components to the peak at 15 m depends strongly on the assumed return stroke

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173 speed if the return stroke speed is assumed to be < 2*108 m/s. The relative contribution of the three components doe s not change much for speeds between 2*108 m/s and 3*108 m/s. For dB/dt at 15 m the contribution of radiation and induction components to the peak is about 40% and 60%, respectivel y. The relative contribution of radiation and induction component to the total dB/dt is relatively invarian t for all examined speeds. In Section 4.4.2 electromagnetic field deri vatives were calculated at 1 m, 10 m, and 100 m using the TLM for v = c. The following dependencies of the calculated electromagnetic field derivatives on distances within the examined distance range were observed: For dE/dt and dB/dt at any distance the wa veshapes are identical to the causative dI/dt for the special case v = c. For dE/dt at very close distances (1 m) essentially only the static and induction components contribute to the peak value with the static component being the largest component (140% of the peak va lue) and the induction component being of opposite polarity (-40%). For distances near 15 m the static, induction, and radiation component contribu te roughly equally to the peak values. For large distances the radiation compone nt is the dominant component. For dB/dt at very close distances (1 m) the induction component is dominant. For dB/dt near 15 m the induction compone nt and radiation components contribute approximately equally to the peak value. For dB/dt at large distances (> 100 m) the radiation component is the dominant component. Thottappillil et al. [2001] applied the TLM for v = c. They showed analytically that the electric and magnetic fields/field de rivatives at any point in space (except for points along the direction of the channel) have exactly the same waveshapes as the waveshape of the causative current/current de rivative. Additionally they showed that the field/field derivatives decay as 1/r at all distances. The simila rities in waveshapes and the inverse distance dependence of the fields/field derivatives are also a characteristic of radiation fields/field derivatives for arbitrary return stroke speeds. In fact, Uman et al.

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174 [2000] considered the po ssibility of a dominant radiati on field in their electric field derivative data between 10 and 30 m based on th e similarities between their electric field derivative waveforms at the two distances and the corresponding current derivative waveform. One result presented in this thesis is that, if the transmission line model is applicable at early times in the triggered light ning return stroke pro cess, the electric and magnetic radiation field components become the largest components beyond distances of about 15 m but are by no means dominant for dist ances well less than 100 m, as shown in Section 4.4. Therefore, assuming the TLM is valid, the cause for the waveshape similarities observed by Uman et al. [2000] is likely a return stroke speed near the speed of light and not a dominant radiation fiel d. It is worth noting that, although the waveshapes of the total field and current deri vatives are exactly the same for v = c, the waveshapes of the individual electric and ma gnetic field components change drastically with distance and different components are dom inant at different distances. This implies that the traditional division of field components is not unique. Thottappillil and Rakov [2001] showed this analytically by dividing the fields in othe r ways while maintaining the same total field. 4.6.2 Similarities of Waveshapes in Ou r Measured Field and Current Derivative Data The experimental data presented in Secti on 4.5.2 show that dE/dt, dB/dt, and dI/dt waveshapes are very similar for the first 150 ns or so after the init iation of the return stroke. It is shown in S ection 4.5.4 that, based on tran smission line modeling, the waveshapes of the dE/dt and dB/dt rising edges are relatively invariant for a return stroke speed v 2*108 m/s and the total waveshapes are exactly the same for v = c. Furthermore, it is shown in the same sect ion that the waveshape does not depend much

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175 on channel inclination, for inclinations less than 20 ° , if the return stroke speed is larger than 108 m/s. Therefore, the observed similarity in dE/dt, dB/dt, and dI/dt waveshapes for the first 150 ns or so implies that the return stroke speed is equal or larger than 2*108 m/s for this time. 4.6.3 Modeling dE/dt and dB/dt Peaks using the TLM The TLM fails to reproduce well the electric field derivative peaks if a shifted inclined channel and a channel origin at the bottom of the st rike rod (geometry II described in Section 4.5.1) is assumed. The peak values of the calculated dE/dt for strokes S9934-6 and S9934-7 using speeds between 1*108 m/s and c and assuming geometry II are considerably lower (about 30%) than the measured dE/dt peaks. The TLM models the electric field derivatives very well if the inclined channel in its original position and a shifted channel origin are a ssumed (geometry III described in Section 4.5.1). The calculated dE/dt peaks for stroke S9934-6 are 12%, 7%, and 3% smaller than the measured peaks for v = 1*108 m/s, v = 2*108 m/s, and v = c, respectively. The calculated dE/dt peaks for stroke S9934-7 are es sentially identical to the measured peaks for v = 1*108 m/s, v = 2*108 m/s, and v = c. Although the best match between calculated and measured dE/dt peaks for stroke S9934-6 is achieved for v = c (3%), the difference between calculated and measured dE/dt peaks for v = 2*108 m/s (7%) is probably smaller than the measurement error and errors in the calculated dE/dt peaks caused by inaccuracies in determining the channel ge ometry. Note that dE/dt peaks are very sensitive to the channel geometry and relativ ely insensitive to speed variation, as shown in Section 4.5.4. Therefore, it is not appropriate to infer th e exact return stroke speed based on the comparison between measured and calculated dE/dt peaks. However, it is

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176 important to note how well the TLM works in reproducing the measured dE/dt peaks if the channel geometry is pr operly taken into account. The measured dB/dt peaks for strokes S9934-6 and S9934-7 are reasonably well modeled for a shifted inclined channel and a channel origin at the bottom of the strike rod (geometry II) if a speed about 2*108 m/s is used as an input to the TLM. For an inclined channel in its original position and a shif ted channel origin (geometry III) a good match between measured and model predicted dB/dt peaks is achieved for a speed between v = 1*108 m/s and 2*108 m/s (S9934-6), and v = 1*108 m/s (S9934-7). The dB/dt antennas were aligned to measure the dB/dt of a channe l originating at the bottom of the strike rod and not aligned to measure the total dB/dt of the channel or iginating from the “virtual” channel origin. Therefore, the measured dB/d t is underestimated (assuming that geometry III gives the best approximation of the actual channel geometry), since the magnetic flux through the dB/dt antenna loop is smaller due to the misalignment. Consequently, the return stroke speeds determined above fr om matching measured and calculated dB/dt peaks for geometry III are also underestimated. Therefore, in ference on the re turn stroke speed from matching measured and calculated dB/dt peaks is error-prone since the dB/dt antenna does not measure the total dB/dt if the channel origin (“virtual” or actual) is shifted. Note that if the channel is straight and vertical, our dB/d t antenna measures the total dB/dt and the return stroke speed in ferred from matching meas ured and calculated dB/dt peaks should be close to th e actual return stroke speed if the TLM is valid at early times. 4.6.4 Initial Fast Rise in Our dE/dt and dB/dt Data The waveshapes of the measured dE/dt and dB/dt of stroke S9934-6 and the measured dE/dt of stroke S9934-7 are faster in their ini tial rise than the calcu lated field derivatives

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177 using the TLM and v = c (the speed that give s the fastest rise of the calculated field derivatives is the speed of light c). It is s hown in Section 4.4 that the radiation component of the electromagnetic field derivative is domin ant for the first 50 ns or so. Therefore, the fast rise might be indicative of an enhanced radiation field. Possible causes for this could be the eff ect of the 2-m strike rod and a potential upward-going connecting leader of some meter length initiated at the top of the rod prior to return stroke formation [Wang et al ., 1999], and the poorly modeled lower-channel geometry. The return stroke can be viewed as starting at the top of the upward connecting leader and propagating both upward and downw ard, with some fraction of the downward wave reflecting upward from the strike object and also from the ground. The electromagnetic field radiated in this process is of the same polarity as the electromagnetic field radiated by the upward going return st roke, since the two return strokes are traveling in oppos ite directions and neutralize charge of opposite polarities. The measured electromagnetic field derivatives necessarily contain contributions of both return stroke waves while the calculated field derivatives is found from the current derivative measured at the channel base, whic h is thought to be associated only with the downward return stroke and its reflection at ground [Rakov and Uman, 1998]. Therefore, the measured electromagnetic field derivatives are expected to be faster for the time required for the downward return stroke wave to reach ground. For the following considerations it is assumed that the reflected wave s at the strike rod do not contribute signifi cantly to the measured electromagnetic fields–a simplification that might not necessarily be true but might be a ppropriate to give a r easonable estimation of the upward connecting leader le ngth. In Section 4.5.3 the durati on of the fast rise in the

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178 dE/dt and dB/dt data was estimated to be 50 ns for stroke S9934-6 and 12 ns for stroke S9934-7. The propagation speed of the return stroke through the 2-m strike rod is expected to be the speed of light. Therefore, the return st roke would travel about 7 ns through the strike rod and for th e rest of the time, i.e., 43 ns for stroke S9934-6 and 5 ns for stroke S9934-7, through the upward connect ing leader channel. Assuming that the return stroke propagates through the channel with at speed between 2*108 m/s and c, the length of the upward propagating leader can be estimated to be 9-13 m for stroke S99346 and 1-2 m for stroke S9934-7. Wang et al . [1999] estimated the upward connecting discharge length of two stroke s to be 7-11 m and 4-7 m, respectively. Note that the bottom 5 m or so of the return stroke channel is inclined in a different direction from the top part of the channel, as seen the middle a nd right frame in Figure 4-13 b). It might be that the bottom part of the channel was pr eceded by an upward connecting leader that was inclined in a different di rection from the top part of the channel, which was preceded by a downward directed leader following the triggering wire.

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179 CHAPTER 5 RECOMMENDATIONS FOR FUTURE RESEARCH The results presented in this chapter were based on dI/dt data, dB/dt data at 15 m, and dE/dt data at 15 m for two return strokes. It is necessary to determine the channel geometry accurately in order to test return stroke models, since the channel geometry has a considerable impact on the calculated el ectromagnetic field derivatives at close distances, as shown in this chapter. It is recommended that for future close field derivative calculations more care must be taken in determining the channel geometry. Using two high speed video cameras that record the bottom 50 m of the channel1 and that are positioned so that their lines of view are at an angle of 90 ° to each other would be sufficient to determine accurately the ch annel geometry. Additionally, it would be interesting to do return stroke modeling for strokes where the return stroke channel was determined to be straight and vertical, so th at more general results could be obtained and simpler equations could be used fo r the field derivative calculations. A comparison of different return stroke m odels would also be interesting, since the transmission line model might not be th e best model to use for reproducing the measured electromagnetic field derivatives. Measuring electromagnetic signatures of the return stroke at different distances and applying various return stroke models to reproduce the measured data would give further insight into the close lightning electromagnetic environment. 1 The bottom 50 m of the lightning cha nnel produces the major part of the electromagnetic field derivative waveforms.

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180 LIST OF REFERENCES Bach, J.A.; "Instrumentation for Measuri ng Electric and Magnetic Fields at Different Distances from a Lightning Disc harge"; Master's thesis, University of Florida; 1996 Baum, C. E.; "Return-Stroke Initiati on"; Lightning Electromagnetics, pp. 101-114, Hemisphere, New York; 1990 Borovsky, J. E.; "An Electrodynamic Decrip tion of Lightning Return Strokes and Dart Leaders: Guided Wave Propagati on along Conducting Cylindrical Channels"; Journal of Geophysical Res earch, Vol. 100, pp. 2697-2726; 1995 Diendorfer, G. and M. A. Uman; “A n Improved Return Stroke Model with Specified Channel-Base Current”; Journa l of Geophysical Research, Vol. 95, No. D9, pp. 13621-13644; 1990 Henry, J. A., K. M. Portier, and J. Co yne; The Climate and Weather of Florida; Pineapple Press, Sarasota, Florida; 1994 Idone, V.P. and R. E. Orville; "Light ning Return Stroke Velocities in the Thunderstorm Research International Pr ogram (TRIP)"; Journal of Geophysical Research, Vol. 87, pp. 4903-4915; 1982 Idone, V. P., R. E. Orville, P. Hubert, L. Barret, and A. Eybert-Berard; "Correlated Observations of Three Triggered Ligh tning Flashes"; Journal of Geophysical Research, Vol. 89, pp. 1385-1394; 1984 Jordan, D., M. A. Uman; "Variations of Li ght Intensity with Height and Time from Subsequent Return Strokes"; Journal of Geophysical Research, Vol. 88, pp. 65556562; 1983 Krider, E. P.; "On the Electromagnetic Fi elds, Poynting Vector, and Peak Power Radiated by Lightning Return Strokes"; Jo urnal of Geophysical Research, Vol. 97, No. D14, pp. 15913-15917; 1992 Kuehr, W.; “Der Privatflugzeugfuehr er”; Schiffmann Verlag, Forchheim; 1996 Leteinturier, C., C. Weidman, and J. Hamelin; "Current and Electric Field Derivatives in Triggered Lightning Retu rn Strokes"; Journal of Geophysical Research, Vol. 95, pp. 811-828; 1990

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181 Le Vine, D. M. and J. C. Willet; "Comment on the Transmission-Line Model for Computing Radiation From Lightning"; J ournal of Geophysical Research, Vol. 97, No. D2, pp. 2601-2610; 1992 Moini, R., V. A. Rakov, M. A. Uman, and B. Kordi; "An Antenna Theory Model for the Lightning Return Stroke"; Proc. 12th Int. Zurich Symp. Electromagnetic Compat., Zurich, Switzerland"; 1997 Moore, Gene, Lightning and Storms; http://www.chaseday.com/lightning.htm; 04/24/2002 Nucci, C. A., G. Diendorfer, M. A. Uman, F. Rachidi, M. Ianoz, and C. Mazzetti; "Lightning Return Stroke Current Models With Specified Channel-Base Current: A Review and Comparison"; Journal of Ge ophysical Research, Vol. 95, No. D12, pp. 20395-20408; 1990 Oetzel, G. N.; "Computation of the Diameter of a Lightning Return Stroke"; Journal of Geophysical Research, Vol. 73, pp. 1889-1896; 1968 Paxton, A. H., R. L. Gardner, and L. Bake r; "Lightning Return Stroke: A Numerical Calculation of the Optical Radiation" ; Phys. Fluids, Vol. 29; pp. 2736-2741; 1986 Paxton, A. H., R. L. Gardner, and L. Bake r; "Lightning Return Stroke: A Numerical Calculation of the Optical Radiation" ; Lightning Electromagnetics, pp. 47-61, Hemisphere, New York; 1990 Podgorski, A. S. and J. A. Landt; "Thr ee Dimensional Time Domain Modeling of Lightning"; IEE Trans. Power Del., Vol. PWRD-2, pp. 931-938; 1987 Rakov, V. A.; "Lightning Discharges triggered using Rocket-and-Wire Techniques"; Recent Res. Devel. Geophysics, pp. 141-171; 1999 Rakov, V.A.; EEL 5490 “Lightning” classnotes; University of Florida, Spring Term 2001 Rakov, V. A. and M. A. Uman; "Review a nd Evaluation of Lightning Return Stroke Models Including Some Aspects of Thei r Application"; I EE Transactions on electromagnetic compatibili ty, Vol. 40, No. 4; 1998 Schonland, B. F. J. and H. Collens; "Progr essive Lightning"; Proc. R. Soc. London Ser. A, Vol. 143, pp. 654-674; 1934 Schonland, B. F. J., D. J. Malan, and H. Collens; "Progressive Lightning II"; Proc. R. Soc. London Ser. A, Vol. 152, pp. 595-625; 1935

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182 Simpson, G. and F.J. Scrase; “The Distribution of Electricity in the Thunderclouds”; Proc. R. Soc. London Ser. A, 161: 309-352, 1937 Strawe, D. F.; "Non-Linear Modeling of Lightning Return Strokes"; Proc. Fed. Aviat. Admin./Florida Inst. Technol . Workshop Grounding Lightning Technol., pp. 9-15; 1979 Thottappillil, R., D. K. McLain, M. A. Um an, and G. Diendorfer; "Extension of the Diendorfer-Uman Lightning Return Stroke Mo del to the Case of a Variable Upward Return Stroke Speed and a Variable Down ward Discharge Current Speed"; Journal of Geophysical Research, Vol. 96, No. D9, pp. 17143-17150; 1991 Thottappillil, R. and M.A. Uman; "Com parison of Lightning Return-Stroke Models"; Journal of Geophysical Re search, Vol. 98, No. D12, pp. 22903-22914; 1993 Thottappillil, R., and M.A. Uman; "Light ning Return Stroke Model with HeightVariable Discharge Time C onstant"; Journal of Geophysic al Research, Vol. 99, No. D11, pp. 22773-22780; 1994 Thottappillil, R., V. A. Rakov, and M. A. Uman; "Distribution of Charge along the Lightning Channel: Relation to Remote Electr ic and Magnetic Fiel ds and to ReturnStroke Models"; Journal of Geophysi cal Research, Vol. 102, No. D6, pp. 69877006; 1997 Uman, M.A.; "The Lightning Discharge"; Dover Publications, Mineola, New York; 1987 Uman, M. A., D. K. McLain, and E. P. Krider; "The Electromagnetic Radiation from a Finite Antenna"; Amer. J. Phys., no. 43, pp. 33-38; 1975 Uman, M.A., Y. T. Lin, and E. P. Krid er; "Errors in Magnetic Direction Finding due to Nonvertical Lightning Channels"; Radio Science, Volume 15, No. 1, pp. 3539; 1980 Uman, M.A., V.A. Rakov, R. Thottappillil, J. Versaggi, A. EyebertBerard, L. Barret, P.P. Barker, S.P. Hnat; "Multip le-Station Measurement of Close Electric and Magnetic Fields Produced by Triggered Lightning Discharges"; Fall meeting of the AGU, San Fransisco; 1993 Uman, M. A., Rakov, G. H. Schnetzer, K. J. Rambo, D. E. Crawford, and R. J. Fisher; "Time Derivative of the Electri c Field 10, 14, and 30 m from Triggered Lightning Strokes"; Journal of Geophysic al Research, Vol. 105, No. D12, pp. 15577-15595; 2000

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183 Wang, D., V. A. Rakov, M. A. Uman, N. Taka gi, T. Watanabe, D. E. Crawford, K. J. Rambo, G. H. Schnetzer, R. J. Fisher , and Z.-I. Kawasaki; "Attachment Process in Rocket-Triggered Lightning Strokes"; Journal of Geophysical Research, Vol. 104, No. D2, pp. 2143-2150; 1999b Willett, J.C., V. P. Idone, R. E. Orville, C. Leteinturier, A. Eybert-Berard, L. Barret, and E. P. Krider; "An Experimental Test of the "Transmission-Line Model" of Electromagnetic Radiation From Triggered Lightning Return Strokes"; Journal of Geophysical Research, Vol. 93, No. D4, pp. 3867-3878; 1988 Willett, J.C., J.C. Bailey, V. P. Idone, A. Eybert-Berard, and L. Barret; "Submicrosecond Intercomparison of Radia tion Fields and Currents in Triggered Lightning Return Strokes Based on the Tr ansmission-Line Model"; Journal of Geophysical Research, Vol. 94, No. D11, pp. 13275-13286; 1989 Williams, E. R., "Das Gewitter als elektrischer Generator"; Spektrum der Wissenschaft, pp.80-89; January 1989

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184 BIOGRAPHICAL SKETCH Jens Schoene was born in Neheim, Germ any, in 1972. He graduated with a degree in electrical engineering from the University of Paderborn, Department Soest, in 1999. In 1999 he moved to the United States to pursue graduate studies at the University of Florida.