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Triggered-Lightning Properties Inferred from Measured Currents and Very Close Magnetic Fields


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TRIGGERED-LIGHTNING PROPERTIES INFERRED FROM MEASURED CURRENTS AND VERY CLOSE MAGNETIC FIELDS By ASHWIN B. JHAVAR A THESIS 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 2005

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Copyright 2005 by Ashwin B. Jhavar

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iii ACKNOWLEDGMENTS I would like to thank Dr. Vladimir A. Rakov for his infinite patience, guidance, and support throughout my graduate studies at the Un iversity of Florida. I would like to thank Dr. Martin A. Uman and Dr. Douglas M. Jord an for their valuable suggestions during the weekly lightning meetings. I sincerely tha nk Jens Schoene, Jason Jerauld, Rob Olsen, Brian DeCarlo, and Vinod Jayakumar for helpi ng me with the data and software, and for other innumerable favors (without which I woul d not have been able to complete my thesis). Research in my thesis was funde d in part by National Science Foundation. The data analyzed in the thesis were orig inally acquired with NSF and FAA funding.

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iv TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iii LIST OF TABLES.............................................................................................................vi LIST OF FIGURES..........................................................................................................vii ABSTRACT.....................................................................................................................xi ii CHAPTER 1 INTRODUCTION........................................................................................................1 2 LITERATURE REVIEW.............................................................................................3 2.1 Cumulonimbus........................................................................................................3 2.2 Cloud Charge Distribution......................................................................................4 2.3 Mechanisms of Cloud Electrification.....................................................................6 2.3.1 Convection Mechanism................................................................................7 2.3.2 Graupel-ice Mechanism................................................................................7 2.4 Downward Negative Lightni ng Discharges to Ground........................................10 2.5 Artificial Initiation (Tri ggering) of Lightning Us ing the Rocket-and-Wire Technique...............................................................................................................15 2.5.1 Classical Triggering....................................................................................16 2.5.2 Altitude Triggering.....................................................................................18 2.6 Previous Studies of Displacement Current Associated with Triggered Lightning................................................................................................................19 2.6.1 Theory.........................................................................................................19 2.6.2 Estimation of Displacement Current Contribution at 50 m........................21 3 CHARACTERIZATION OF EXPERIMENTAL DATA USED IN THIS STUDY.25 3.1 Magnetic Field Measuring Techniques................................................................25 3.2 Experimental Setup...............................................................................................27 3.2.1 ICLRT Overview........................................................................................27 3.2.2 1997 Experiments.......................................................................................29 3.2.3 1999 Experiments.......................................................................................30 3.2.3.1 Instrumentation for Current Measurements.....................................32 3.2.3.2 Instrumentation for Electric Field Measurements............................33

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v 3.2.3.3 Instrumentation for Electric Field Derivative Measurement............33 3.2.4 2000 Experiments.......................................................................................33 3.2.5 2001 Experiments.......................................................................................35 3.3 Data Presentation..................................................................................................36 3.3.1 General Information...................................................................................36 3.3.2 Channel-base current..................................................................................40 3.3.3 Magnetic Field............................................................................................42 3.3.4 Electric field derivative (dE/dt)..................................................................47 4 ESTIMATION OF LEADER AND RE TURN-STROKE CURRENTS FROM MEASURED MAGNETIC FIELDS..........................................................................51 4.1 Introduction...........................................................................................................51 4.2 Estimation of Currents Using Amperes Law......................................................51 4.3 Discussion and Summary.....................................................................................77 5 DISPLACEMENT CURRENT ASSOCI ATED WITH LEADER/RETurN STROKE SEQUENCES IN TRIGGERED LIGHTNING.........................................80 5.1 Displacement Current Estimates fr om Measured Magnetic Fields and Channel-Base Currents..........................................................................................80 5.2 Displacement Current Estimates from dE/dt Signatures at 15 and 30 m.............92 5.3 Discussion and Summary...................................................................................106 6 SUMMARY..............................................................................................................108 7 RECOMMENDATIONS FOR FUTURE RESEARCH..........................................112 APPENDIX DISPLACEMENT CURRENT GRAPHS.................................................113 LIST OF REFERENCES.................................................................................................144 BIOGRAPHICAL SKETCH...........................................................................................147

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vi LIST OF TABLES Table page 2-1 Displacement currents Id estimated from measured electric field data at times prior to and at the onset of a 20 kA peak stroke current..........................................22 3-1 Summary of mean, standard deviation, GM (geometric mean), and sample sizes of measured peak current, peak magnetic field and electric field derivative...........37 5-1 Displacement currents estimated using eq. 5.4 (step-wise approximation of dE/dt distance dependence) and eq. 5.5 (linear approximations of dE/dt distance dependence)..............................................................................................................95 5-1 (Contd.) Displacement currents estimated using eq. 5.4 (step-wise approximation of dE/dt distance dependen ce) and eq. 5.5 (linear approximations of dE/dt distance dependence)..................................................................................96

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vii LIST OF FIGURES Figure page 2-1 An isolated thundercloud in central New Mexico, with a ru dimentary indication of how electric charge is thought to be distribu ted inside and around the thundercloud, as inferred from the remote and in situ observations..........................5 2-2 Balloon measurements of corona current and the inferred vertic al electric field E versus altitude and air te mperature inside a small st orm in New Mexico on 16 August 1981, which produced no lightning...............................................................6 2-3 Illustration of the convection m echanism of cloud electrification.............................8 2-4 Charge transfer by collision in the graupel-ice mechanism of cloud electrification. It is assumed that the reversal temperature TR is -15 oC and that it occurs at a height of 6 km.......................................................................................9 2-5 A vertical tripole representing the idealized gross charge structure of a thundercloud such as that shown in Fi gure 2-1; the negati ve screening layer charges at the cloud top and the posit ive corona space charge produced at ground are ignored here............................................................................................10 2-6 Various processes comprising a ne gative cloud-to-ground lightning flash.............11 2-7 Sequence of events in classical trig gered lightning. The upward positive leader and initial continuous current constitute the initial stage.........................................16 2-8 Sequence of events in altitude-triggere d lightning leading to the establishment of a relatively low-resistance connectio n between the upward-moving positive leader tip and the ground. The processe s that follow the sequence shown, an initial continuous-current and possibly one or more downward-leader--upwardreturn-stroke sequences, are similar to th eir counterparts in classical triggered lightning. The rocket speed is of the order of 102 m s-1...........................................18 2-9 Qualitative illustration of the shape of the time derivative of the ground level vertical electric field of a nearby return stroke Since displacement current density is simply related to the derivativ e of electric field by a constant, it has the same waveshape.................................................................................................24

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viii 2-10 From top to bottom, magnetic field m easured at 50 m during stroke 5 of Flash 96-23, the corresponding field according to Amperes law for magnetostatics, as applied to the measured channel-base current, and the difference between the two............................................................................................................................ 24 3-1 Thevenin equivalent circuit of a loop antenna.........................................................25 3-2 Norton equivalent circ uit for a loop antenna............................................................26 3-3 An overview of the ICLRT at Camp Blanding, Florida, 1999-2001. Not all test objects are shown.....................................................................................................28 3-4 Photograph of lightning flash S0012 tr iggered from the underground launcher.....28 3-5 Locations of different instrument ation stations for 1997 multiple station experiment................................................................................................................30 3-6 Data acquisition system used in the 1997 multiple-station experiment...................31 3-7 Experimental setup (placement of elect ric and magnetic field antennas) used in SATTLIF for 2000...................................................................................................34 3-8 Setup of strike rod and ring m ounted over launch tubes in 2000.............................35 3-9 Measured channel-base cu rrent, Flash S9901, Stroke 3...........................................37 3-10 Magnetic field at 15 m, Flash S9901, Stroke 3........................................................38 3-11 Magnetic field at 30 m, Flash S9901, Stroke 3........................................................38 3-12 Electric field derivative (dE/dt) at 15 m, Flash S9901, Stroke 3.............................39 3-13 Electric field derivative (dE/dt) at 30 m, Flash S9901, Stroke 3.............................39 3-14 Return-stroke peak currents in (a) 1997, (b) 1999, (c) 2000, and (d) 2001.............40 3-15 Return-stroke peak currents in 1997, 1999, 2000 and 2001.....................................41 3-16 Peak magnetic fields measured at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997..........................................................................................................................4 2 3-17 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1999...........................43 3-18 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 2000...........................44 3-19 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 2001...........................45 3-20 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1997, 1999, 2000 and 2001..........................................................................................................................4 6

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ix 3-21 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999.................................47 3-22 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 2000.................................48 3-23 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 2001.................................49 3-24 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999, 2000 and 2001.......50 4-1 A straight current channel of in finite length and B at a distance r...........................51 4-2 A streaked-image diagram of a dart l eaderreturn-stroke sequence in a rockettriggered lightning flash...........................................................................................52 4-3 Magnetic field at 15 m, Flash S9901, Stroke 3........................................................54 4-4 Magnetic field at 30 m, Flash S9901, Stroke 3........................................................54 4-5 Dart leader current inferred usi ng Amperes Law for magnetostatics from measured magnetic fields at (a) 5 m, (b ) 10 m, (c) 20 m, and (d) 30 m in 1997......55 4-6 Dart leader current inferred usi ng Amperes Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 1999....................................56 4-7 Dart leader current inferred usi ng Amperes Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 2000....................................57 4-8 Dart leader current inferred usi ng Amperes Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 2001....................................58 4-9 Dart leader current inferred usi ng Amperes Law for magnetostatics from measured magnetic fields at 15 m in 1999, 2000, and 2001....................................59 4-10 Dart leader current inferred usi ng Amperes Law for magnetostatics from measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001..........................60 4-11 Dart leader current inferred usi ng Amperes Law for magnetostatics from measured magnetic fields measured at 30 m vs. that at 15 m in 1999, 2000, and 2001..........................................................................................................................6 1 4-12 Dart leader current inferred usi ng Amperes Law for magnetostatics from magnetic fields measured at 15 m vs. leader current inferred from dE/dt measurements in 1999, 2000, and 2001...................................................................62 4-13 Dart leader current inferred usi ng Amperes Law for magnetostatics from magnetic fields measured at 30 m vs. leader current inferred from dE/dt measurements in 1999, 2000, and 2001...................................................................63

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x 4-14 Return-stroke peak currents inferred using Amperes Law for magnetostatics from measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997..........................................................................................................................6 4 4-15 Return-stroke peak currents inferred using Amperes Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 1999...........................65 4-16 Return-stroke peak currents inferred using Amperes Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 2000...........................66 4-17 Return-stroke peak currents inferred using Amperes Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 2001...........................67 4-18 Return-stroke peak currents inferred using Amperes Law for magnetostatics from measured magnetic fields at 15 m in 1999, 2000, and 2001...........................68 4-19 Return-stroke peak currents inferred using Amperes Law for magnetostatics from measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001.................69 4-20 Return-stroke peak current inferred using Amperes Law for magnetostatics from measured magnetic fields at 30 m vs. that inferred from measured magnetic fields at 15 m in 1999, 2000, and 2001....................................................70 4-21 Return-stroke peak current inferred using Amperes Law for magnetostatics from measured magnetic fields at 15 m vs measured return-stroke peak current in 1999, 2000, and 2001...........................................................................................71 4-22 Return-stroke peak current inferred using Amperes Law for magnetostatics from measured magnetic fields at 30 m vs measured return-stroke peak current in 1997, 1999, 2000, and 2001.................................................................................72 4-23 Leader vs. return-stroke current s inferred using Amperes Law for magnetostatics from magnetic fields measured at 15 m in 1999, 2000, and 2001...73 4-24 Leader vs. return-stroke current s inferred using Amperes Law for magnetostatics from magnetic fields measured at 30 m in 1999, 2000, and 2001...74 4-25 Comparison of IRS from (BL+BRS)30m and IRS from (BL+BRS)15m for 1999, 2000, and 2001...................................................................................................................75 4-26 Comparison of IRS from (BL+BRS)15m inferred using Amperes Law for magnetostatics vs. IRS measured at channel base in 1999, 2000, and 2001.............76 4-27 Comparison of IRS from (BL+BRS)30m inferred using Amperes Law for magnetostatics vs. IRS measured at channel base in 1997, 1999, 2000, and 2001...77 5-1 Superposition of measured magnetic fi eld and channel-base current for Flash S9903, stroke 3.........................................................................................................81

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xi 5-2 Displacement current for S9903 RS3 as inferred, using Eq. 5.3, from Imeas and Hmeas at 30 m.............................................................................................................83 5-3 Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999....................................................................84 5-4 Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2000....................................................................85 5-5 Return-stoke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2001....................................................................86 5-6 Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999, 2000, and 2001..........................................87 5-7 Leader peak displacement curr ent estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999..............................................................................88 5-8 Leader peak displacement curr ent estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2000..............................................................................89 5-9 Leader peak displacement curr ent estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2001..............................................................................90 5-10 Leader peak displacement curr ent estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999, 2000, and 2001...................................................91 5-11 Distance dependences of dE/dt used in evaluating displacement current within 30 m of the lightning channel based on measured dE/dt at 15 and 30 m.................92 5-12 Return-stroke displacement current with in 30 m of the lightning channel at the time of dE/dt peak at 15 m estimated using step-wise approximation (with propagation delay taken into acc ount) in (a) 1999 and (b) 2000.............................97 5-13 Return-stroke displacement current with in 30 m of the lightning channel at the time of dE/dt peak at 15 m estimated using step-wise approximation (with propagation delay taken into account) in (a) 2001 and (b) 1999, 2000, and 2001...98 5-14 Return-stroke displacement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m estimated using stepwise approximation (without propagation delay taken into account) in (a) 1999 and (b) 2000.............................................................................................................99 5-15 Return-stroke displacement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m estimated using stepwise approximation (without taking propa gation delay into account) in (a) 2001 and (b) 1999, 2000, and 2001.................................................................................100

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xii 5-16 Return-stroke displacement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m estimated using linear approximation (without propagation delay taken into account) in (a) 1999 and (b) 2000..................................................................................................................101 5-17 Return-stroke displacement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m estimated using linear approximation (without taking propagation dela y into account) in (a) 2001 and (b) 1999, 2000, and 2001.................................................................................102 5-18 Scatter plot showing displacement curre nt estimates from dE/dt measured at 15 and 30 m from the lightning channel (s tep-wise approxima tion) vs. those estimated from measured channel base cu rrent and associated magnetic field. In the former case, the estimate corresponds to the time of peak value of dE/dt at 15 m........................................................................................................................103 5-19 Scatter plot showing displacement curre nt estimates from dE/dt measured at 15 and 30 m from the lightning channel (s tep-wise approxima tion) vs. those estimated from measured channel base cu rrent and associated magnetic field. In the former case, the estimate is obtained using peak values of dE/dt at both 15 and 30 m.................................................................................................................104 5-20 Scatter plot showing displacement curre nt from dE/dt measured at 15 and 30 m from the lightning channel (linear approximation) vs. those estimated from measured channel base current and associat ed magnetic field. In the former case, the estimate is obtained using peak va lues of dE/dt at both 15 and 30 m..............105

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xiii 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 TRIGGERED-LIGHTNING PROPERTIES INFERRED FROM MEASURED CURRENTS AND VERY CLOSE MAGNETIC FIELDS By Ashwin B. Jhavar December 2005 Chair: Vladimir A. Rakov Cochair: Martin A. Uman Major Department: Electrical and Computer Engineering Very close magnetic fields produced by ro cket-triggered lightning measured in 1997, 1999, 2000, and 2001 at Camp Blanding, Florid a, are examined. The leader and return stroke contributions to the total ma gnetic field are estimated and used to infer leader and return-stroke currents. The statistic al characteristics of these inferred currents are examined. The return-stroke currents in ferred from measured magnetic fields are compared with directly measured ones. Lead er currents inferred from measured magnetic fields are compared with those estimated usi ng dE/dt measurements. The statistics of the ratio of leader to return stroke currents are compiled. Current estimates from measured magnetic fields are in reasonable agreem ent with independent measurements and theoretical predictions found in the literature. From the statis tical analysis of 97 records obtained in 1999, 2000, and 2001 the mean leader current inferred from magnetic field at 15 m is 1.87 kA and standard deviation is 1.01 kA. For magnetic fields at 30 m (103 records obtained in 1997, 1999, 2000, and 2001), th e mean leader current is 2.58 kA and

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xiv the standard deviation is 1.57 kA. Typically leader currents are in the range of few kiloamperes. Displacement current associated with lead er/return stroke sequences in triggered lightning is estimated using (1) measured cha nnel-base current and current inferred from measured magnetic field and (2) dE/dt measurements at 15 and 30 m. The displacement currents found using the above two appro aches are compared. Return-stroke displacement current within 30 m of the lightning channel at the time of peak dE/dt at 15 m, estimated using step-wise approximation of dE/dt variation with distance from the lightning channel (after taking propagation delay into account) is characterized by a mean value of 3.1 kA. The minimum valu e is 0.5 kA and maximum is 8.0 kA.

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1 CHAPTER 1 INTRODUCTION Lightning discharges are the cause of ma ny deaths and injuries. Electromagnetic fields generated by lightning can have deleteri ous effects on sensitive electronic devices. A detailed knowledge of electromagnetic fields generated by close li ghtning is needed for developing adequate light ning protection schemes. A review of the lightning literature is presented in Chapter 2. Cloud electrical structure and mechanisms of cloud electrification are discus sed. Salient properties of both natural and triggered lightning are given with focus on triggered lightning. Both classical and altitude rocket-triggered light ning discharges are considered. Chapter 3 presents the characteristics of measured current, magnetic field, and electric field derivative (dE/ dt) waveforms due to rocket-t riggered lightning. It also contains a description of the instrumentati on used to measure these quantities in 1997, 1999, 2000 and 2001. Leader and return-stroke currents inferre d from measured magnetic fields are presented in Chapter 4. These are compared with the directly measured return-stroke currents and with the leader currents inferred from close electric fi eld derivative (dE/dt) measurements. Chapter 5 deals with the disp lacement currents associated with leader/return stroke sequences in triggered lightning. Displacemen t currents are estimated from measured magnetic fields and current records using Maxwells equations. Also included is an estimation of peak displacement currents from dE/dt signatures measured at 15 and 30 m.

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2 Chapter 6 summarizes the data and analysis of the leader and return-stroke currents and the displacement currents asso ciated with triggered lightning. Recommendations for future rese arch are given in Chapter 7. The Appendix has the waveforms of the displacement currents.

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3 CHAPTER 2 LITERATURE REVIEW 2.1 Cumulonimbus The primary source of lightning is the cloud type termed cumulonimbus or thundercloud. A thundercloud develops from a small fair-weather cloud called a cumulus, which is formed when parcels of warm, mois t air rise and cool by adiabatic expansion, that is, without the transfer of heat or mass across the boundari es of the air parcels. When the relative humidity in a rising and cooling parcel exceeds saturation, moisture condenses on airborne particulate matter within it to form the many small water particles that constitute the visible cl oud. The height of the condensat ion level, which determines the height of the visible cl oud base, increases w ith decreasing relative humidity at the ground. This is why cloud bases in Florida ar e generally lower than in arid locations, such as New Mexico or Arizona. Parcels of wa rm, moist air can only co ntinue to rise to form a cumulus and eventually a cumulonim bus if the atmospheric temperature lapse rate, that is, the decrease in temperature with increasing height, is larger than the moistadiabatic lapse rate, about of 0.6 oC per 100 m. The convection of buoyant moist air is us ually confined to the troposphere, the layer of the atmosphere that extends from the Earths surface to the tropopause. The height of tropopause varies from approximate ly 18 km in the tropics in the summer to 8 km in high latitudes in the winter. The tr opopause is a narrow laye r that separates the troposphere from the next layer of the atmos phere, the stratosphere which extends from tropopause to a height of 50 km. In the tr oposphere the temperature decreases with

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4 increasing altitude, while in the stratosphere the temperature at first becomes roughly independent of altitude and then increases with altitude. A zero or positive temperature gradient in the stratosphere serves to s uppress convection and, th erefore, hampers the penetration of cloud tops into the stratosphere. Lightning is usually associated with c onvective cloud systems ranging from 3 to 20 km in vertical extent. The horizontal dimensions of activ e air-mass thunderstorms range from about 3 km to >50 km. 2.2 Cloud Charge Distribution The distribution and motion of thundersto rm electric charges, most resides on hydrometeors but some of which is free ions, is complex and changes continuously as the cloud evolves. Hydrometeors whose motion is predominantly influenced by gravity (with fall speeds > 0.3 m s-1) are called precipitation particles. All other hydrometeors are called cloud particles. The basic features of the cloud charge structure include a net positive charge near the top, a net negative ch arge below it, and an additional positive charge at the bottom of the cloud. These features are illust rated in Figure 2-1. In-situ measurements of electric fields in side the cloud have be en made using free balloons carrying instruments to measure those fi elds. In situ measurements are superior to remote measurements in that a relativel y accurate charge height can be determined. However, since the balloon can sense the field only along a more or less straight vertical path and it samples different portions of that path at different times, the charge magnitude can be estimated only if assumptions regard ing the size and shape of individual charge regions and the charge variation with time are made. The average volume charge density, v, in the cloud is generally found by assuming th at the charge (i) is horizontally uniform and (ii) does not vary in time.

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5 Figure 2-1. An isolated thundercloud in central New Mexico, with a rudimentary indication of how electric charge is t hought to be distributed inside and around the thundercloud, as inferred from the remote and in situ observations. Adapted from Krehbiel (1986). Then according to Gausss law in point form v = o(dEz/dz), that is, v is proportional to the rate at whic h the vertical electric field Ez increases or decreases with increasing altitude z as the balloon ascends. Fi gure 2-2 shows the results of a vertical sounding of the electric field in a small Ne w Mexico storm that produced no lightning. This electric field profile was obtained up to a height of 10 km above mean sea level using a balloon-borne instrument that meas ured the corona current from a 1-m-long vertical wire. The corona cu rrent and the corresponding ver tical electric field reversed sign twice, between 6 and 7 km and above 9 km. The charge structure in Figure 2-2, a negative charge between -5 and -15 oC with positive charges above and below it, appears to be consistent with the classi cal tripolar charge structure.

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6 Figure 2-2. Balloon measurements of corona cu rrent and the inferred vertical electric field E versus altitude and air temp erature inside a small storm in New Mexico on 16 August 1981, which produced no lightning. Adapted from Byrne et al. (1983) 2.3 Mechanisms of Cloud Electrification Any cloud electrification mechanism invol ves (i) a small-scale process that electrifies individual hydrometeros and (ii) a process that spatially separates these charged hydrometeors by their polarity, the re sultant distances betw een the charged cloud regions being of the order of kilometers. Since most charges reside on hydrometeors of relatively low mobility, the cloud is a relativ ely good electrical insulator and leakage

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7 currents between the charged regions are though t to have a small effect on the charge separation process. 2.3.1 Convection Mechanism. In this mechanism the electric charges are supplied by external sources: fairweather space charge and corona near the ground and cosmic rays near the cloud top. Organized convection provides large-scale se paration. According to this mechanism, illustrated in Figure 2-3, warm air currents ( updrafts) carry positive fair-weather space charge to the top of the gr owing cumulus. Negative charge produced by cosmic rays above the cloud, is attracted to the clouds boundary by the positive charges within it. The negative charge attaches, w ithin a second or so, to cloud particles to form a negative screening layer. These charged cloud partic les carry much more charge per unit volume of cloudy air than is carried by precipitation particles. Dow ndrafts, caused by cooling and convective circulation, assumed to carry the negative charge down the sides of the cloud toward the cloud base, this negative charge serving to produce positive corona at the Earths surface. Corona generates additiona l positive charge under the cloud and, hence, provides a positive feedback to the proce ss. The convective mechanism results in a positive cloud-charge dipole, although it seem s unlikely that the negative charge region formed by this mechanism would lie in a sim ilar temperature range for different types of thunderstorms, as suggested by observations. No te that in convection model there is no role for precipitation in formi ng the dipole charge structure. 2.3.2 Graupel-ice Mechanism. In this mechanism the electric charges are produced by collisions between precipitation particles (graupel) and cloud pa rticles (small ice crys tals). Precipitation particles are generally larger than clo ud particles, although th ere is no absolute

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8 Figure 2-3. Illustration of th e convection mechanism of cl oud electrification. Adapted from MacGorman and Rust (1998) demarcation in size to distinguish precipita tion particles, which are falling out of the cloud, from cloud particles, which remain e ssentially suspended or move upward in updrafts. The large-scale separation of charge d particles is provided by the action of gravity. In the graupel-ice mechanism, whic h appears to be capable of explaining the classical tripolar cloud charge structure, the electrification of individual particles involves collisions between gra upel particles and ice crystals in the presence of water droplets. The presence of water droplets is necessary for sign ificant charge transfer, as shown by the laboratory experiments. A simplified illustration of this mechanism is given in Figure 2-4. The heavy graupel particles (two of whic h are shown in Figure 2-4) fall through a suspension of smaller ice crys tals (hexagons) and supercooled water droplets (dots). The droplets remain in a supercooled liquid state unt il they contact an ice surface, whereupon they freeze and stick to the surface in a pr ocess called riming. Laboratory experiments show that when the temperature is below a critical value called the reversal temperature, TR, the falling graupel particles acquire a ne gative charge in collision with the ice particles. At temperature above TR they ac quire positive charge. The charge sign reversal

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9 temperature TR is generally t hought to be between -10 and -20 oC, the temperature range characteristic of the main negative charge region found in thunderclouds. Figure 2-4. Charge transfer by collision in the graupel-ice mechanism of cloud electrification. It is assumed that the reversal temperature TR is -15 oC and that it occurs at a height of 6 km. Taken from Rakov and Uman (2003). It is believed that the polarity of the charge that is sepa rated in ice-graupel collisions is determined by the rates at wh ich the ice and graupe l surfaces are growing. The surface that is growing faster acquires a positive charge. It is possible that the primary electri fication mechanism changes once a storm becomes strongly electrified. For example, co llisions between ice crystals and graupel

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10 could initiate the electrificati on, and then the larger convec tive energies of the storm could continue it. 2.4 Downward Negative Lightning Discharges to Ground The source of lightning is usually a cu mulonimbus, whose idealized charge structure is shown in the Figure 2-5 as three vertically stacked regi ons labeled P and LP for the main positive and the lower positive charge regions and N for the main negative charge region. Figure 2-5. A vertical tripole representing the idealized gross charge structure of a thundercloud such as that shown in Fi gure 2-1; the negati ve screening layer charges at the cloud top and the posit ive corona space charge produced at ground are ignored here. Downward negative lightning discharges, that is, discharges that are initiated in the cloud, initially develop in an overall downward direction, an d transport negative charge to ground, probably account for about 90 perc ent of all cloud-to-ground discharges. The overall cloud-to-ground lightning discharge, termed a flash, is composed of a number of processes, some of which involve channels that emerge from the cloud while others involve channels that are confined to the cloud volume. Only processes occurring in the channels outside the cloud rende r themselves to optical observa tions that can be used to

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11 determine channel geometry, extension speed and other pertinent features of those channels. The sequence of the processes involved in a typical negative downward lightning flash is shown in Figure 2-6. Figure 2-6. Various processes comprising a negative cloud-to-ground lightning flash. Adapted from Uman (1987, 2001) The stepped leader is preceded by an in -cloud process called the preliminary or initial breakdown. There is no consensus on the mechanism of this process. It may be a discharge bridging the main ne gative and the lower positive ch arge regions, as shown in Figure 2-5. The initial breakdown may last fr om a few milliseconds to some tens of milliseconds and serves to provide conditions fo r the formation of the stepped leader. The latter is a negatively charged plasma channe l extending toward the ground at an average speed of 2 x 105 m s-1 in a series of discrete step s. From high-speed time resolved CLOUD CHARGE DISTRIBUTION PRELIMINARY BREAKDOWN STEPPED LEADER FIRST RETURN STROKE K AND J PROCESSES DART LEADER SECOND RETURN STROKE ATTACHMENT PROCESSt = 0 1.10 ms 1.00 ms 1.15 ms 1.20 ms 19 ms 20 ms 20.10 ms 20.15 ms 20.20 ms 40 ms 60 ms 61 ms 62 ms 62.05 ms

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12 photographs, each step is typically 1 s in duration and tens of meters in length, the time interval between steps being 20 to 50 s. The peak value of the current pulse associated with an individual step has been inferred to be 1 kA or greater. The stepped leader serves to form a conducting path or channel between the cloud charge source and ground. Several coulombs of negative charge are di stributed along this pa th, including downward branches. Thus the leader may be viewed as a process removing negative charge from the source and depositing this charge onto th e downward extending channel. The steppedleader duration is typically some tens of milliseconds, and the average leader current is some hundreds of amperes. The electric potential difference between a downward-moving stepped-leader tip and ground is probably some tens of megavolts which is comparable to or a considerable fraction of that between the cloud charge source and ground. The magnitude of the potential difference between two points, one at the cloud charge source and the other on ground, is the line integral of the electric field intens ity between those points. The upper and lower limits for the potent ial difference between the lower boundary of the main negative charge region and ground can be estimated by multiplying, respectively, the typical observe d electric field in the cloud, 105 V m-1, by the height of the lower boundary of the negative charge cen ter above ground, 5 km or so. The resultant range is 50 to 500 MV. As the leader approa ches ground, the electric field at the ground surface, particularly at objects or relief features protruding above the surrounding terrain, increases until it exceeds the critical value for the initiation of one or more upwardconnecting leaders. The initiation of an upward connecting leader from ground in response to the descending stepped leader marks the beginning of the attachment process.

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13 This process ends when contact is made between the downward and upward moving leaders, probably some tens of meters above ground (more above a tall structure), whereafter the first return stroke begins. The re turn stroke serves to neutralize the leader charge, in other words, to transport the nega tive charges stored on the leader channel to the ground. It is worth noting th at the return-stroke proce ss may not neutralize all the leader charge or may deposit some excess positive charge onto the leader channel and into the cloud charge source region. The fina l stage of the attachment process and the initial stage of the return-stroke process are complex. The net result of those stages is a fully formed return stroke, which is somewhat similar to the potential discontinuity that would travel upward along a vertical, negativ ely charged transmission line if the lower end of the line were connected to the ground. The first return-stroke current measured at ground rises to an initial peak of about 30 kA in some microseconds and decays to halfpeak value in some tens of microseconds while exhibiting a number of subsidiary peaks, probably associated with the branches. The re turn stroke effectively lowers to ground the several coulombs of charge originally deposit ed on the stepped-leader channel, including that on all the branches. The high-current return-stroke wave ra pidly heats the channel to a peak temperature near or above 30 000 K and create s a channel pressure of 10 atm or more, resulting in channel expansion, intense opt ical radiation, and an outward propagating shock wave that eventually becomes the thunder (sound wave) we he ar at a distance. When the first return stroke, including any associated in-clo ud discharge activity, ceases, the flash may end. In this case, the lightning is called a single-stroke flash. However, more often the residual first-stroke channe l is traversed downwards by a leader that

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14 appears to move continuously, a dart leader. During the time interval between the end of the first return stroke and the initiation of a dart leader, J (for j unction) and K processes occur in the cloud. K-process can be viewed as transients occurring during the slower Jprocess. The J-processes amount to a redist ribution of cloud charge on a time scale of tens of milliseconds, in response to the preced ing return stroke. The J-process is often viewed as a relatively slow positive leader extending from the flash origin into the negative charge region, the K-process then bei ng a relatively fast r ecoil streamer that begins at the tip of the positive leader and propagates toward the flash origin. Both the Jprocess and the K-process in cloud-to-ground flashes serve to transport additional negative charge into and al ong the existing channel, alt hough not all the way to the ground. In this respect, K-process may be vi ewed as attempted dart leaders. The processes that occur after the on ly stroke in single stroke fl ashes and after the last stroke in multiple-stroke flashes are sometimes termed F (final) processes. These are similar, if not identical, to J-processes. The dart leader progresses downw ard at a typical speed of 107 m s-1, typically ignores the first stroke branches and deposits along the channel a tota l charge of the order of 1 C. The dart-leader current peak is a bout 1 kA. Some leaders exhibit stepping near ground while propagating along the path traver sed by the preceding return stroke, these leaders being termed dart-stepped leaders. Wh en a dart leader or dart-stepped leader approaches the ground, an attachment process sim ilar to that described for the first stroke takes place, although it probably occurs over a shorter distance and consequently takes less time, the upward connecting-leader length being of the order of some meters. Once the bottom of the dart or the dart-stepped leader channel is connected to the ground, the

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15 second return-stroke wave is launched upward and again serves to neutralize the leader charge. The subsequent return-stroke current at ground typically rises to a peak value to 10 to 15 kA in less than a microsecond and deca ys to half-peak value in a few tens of microseconds. The upward propagation speed of such a subsequent return stroke is similar to that of the first re turn stroke, although due to the absence of branches the speed variation along the channel doe s not exhibit abrupt drops. The impulsive component of the current in a subsequent return stroke is often followed by a continuing current that has a ma gnitude of tens to hundreds of amperes and duration up to hundreds of milliseconds. Continui ng currents with a duration in excess of 40 ms are traditionally termed long continui ng currents. The source for the continuing current is the cloud charge, as opposed to the charge distributed along the leader channel, the latter charge contributing to at least the initial fe w hundred microseconds of the return-stroke current observed at ground. The time interv al between successive return strokes in a flash is usually several tens of milliseconds, al though it can be as large as many hundreds of milliseconds if a long continuing current is involved and as small as one millisecond or less. The total duration of a flash is typically some hundreds of milliseconds, and the total charge lowered to ground is some tens of coulombs. 2.5 Artificial Initiation (Triggering) of Lightning Using the Rocket-and-Wire Technique Two techniques for triggering lightning with a small rocket that extends a thin wire in the gap between a thundercloud and th e ground are classi cal triggering and altitude triggering. These descriptions primar ily apply to triggeri ng negative lightning. These two techniques are discussed in the next two sections. Figure 2.7 and Figure 2.8 show the sequence of events for these two techniques.

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16 2.5.1 Classical Triggering The most effective technique for trigge ring lightning involves the launching of a small rocket trailing a th in grounded wire toward a charged cloud overhead. This triggering method is usually called classical triggering and is illustrated in Figure 2-7. Figure 2-7. Sequence of events in classica l triggered lightning. The upward positive leader and initial continuous current cons titute the initial stage. Adapted from Rakov et al. (1998) The triggering success rate is generally re latively low during very active periods of thunderstorms, one reason being that during such periods the electric fi eld is more likely to be reduced by a natural lightning discharge be fore the rocket rises to a height sufficient for triggering. When the rocket, ascending at about 200 m s-1, is about 200 to 300 m high, the enhanced field near the rocket tip results in a positively charged leader that propagates upward toward the cloud. This upward positive leader (UPL) vaporizes the trailing wire, bridges the gap between th e cloud and ground, and establis hes an initial continuous current (ICC) with a duration of some hundreds of milliseconds that effectively transports

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17 negative charge from the cloud charge source to the triggering facility. The ICC can be viewed as a continuation of the UPL when the latter has reached the main negative charge region in the cloud. At that time the upper extremity of the UPL is likely to become heavily branched. The UPL and ICC constitute the initial stage (IS) of a classical triggered-lightning discharge. After cessation of the initial continuous current, one or more downward dart-leader--upw ard-return-stroke sequence may traverse the same path to the triggering facility. The dart leaders a nd the following return strokes in triggered lightning are similar to dart-leader retu rn-stroke sequences in natural lightning, although the initial processes in natural downw ard and in classical triggered lightning are distinctly different. In summer, the triggering success rate for positive lightning is apparently lower than for the negative lightning. There is contradictory information regardi ng whether the height H of the rocket at the time of lightning triggering depends on th e electric field intens ity E at ground at the time of launching the rocket. A strong correlation (with co rrelation coefficient 0.82) between H and E for triggered lightning in New Mexico was given by H = 3900E-1.33 where H is in meters and E in kV m-1. In Florida it was found that lightning can be initiat ed with grounded triggering wires approximately 400 m long when the ambien t fields aloft are as small as 13 kV m-1. When lightning occurred, ambient potentials with respect to earth at the triggering-rocket altitude were 3.6 MV (negative with respect to earth). These potentials are referred to as triggering potentials. The first measurable current pulses at the bottom of the triggering wires were observed at similar fields aloft but at wire heights only about half as large, the corresponding potential being 1.3 MV.

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18 2.5.2 Altitude Triggering A stepped leader followed by a first return stroke in natural downward lightning can be reproduced to some degree by triggeri ng lightning via a metallic wire not attached to the ground. This ungrounded-wire technique is usually called alt itude triggering. In this type of lightning, illustrated in Figure 2-8, a bidirectional ( positive charge up and negative charge down) leader process is involve d in initiating the firs t return stroke from ground. Figure 2-8. Sequence of events in altitude-triggered lightning leading to the establishment of a relatively low-resistance connec tion between the upward-moving positive leader tip and the ground. The processe s that follow the sequence shown, an initial continuous-current and possibly one or more downward-leader-upward-return-stroke sequences, are simila r to their counterparts in classical triggered lightning. The rocket speed is of the order of 102 m s-1. Adapted from Rakov et al. (1998) Note that the gap, in this case, the le ngth of the insulating Kevlar cable, between the bottom end of the upper (triggering) wire and the top end of the grounded

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19 (intercepting) wire is some hundreds of meters. Altitude triggering can also be accomplished without using an intercepting wire whose only function is to increase the probability of lightning attachment to instrumented rocket-launching facility. 2.6 Previous Studies of Displacement Curren t Associated with Triggered Lightning Schnetzer et al. (1998) in a study reported only in a conference proceeding, carried out a numerical evaluation of Maxwells in tegral equation relating azimuthal magnetic field to its sources to in vestigate the relative cont ributions of conduction and displacement currents to the to tal ground level azimuthal magne tic field at a distance of 50 m from the base of a triggered lightning stroke. The results revealed differences between observed magnetic fields measured at 50 m from expectations based on Amperes law for magnetostatics. It is conc luded that Amperes law for magnetostatics, which neglects displacement current contribu tions, provides an inadequate representation of the total magnetic field due to a li ghtning ground stroke at distances beyond approximately 30 m. The rest of this secti on contains an overview of Schnetzer et al. (1998), which is the only publica tion, as of today, on the subject of displacement current in triggered lightning. 2.6.1 Theory The following simple expression based on Amperes law for magnetostatics is often used to estimate the azimuthal magnetic field intensity at th e ground due to nearby lightning: H(r,t)=I(t)/2 r (2.1) where I(t) is the channel current, H(r,t) is th e magnetic field intensity, and r is the radial distance from the strike point on the earth. Schnetzer et al (1998) observed that beyond 30 m, peak amplitudes of the measured magne tic fields are somewhat lower than their

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20 counterparts predicted by equation (2.1) when measured currents are substituted in it. To understand the sources of this observed behavi or, a first-order nume rical evaluation was carried out using as a starting point Maxwe lls integral equation relating the azimuthal magnetic field to its arbitr ary, time-varying sources, o lSSE HdlJdSdS t o SE I dS t (2.2) Here the first term on the right corres ponds to I(t) in Eq. 2.1. The second term constitutes the contribution to the azimuthal magnetic field due to displacement current through the integration surface S bounded by l When applied to a lightning stroke to earth with S being defined as a flat, circular area of integra tion lying on the surface of the ground and centered at the strike point, th e first terms accounts for the effects of conduction currents flowing normally thr ough the designated surface. These would include corona and upward leader currents prior to the attachment of the descending leader, and the return-stroke current after that time. The second term accounts for the effects of time variations of the vertical elect ric field associated w ith the changing charge density distribution along the lightning channe l during both the approach of the leader and the resultant return stroke. On the basis of circular symmetry considerations, ()1 (,) () 22z o SIt Ert HtdS t rr (2.3) To the degree that an average z E t can be treated as constant over the area of integration, H can be approximated as

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21 ()() () 22oz I trdEt Ht rdt = Hc + Hd (2.4) where Hc and Hd are the contribution to the total magnetic field H from conduction and displacement current, respectively. Alternately, average values of dEz/dt can be defined for different ring-shaped parts of S, in whic h case the second term on the right side of Eq. 2.4 becomes the sum of all individual contri buting subareas of S. The first term on the right of Eq. 2.4 is recognized as correspondi ng to Amperes law for magnetostatics, and therefore any effects due to the current variat ion with height and ra diation field must be accounted for by the second, displacement curre nt term. Since the de scending leader does not penetrate the surface of integration, during the leader phase I(t) is approximately zero, except for assumed-to-be-negligibly-small corona or upward leader currents emitted from the prospective attachment point During that time, therefore, the magnetic field intensity is related solely to the displacement current Commencing with the onset of the return stroke, both terms contribute. Howeve r, close to the channel, where r 0, the displacement current contribution tends to zer o, and the total field is dominated by the contribution from the channel conduction current term. 2.6.2 Estimation of Displacemen t Current Contribution at 50 m In order to investigate th e distance at which the c onduction current term alone ceases to provide an adequate representation of the total magnetic field, Schnetzer et al (1998) carried out a numerical evaluation of the relative contributions of both terms in Eq. 2.4 for a typical 20-kA stroke using av ailable recorded channel-base current and associated magnetic field at 50 m and electric field data at two distances, 5 and 20 m, from the strike point. The first step was to derive estimates of the displacement current for r ranging from 0 to 10 m and from 10 to 50 m from electric fields measured at 5 and

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22 20 m, respectively. Because electric fields were not recorded beyond 20 m, estimates of the displacement current contributed by th e annular area between 10 and 50 m were obtained by assuming that the electric field ove r that area was, on average, the same as the value measured at 20 m. Electric field wa veforms were numerically differentiated to obtain dEz/dt waveforms to be substituted in Eq. (2.4). The resulting estimated amplitudes of displacement currents calculate d at four time points prior to and at the return-stroke onset are listed in Table 2.1. Table 2-1. Displacement currents Id estimated from measured electric field data at times prior to and at the onset of a 20 kA peak stroke current. Taken from Schnetzer et al. (1998). A qualitative representation of the electric fi eld derivative is given in Figure 2-9. According to Table 2-1, prior to the retu rn stroke, while there is no appreciable conduction current flowing through the in tegration surface at ground level, the magnitudes of displacement currents out to 10 m at the various time steps are negligible relative to the prospective returns stroke peak current of 20 kA. On the other hand, during

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23 that same period the displacement current c ontribution from the area between 10 and 50 m becomes increasingly significant in comparis on to 20 kA. Consistent with Figure 2-10, the displacement current increases in amplitude with time and is negative in polarity up to the point of onset of the return stroke. U pon initiation of the return stroke, the local electric field abruptly changes sign and its derivative reaches its peak. The corresponding magnitude of the total displacement current at that point becomes comparable to that of the channel current, which then begun to flow but has not reached its peak. Contribution of the displacem ent current in addition to the return-stoke channel conduction current contribution clearly alters both the wave shape and amplitude of the return-stroke portion of the total magnetic fiel d compared to that predicted by Amperes law for magnetostatics. This is demonstrat ed in Figure 2-10. Here, the magnetic field measured at 50 m (labeled Measured) during st roke 5 of flash 96-23 is plotted along with the magnetic field (labeled Amperes Law) that would be predicted by Eq. 2.1 when applied to the recorded channel-base curre nt of that stroke. Finally, the difference between the two, which is qualitatively cons istent with the results of Table 2-1 and apparently represents the cont ribution due to the displacement current term of Eq. 2.4, is also plotted. As can be seen in Figure 2-10, the shape of the difference curve corresponds well to the anticipated shape of the electric field derivativ e, and hence of displacement current density, illustrated in Figure 2-9. Prior to the retu rn stroke, while no channel current is flowing at ground leve l, the effect of the displacemen t current is apparent in the initial ramp of the measured magnetic field. Further effects of the displacement current component on the total field are the rounding and reduction in amplitude of the peak of the magnetic field waveform.

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24 Figure 2-9. Qualitative illustra tion of the shape of the time derivative of the ground level vertical electric field of a nearby return stroke Since displacement current density is simply related to the derivative of electric field by a constant, it has the same waveshape. Taken from Schnetzer et al. (1998). Figure 2-10. From top to bottom, magnetic fi eld measured at 50 m during stroke 5 of Flash 96-23, the corresponding field according to Amperes law for magnetostatics, as applied to the measured channel-base current, and the difference between the two. Take n from Schnetzer et al. (1998).

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25 CHAPTER 3 CHARACTERIZATION OF EXPERIMENTAL DATA USED IN THIS STUDY 3.1 Magnetic Field Measuring Techniques To measure the magnetic fiel d from lightning a loop of wire can be used as an antenna. According to Faradays Law a cha nging magnetic field passing through an open circuited loop of wire will induce a voltage at the terminals of the wire. The voltage at the terminals of the wire is dt dB A vn out where A is the area of the antenna and B is the magnetic flux density passing through the loop, perpendicular to the pl ane of the loop. Since the out put voltage is proportional to the time derivate of the magnetic field, this voltage will have to be integrated to obtain the signal proportional to the field. The Theven in equivalent circuit of a loop antenna is the open circuit source voltage dB A dt in series with the source impedance (primarily inductive). The Thevenin equiva lent is shown in Figure 3-1. Figure 3-1. Thevenin equivale nt circuit of a loop antenna

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26 A Norton equivalent circuit model for the antenna can be derived from the Thevenin equivalent with thVAjBAB I j LjLL The Norton equivalent circuit is shown in Figure 3-2 Figure 3-2. Norton equivalent circuit for a loop antenna. Since the loop antenna has an inductance L a ssociated with it, the impedance of the antenna will change with frequency. In the frequency domain that impedance is L where is the angular frequency. This fr equency-dependent impedance will cause distortion in the derivative signal. To elimin ate the distortion a resi stor can be placed in series with the antenna with the resistive impedance R much higher than the inductive impedance L of the antenna at the highest frequency of interest. The decay time constant of the overall circuit in Figure 3-1 and Figure 3-2 will be = RC as long as R is much smaller then the input resistance of the recorder and C is much larger then the input capacitance of the recorder, both conditions be ing usually met. In the frequency domain the output voltage across the capacitor is 1 ()() 1outAjB jC V RjL jC

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27 If we choose R >> j L and R >> 1 jC for the highest and lowest frequencies of interest respectively, as discussed above, then outAB V R C In this way magnetic field from lightning can be measured from a loop antenna. Using the output voltage, Vout, area of the loop antenna A, and choosing appropriate resistance R the magnetic field B can be estimated. 3.2 Experimental Setup 3.2.1 ICLRT Overview In this section, an overview of Intern ational Center for Lightning Research and Testing (ICLRT) is presented. The ICLRT is located at Camp Bl anding, Florida, at coordinates 29 56 N, 82 02 W, 8 km east of Starke It was constructed by Power Technologies in 1993 to study the effect of lig htning on power lines. It has been operated by the University of Florida since 1994. Th e rocket-and-wire tec hnique (e.g., Rakov et al., 1998) was used to artificially initiate (t rigger) lightning from na tural thunderclouds. An overview of the ICLRT during the 1999, 2000, and 2001 experiments is found in Figure 3-3 and a photograph of Flash S0012, tr iggered in 2000, in Figure 3-4. Flash S0012 was triggered using the underground launcher. The triggered-lightning experiments are usually conduc ted from May through September. As can be seen from Figure 3-3, the ICLRT includes a tower launch er 11 m in height. Ot her launchers placed at different positions on the site were also used in different years. Apart from the launchers, the ICLRT includes test overh ead power lines, under-ground cables, four instrumentation stations, a test house, test runway, other test objects and systems and various office and storage trailers.

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28 Figure 3-3. An overview of the ICLRT at Camp Blanding, Florida, 1999-2001. Not all test objects are shown. Figure 3-4. Photograph of li ghtning flash S0012 triggered fr om the underground launcher (see Figure 3-3).

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29 3.2.2 1997 Experiments In this section, a brief discussion of instrumentation used in the 1997 multiple station experiment is discussed. The multiple station experiment involved a 5 m rocket launcher located at northeast corner of th e ICLRT and grounded through three 8 foot (2.43 m) galvanized steel rods driven into sandy soil. Seven field measuring stations were located (see Figure 3-5) south of the rocket launcher with di stances ranging from 5 to 500 m. Each station had electric field and magnetic field antennas. The lightning channel base current was measured using 0.5 milliohm CVR (Current Viewing Resistor) located at the launcher. Three digitizing systems (see Figure 3-6) were used in this experiment, two were provided by the University of Florida and were located at SATTLIF trailer (see Figure 3-5) and launch contro l, the third digitizing syst em was provided by Sandia and was located at SATTLIF trailer. When the current measured by the CVR located at SATTLIF launcher exceeded 4 kA a digital pul se was generated by a current threshold triggering circuit, which triggered all three digitizing systems. The digitizing system at SATTLIF trailer consisted of a single Nico let Multipro 150 digitizer and five LeCroy model RM9400 digital oscilloscopes. Nicolet Multipro consisted of 8 data acquisition cards of 4 channels each, but for this experi ment only two cards were used of which one was faulty. Each channel had 12-bit resolution with a sampling rate of 10 MHz for a total record length of 51.2 ms. The LeCroy oscillos copes were segmented for multiple triggers and provided 8-bit resolution w ith a sampling rate of 25 MHz for a total record length of 100 s. At launch control five Nicolet model pr o90 digital oscilloscopes were used. Pro90 consists of 4 channels; channels 1 and 2 ha d 8-bit resolution and a sampling rate up to 200 MHz, and channels 3 and 4 had 12-bit re solution and a sampli ng rate up to10 MHz.

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30 The first channel had a pretrigger delay of 2 ms and second channel had a 23.6 ms pretrigger delay that allowed continuous recording of the same quantity for 51.2 ms. Nicolet Isobe 3000 fiber optic links were used to transmit analog data from antennas to digitizing systems. More deta iled description of 1997 instrumentation can be found in Chapter 4 of David E. Crawfords thesis (Crawford 1998). NWES SATTLIF LAUNCHER UF LAUNCH CONTROL TRAILER 100m OFFICE AND STORAGE UF TOWER LAUNCHER SATTLIF TRAILER A NTENNA FIELD TEST POWERLINE Figure 3-5. Locations of different instru mentation stations for 1997 multiple station experiment. Taken from Crawford (1998). 3.2.3 1999 Experiments The rocket launcher consisted of six meta llic tubes aligned vertically from which rockets were launched. The rocket launcher was mounted on insulating fiberglass legs and placed underground, with the top of the launcher flush with ground, in a 4 m 4 m 4 m pit. The pit and the launcher we re located in the center of a 70 m 70 m buried metallic grid (see Figure 3-3) intended to simulate a perfectly conducting ground. This configuration eliminates gr ound surface arcing (e.g., Rakov et al., 1998) and minimizes field propagation effects due to a finite ground conductivity. The low frequency, low current grounding resistance of the buried grid was measured to be 6 A hollow metal rod with an outside diameter of 3.8 cm a nd a wall thickness of 0.6 cm protruding 1 m

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31 ANTENNAS 10 m UF LAUNCH CONTROL REC IN NICOLET DSOs10 Channels 256 Ksamples/ch 10 Msamples/sec 12 bit res. TRIG IN ANALOG FIELD DATA110 m 500 m 20 m 30 m 50 m LEGEND:ELECTRIC FIELD ANTENNA (.155 m) MAGNETIC FIELD ANTENNA (.27 m) DSO = Digital Storage Oscilloscope SATTLIF LAUNCHER 5 m TRIG IN 10 Channels 4 Ksamples/seg 25 Msamples/sec 8 bit res.4 Channels 512 Ksamples/ch 10 Msamples/sec 12 bit res. REC IN ANALOG FIELD DATA REC IN NICOLET DIGITIZER TRIG OUT TRIG INANALOG MAG TAPE RECORDER GEN. (4 kA Thresh.) CHANNEL BASE CURRENT SHUNT REC IN FIRE CONTROLCONTROL LECROY DSOs TRIGGER SATTLIFLAUNCH Figure 3-6. Data acquisition system used in the 1997 multiple-station experiment. Taken from Crawford (1998). above the ground surface was used as the strike object for flashes S9901S9918 in 1999. For the other flashes triggered in 1999 (fla shes S9925 S9935), a 2 m rod was used in order to increase the probabil ity of lightning attachment to the rod. During 1999, the underground launcher was connected via four metal straps to the buried grid and the base of the launcher was connected via two metal straps to a 16.5 m long vertical ground rod whose low frequency, low current groundi ng resistance was measured to be 40 The electric field, magnetic field, and their time derivatives produced by lightning strokes were measured 15 and 30 m from the st rike rod. A TTL-level digital pulse trigger signal was generated when the magnetic fiel d sensor located 15 m from the rocket launcher detected a magnetic field that correspon ded to a current of at least 5 kA (using

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32 Amperes law of magnetostatics). The TTL signa l was transmitted to the external trigger input of the oscilloscopes located in the SA TTLIF trailer (see Figure 3-3) to trigger the digitizing system. The oscilloscopes for the field and current measurements had a pretrigger (stored data recorded prior to the tr igger pulse) that ranged from 10% to 50% of the total record length. Fiber optic transmitte rs (FOT) converted the analog output signals from the antennas to optical signals and transm itted those signals via fiber optic cables to fiber optic receivers (FOR). Meret and Nanofas t fiber optic links (FOL) were used in the experiment. The bandwidth of the Meret a nd Nanofast FOL was dc to 35 MHz and 5 Hz to 175 MHz, respectively. The FOT were power ed with 12 V dc lead -acid batteries. RG58 or RG-223 coaxial cables (both 50 ) connected the FOT to the antennas, which were located in metal boxes near the antennas. The FORs in the SATTLIF trailer were powered with 120 V ac uninterruptible power supplies (UPS). RG-58 or RG-223 coaxial cables connected the FOR to the digitizing system. The optical fibers transmitting the signal from the FOT to the FOR were 200 m glass, Kevlar-reinforced, duplex cables. 3.2.3.1 Instrumentation for Current Measurements Six P110A current transforme rs (CTs) with a lower frequency response of 1 Hz and an upper frequency response of 20 MHz were used to measure the current at the lightning channel base, two measured the current fl ow to the vertical ground rod, and four measured the current flow to the buried grid The current amplitude range of each sensor is from a few amperes to approximately 20 kA. A passive combiner summed the two signals from the ground rod CTs to obtain a total ground rod current, and another one summed the four signals from the buried grid CTs to obtain a total grid current. The total ground rod current signal and the total grid cu rrent signal were then each transmitted via

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33 separate Meret FOL (35 MHz bandwidth) to the SATTLIF trailer. Both signals were filtered with a 20 MHz, 3 dB anti-aliasing filt ers and then digitized at 50 MHz. The total current at the lightning cha nnel base was obtained by nume rically summing the ground rod current and the bur ied-grid current. 3.2.3.2 Instrumentation for Electric Field Measurements Electric fields were measured using flat plate antennas with an area of 0.16 m2. The output of each electric field antenna was connected to an integrating capacitor of value 105 nF at 15 m and 55 nF at 30 m. The input impedance of the fibe r optic transmitter was about 1 M Meret fiber optic links with a bandwi dth of 35 MHz were used to transmit the signal to the SATTLIF traile r where the 15-m electric field signals were filtered using 10 MHz, 3 dB anti-aliasing filters and digitized at 25 MHz, and the 30-m electric field signals were filtered using 20 MHz, 3 dB anti-aliasing filters and digitized at 25 MHz. 3.2.3.3 Instrumentation for Electric Field Derivative Measurement Electric field derivatives were measured us ing flat plate antennas with an area of 0.16 m2. The output of each electric field deri vative antenna was terminated using 50 and the input impedance of the fiber optic transmitter was about 1 M Meret fiber optic links with a bandwidth of 35 MHz were used to transmit the 15-m signal, and a Nanofast FOL was used to transmit the 30-m signal to SATTLIF trailer. Signals of dE/dt at 15 and 30 m were filtered using 20 MHz, 3 dB anti-a liasing filters and digitized at 250 MHz. 3.2.4 2000 Experiments The strike object was a 2 m vertical rod surrounded by a 3 m diameter horizontal ring elevated to 1.5 m height and electrically connected to the base of the rod (see Figure 3-8). Most of the 2000 instrumentation was th e same as the 1999 instrumentation except for the two major changes made in 2000 and listed below: (1) The triggering signal was

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34 generated when the current measured at the st rike rod base exceeded 3 kA. (2) Current at the channel base was measured simultaneously by two different methods (a) the total lightning current was measured using a single current viewing resist or installed just below the strike object (new measurement) and (b) the current components flowing to the vertical ground rod and to the buried grid were meas ured individually and added numerically to obtain the total lightning cu rrent. The current to the ground rod was measured as in 1999, while the currents to the buried grid were measured with two current viewing resistors in the two connec tions rather than with the four current transformers and four connections used in 1999. Electric field and elec tric field derivative instrumentation in 2000 was the same as in 1999. SATTLIF Pit & Launch Tubes B(15) B(30) E(15) E(30) dB(30) dB(15) dE(15) dE(30) M-E15 M-E30 M-B15 M-B30 sh(15) E(5) sh(30) Camcorder Camcorder Video & 35-mm Cameras Edge of Ground Screen Pockel Cell sh(3) 30 o 30 o o o 15 15 Figure 3-7 Experimental setup (placement of electric and magnetic field antennas) used in SATTLIF for 2000 [Courtesy G. Schnetzer].

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35 Figure 3-8 Setup of strike rod and ri ng mounted over launch tubes in 2000. 3.2.5 2001 Experiments The experiment set-up was the same as in 2000, except for the strike ring and the ground rod connection were removed. Additionall y, the 2 m strike rod was replaced with 4.5 m section of gas pipeline for the expe riments on August 18, 2001. The pipeline was mounted directly onto the base of the incide nt current CVR (current viewing resistor) and nylon fishing line was used to support the st ructure. The pipeline consisted of four sections of different diameters, the sections being connected by thr ee different insulating joints. Current was measured in the same way as in 2000, but was digitized at 25 MHz (instead of 50 MHz as in 1999 and 2000). The el ectric field and electr ic field derivative instrumentation in 2001 was the same as in 1999 and 2000.

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36 3.3 Data Presentation 3.3.1 General Information In this section the statistical distributions of measured peak magnetic fields, returnstroke peak currents and peak dE/dt fields are presented. Corresponding waveforms are shown in Figures 3-9 to 3-13. For measured return-stroke current which ar e not saturated the sample size is 88. For 1997, 1999, 2000, and 2001 data combined, the mean value of peak current is 15.3 kA and standard deviation is 7.50 kA. The magnetic fields are used in Chapter 4 to estimate the leader and return-stroke currents. For measured peak magnetic fields which are not saturated at 15 m for 1999, 2000 and 2001 the mean value is 201 Wb/m2 and the standard deviation is 96.8 Wb/m2. At 30 m for 1997, 1999, 2000 and 2001 the mean value is 104 W/m2 and the standard deviation is 49.2 W/m2. The sample size for 15 m data is 97, and for 30 m data the sample size is 103. Histograms are shown in Figures 3.17-3.22. For measured dE/dt waveforms which are not saturated the sample size is 50 for both 15 and 30 m. At 15 m for 1999, 2000 and 2001 the mean value is 355 kV/m/s and the standard deviation is 154 kV/m/s. At 30 m for those three year s the mean value is 118 kV/m/s and the standard deviation is 56 kV/m/s. Table 3-1 summarizes the mean, standard deviation, geometric mean and sample sizes for 1999, 2000 and 2001 combined.

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37 Table 3-1. Summary of mean, standard devi ation, GM (Geometric Mean), and sample sizes of measured peak current, p eak magnetic field and electric field derivative Parameter Mean St. Dev. GM Sample size Peak current, kA 15.3 7.5 13.4 88 Peak magnetic field at 15 m, Wb/m2 201 96.8 179 97 Peak magnetic field at 30 m, Wb/m2 104 49.2 92.9 103 Peak dE/dt field at 15 m, kV/m/s 355 145 315 50 Peak dE/dt field at 30 m, kV/m/s 118 56 103 50 Figure 3-9. Measured channel-base current, Flash S9901, Stroke 3.

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38 Figure 3-10. Magnetic field at 15 m, Flash S9901, Stroke 3. Figure 3-11. Magnetic field at 30 m, Flash S9901, Stroke 3.

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39 Figure 3-12. Electric field derivative (dE/ dt) at 15 m, Flash S9901, Stroke 3. Figure 3-13. Electric field derivative (dE/ dt) at 30 m, Flash S9901, Stroke 3.

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40 3.3.2 Channel-base Current 0481216202428323640 Number 0 2 4 6 8 Return-Stroke Peak Current [kA] 0481216202428323640 Number 0 2 4 6 8 10 12 Return-Stroke Peak Current [kA] 0481216202428323640 Number 0 1 2 3 4 Return-Stroke Peak Current [kA] 0481216202428323640 Number 0 1 2 3 4 Return-Stroke Peak Current [kA] (a) (b) (c) (d) 1997 1999 2001 2000Mean13.1 kA St. Dev.5.60 kA Min5.70 kA Max23.0 kA GM12.1 kA Sample Size11Mean16.7 kA St. Dev.6.80 kA Min2.80 kA Max30.0 kA GM15.1 kA Sample Size24Mean13.2 kA St. Dev.6.90 kA Min1.10 kA Max36.8 kA GM11.3 kA Sample Size40Mean21.1 kA St. Dev.9.30 kA Min9.20 kA Max38.9 kA GM19.3 kA Sample Size13 Figure 3-14. Return-stroke peak currents in (a) 1997, (b) 1999, (c) 2000, and (d) 2001.

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41 0481216202428323640 Number 0 2 4 6 8 10 12 14 16 18 20 1999 n = 24 Mean = 16.7 kA St. Dev. = 6.80 kA 2000 n = 40 Mean = 13.2 kA St. Dev. = 6.90 kA 2001 n = 13 Mean = 21.1 kA St. Dev. = 9.30 kA 1997 n = 11 Mean = 13.1 kA St. Dev. = 5.60 kA Return-StrokePeakCurrent [kA] 1997, 1999, 2000, & 2001 Mean15.3 kA St. Dev.7.54 kA Min1.05 kA Max38.9 kA GM13.4 kA Sample Size88 Figure 3-15. Return-stroke peak currents in 1997, 1999, 2000 and 2001.

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42 3.3.3 Magnetic Field 02004006008001000 Number 0 1 2 3 4 Peak Magnetic Field [Wb/m 2 ]Distance 5 m, 1997 Mean 511 Wb/m2St. Dev. 274 Wb/m2Min 176 Wb/m2Max 916 Wb/m2GM 443 Wb/m2Sample Size7 0100200300400500 Number 0 1 2 3 4 5 Peak Magnetic Field [Wb/m 2 ]Distance 10 m, 1997 Mean 247 Wb/m2St. Dev. 101 Wb/m2Min 100 Wb/m2Max 395 Wb/m2GM 227 Wb/m2Sample Size9 050100150200250 Number 0 1 2 3 4 5 Peak Magnetic Field [Wb/m 2 ]Distance 20 m, 1997 Mean 111 Wb/m2St. Dev. 47.3 Wb/m2Min 51.3 Wb/m2Max 183 Wb/m2GM 103 Wb/m2Sample Size7 0255075100125150 Number 0 1 2 3 4 Distance 30 m, 1997 Peak Magnetic Field [Wb/m 2 ] Mean 79.8 Wb/m2St. Dev. 33.7 Wb/m2Min 37.8 Wb/m2Max 118 Wb/m2GM 73.4 Wb/m2Sample Size6(a) (b) (c) (d) Figure 3-16. Peak magnetic fields measured at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997.

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43 050100150200250300350400450500 Number 0 2 4 6 8 10 12 Peak Magnetic Field [Wb/m 2 ]Distance 15 m, 1999 Mean 223 Wb/m2St. Dev. 96.5 Wb/m2Min 74.1 Wb/m2Max 434 Wb/m2GM 202 Wb/m2Sample Size39(a) 0255075100125150175200225250 Number 0 2 4 6 8 10 12 Distance 30 m, 1999 Peak Magnetic Field [Wb/m 2 ]Mean 118 Wb/m2St. Dev. 48.2 Wb/m2Min 46.4 Wb/m2Max 225 Wb/m2GM 108 Wb/m2Sample Size39(b) Figure 3-17. Peak magnetic fields measur ed at (a) 15 m and (b) 30 m in 1999.

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44 050100150200250300350400450500 Number 0 2 4 6 8 10 12 14 Peak Magnetic Field [Wb/m 2 ]Distance 15 m, 2000 Mean 180 Wb/m2St. Dev. 92.0 Wb/m2Min 49.5 Wb/m2Max 467 Wb/m2GM 159 Wb/m2Sample Size47(a) 0255075100125150175200225250 Number 0 2 4 6 8 10 12 Distance 30 m, 2000 Peak Magnetic Field [Wb/m 2 ]Mean 93.1 Wb/m2St. Dev. 47.2 Wb/m2Min 25.4 Wb/m2Max 235 Wb/m2GM 82.5 Wb/m2Sample Size47(b) Figure 3-18. Peak magnetic fields measur ed at (a) 15 m and (b) 30 m in 2000.

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45 050100150200250300350400450500 Number 0 1 2 3 4 5 Peak Magnetic Field [Wb/m 2 ]Distance 15 m, 2001 Mean 212 Wb/m2St. Dev. 107 Wb/m2Min 97.6 Wb/m2Max 470 Wb/m2GM 192 Wb/m2Sample Size11(a) 0255075100125150175200225250 Number 0 1 2 3 4 Distance 30 m, 2001 Peak Magnetic Field [Wb/m 2 ]Mean 113 Wb/m2St. Dev. 56.7 Wb/m2Min 48.8 Wb/m2Max 248 Wb/m2GM 102 Wb/m2Sample Size11(b) Figure 3-19. Peak magnetic fields measur ed at (a) 15 m and (b) 30 m in 2001.

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46 050100150200250300350400450500 Number 0 5 10 15 20 25 30 1999 n = 39 Mean = 223 Wb/m2 St. Dev. = 96.5 Wb/m2 2000 n = 47 Mean = 180 Wb/m2 St. Dev. = 92.0 Wb/m2 2001 n = 11 Mean = 212 Wb/m2 St. Dev. = 107 Wb/m2 Peak Magnetic Field [Wb/m 2 ]Distance 15 m (1999, 2000, & 2001) Mean 201 Wb/m2St. Dev. 96.8 Wb/m2Min 49.5 Wb/m2Max 470 Wb/m2GM 179 Wb/m2Sample Size97(a) Distance 30 m (1997, 1999, 2000, and 2001) 0255075100125150175200225250 Number 0 5 10 15 20 25 30 1999 n = 39 Mean = 118 Wb/m2 St. Dev. = 48.2 Wb/m2 2000 n = 47 Mean = 93.1 Wb/m2 St. Dev. = 47.2 Wb/m2 2001 n = 11 Mean = 112 Wb/m2 St. Dev. = 56.7 Wb/m2 1997 n = 6 Mean = 79.8 Wb/m2 St. Dev. = 33.7 Wb/m2 Peak Magnetic Field [Wb/m 2 ]Mean 104 Wb/m2St. Dev. 49.2 Wb/m2Min 25.4 Wb/m2Max 248 Wb/m2GM 92.9 Wb/m2Sample Size103(b) Figure 3-20. Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1997, 1999, 2000 and 2001.

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47 3.3.4 Electric Field Derivative (dE/dt) 0100200300400500600700800 Number 0 1 2 3 4 5 Peak dE/dt [kV/m/s] Distance 15 m, 1999 Mean304 kV/m/s St Dev107 kV/m/s Min72.0 kV/m/s Max450 kV/m/s GM280 kV/m/s Sample Size15(a) 0255075100125150175200225250 Number 0 1 2 3 4 5 6 7 Distance 30 m, 1999 Peak dE/dt [kV/m/s] (b)Mean92.6 kV/m/s St Dev31.0 kV/m/s Min23.0 kV/m/s Max145 kV/m/s GM86.1 kV/m/s Sample Size15 Figure 3-21. Peak dE/dt fields measur ed at (a) 15 m and (b) 30 m in 1999.

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48 0100200300400500600700800 Number 0 2 4 6 8 10 Peak dE/dt [kV/m/s] Distance 15 m, 2000 Mean350 kV/m/s St Dev156 kV/m/s Min50.0 kV/m/s Max673 kV/m/s GM308 kV/m/s Sample Size31(a) 0255075100125150175200225250 Number 0 2 4 6 8 Distance 30 m, 2000 Peak dE/dt [kV/m/s] Mean178 kV/m/s St Dev56.0 kV/m/s Min16.0 kV/m/s Max235 kV/m/s GM102 kV/m/s Sample Size31(b) Figure 3-22. Peak dE/dt fields measur ed at (a) 15 m and (b) 30 m in 2000.

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49 0100200300400500600700800 Number 0 1 2 3 4 Peak dE/dt [kV/m/s] Distance 15 m, 2001 Mean590 kV/m/s St Dev61.0 kV/m/s Min519 kV/m/s Max644 kV/m/s GM579 kV/m/s Sample Size4(a) 0255075100125150175200225250 Number 0 1 2 3 4 Distance 30 m, 2001 Peak dE/dt [kV/m/s] Mean210 kV/m/s St Dev27.0 kV/m/s Min181 kV/m/s Max241 kV/m/s GM209 kV/m/s Sample Size4(b) Figure 3-23 Peak dE/dt fields measur ed at (a) 15 m and (b) 30 m in 2001.

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50 0100200300400500600700800 Number 0 2 4 6 8 10 12 14 1999 n = 15 Mean = 304 kV/m/s St. Dev. = 107 kV/m/s 2000 n = 31 Mean = 350 kV/m/s St.Dev. = 156 kV/m/s 2001 n = 4 Mean = 590 kV/m/s St. Dev. = 61.0 kV/m/s Peak dE/dt [kV/m/s] Distance 15 m (1999, 2000, & 2001)(a)Mean355 kV/m/s St Dev154 kV/m/s Min50.0 kV/m/s Max673 kV/m/s GM315 kV/m/s Sample Size50 0255075100125150175200225250 Number 0 2 4 6 8 10 12 1999 n = 15 Mean = 92.6 kV/m/s St. Dev. = 31.0 kV/m/s 2000 n = 31 Mean = 118 kV/m/s St. Dev. = 56.0 kV/m/s 2001 n = 4 Mean = 211 kV/m/s St. Dev. = 27.0 kV/m/s Distance 30 m (1999, 2000, & 2001) Peak dE/dt [kV/m/s] (b)Mean118 kV/m/s St Dev56.0 kV/m/s Min16.0 kV/m/s Max241 kV/m/s GM103 kV/m/s Sample Size50 Figure 3-24 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999, 2000 and 2001.

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51 CHAPTER 4 ESTIMATION OF LEADER AND RETU RN-STROKE CURRENTS FROM MEASURED MAGNETIC FIELDS 4.1 Introduction Magnetic fields measured at 15 and 30 m are available for 1999, 2000, and 2001. In 1997, magnetic field records were measured at 5, 10, 20, and 30 m. 4.2 Estimation of Currents Using Ampere’s Law According to Ampere’s law for magnetostatics, enc 0I dl B, the line integral of magnetic flux density, B, around a closed pa th is proportional to the enclosed current, Ienc. The constant of proportionality o is the permeability of free space. In SI units o = 4 x 10-7 H/m. For a straight wire of infinite length the magnetic flux density external to the wire at a distance r from its axis is given by r 2 I Bo (4.1) Figure 4-1. A straight curre nt channel of infinite le ngth and B at a distance r.

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52 Here we have used the fact that the magnetic field is constant and tangential at any point on the circular integra tion path. Equation (4.1) is essentially the same as equation (2.1). If we assume that earth is a perfect conductor, and cons ider a very close observation point (a distance 15 or 30 m co mpared to the lightni ng channel of some kilometers) (4.1) will apply to a lightni ng channel above ground. Thus, knowing the magnetic field at distance r, from the light ning channel and using (4.1) one can estimate the current flowing in the channel if th e magnetostatic approximation is valid. Typical magnetic field waveforms with re spect to time are shown in Figures 3.10 and 3.11. They usually exhibit a relatively sl ow initial front followed by a fast rise to peak and then decay, as discussed below. Figure 4-2. A streaked-image diagram of a dart leader—return-stroke sequence in a rocket-triggered lightning flash

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53 As the downward leader tip approach es ground surface the magnetic field on ground associated with the leader current increases with time. When the leader attaches to the ground, return stroke is initiated. Hence the current increases ab ruptly and there is a fast rise in magnetic field. The initial rising portion (up to the peak ) of each magnetic field record can be divided into two parts: a slow rise part corresponding to leader and steep rise part corresponding to the return stroke. The divisi on is illustrated in Figures 4-3 and 4-4, where the magnitude of the leader part is labeled BL and that of the re turn stroke part BRS. For each part the corresponding current was esti mated using equation 4.1. It is important to note that the leader current corresponds to the final stage of the dart-leader process, when leader channel attaches to the ground, and the return-stroke cu rrent represents the peak value based on the assumption that the leader current continues to flow in the channel during the return-strok e process. Thus, the total p eak current flowing in the channel during the return-stroke stage is th e sum of leader current inferred from BL and return stroke current estimated from BRS. Using this approach, leader and the retu rn stroke currents for the years of 1997, 1999, 2000 and 2001 are evaluated. The histograms showing the statisti cs of leader and return-stroke currents for 1997, 1999, 2000 and 2001 are shown in Figure 4-5 through Figure 4-9. The scatter plots (see Figures 4-13 and 4-14) show comparisons of leader currents obtained from dE/dt (Kodali et al. 2005) vs those obtained from magnetic fields (BL) and of measured return stroke currents (see secti on 3.3) vs. those obtained from magnetic fields (BRS).

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54 Figure 4-3 Magnetic field at 15 m, Flash S9901, Stroke 3. Figure 4-4. Magnetic field at 30 m, Flash S9901, Stroke 3.

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55 Distance 5 m, 1997 Leader Current [kA] 0123456789 Number 0 1 2 3 4 5 6 Distance 10 m, 1997 Leader Current [kA] 0123456789 Number 0 1 2 3 4 5 6 Distance 20 m, 1997 Leader Current [kA] 0123456789 Number 0 1 2 3 4 5 6 Distance 30 m, 1997 Leader Current [kA] 0123456789 Number 0 1 2 3 4 5 6 (a) (b) (c) (d)Mean 1.80 kA St Dev 1.08 kA Min 0.94 kA Max 3.95 kA GM 1.58 kA Sample Size 7 Mean 1.80 kA St Dev 0.70 kA Min 1.05 kA Max 2.84 kA GM 1.69 kA Sample Size 9Mean 2.02 kA St Dev 1.00 kA Min 1.10 kA Max 3.93 k A GM 1.84 kA Sample Size 7Mean 2.06 kA St Dev 0.72 kA Min 1.34 kA Max 3.11 kA GM 1.95 kA Sample Size 6 Figure 4-5. Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 5 m, (b ) 10 m, (c) 20 m, and (d) 30 m in 1997.

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56 Distance 15 m, 1999 Leader Current [kA] 0123456789 Number 0 2 4 6 8 10 12 14 16 18 Mean2.25 kA St. Dev.1.02 kA Min0.52 kA Max4.29 kA GM2.01 kA Sample Size39(a) Distance 30 m, 1999 Leader Current [kA] 0123456789 Number 0 2 4 6 8 10 12 14 16 Mean3.21 kA St. Dev.1.61 kA Min0.71 kA Max7.87 kA GM2.82 kA Sample Size39(b) Figure 4-6. Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 1999.

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57 Distance 15 m, 2000 Leader Current [kA] 0123456789 Number 0 5 10 15 20 Mean1.53 kA St. Dev.0.82 kA Min0.38 kA Max3.83 kA GM1.32 kA Sample Size47(a) Distance 30 m, 2000 Leader Current [kA] 0123456789 Number 0 2 4 6 8 10 12 14 16 Mean2.13 kA St. Dev.1.30 kA Min0.40 kA Max6.36 kA GM1.80 kA Sample Size47(b) Figure 4-7. Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 2000.

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58 Distance 15 m, 2001 Leader Current [kA] 0123456789 Number 0 1 2 3 4 5 Mean2.03 kA St. Dev.1.28 kA Min0.85 kA Max5.45 kA GM1.76 kA Sample Size11(a) Distance 30 m, 2001 Leader Current [kA] 0123456789 Number 0 1 2 3 4 5 Mean2.57 kA St. Dev.2.18 kA Min0.87 kA Max8.63 kA GM2.04 kA Sample Size11(b) Figure 4-8. Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 2001.

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59 Distance 15 m, 1999,2000,&2001 Leader Current [kA] 0123456789 Number 0 10 20 30 40 50 1999 n = 39 Mean = 2.25 kA St. Dev. = 1.02 kA 2000 n = 47 Mean = 1.53 kA St. Dev. = 0.82 kA 2001 n = 11 Mean = 2.03 kA St. Dev. = 1.28 kA Mean1.87 kA St. Dev.1.01 kA Min0.38 kA Max5.40 kA GM1.62 kA Sample Size97 Figure 4-9. Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at 15 m in 1999, 2000, and 2001.

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60 Distance 30 m, 1997 1999, 2000, and 2001 Leader Current [kA] 0123456789 Number 0 5 10 15 20 25 30 35 1999 n = 39 Mean = 3.21 kA St. Dev. = 1.61 kA 2000 n = 47 Mean = 2.13 kA St. Dev. = 1.30 kA 2001 n = 11 Mean = 2.57 kA St. Dev. = 2.18 kA 1997 n = 6 Mean = 2.10 kA St. Dev. = 0.70 kA Mean2.58 kA St. Dev.1.57 kA Min0.40 kA Max8.63 kA GM2.17 kA Sample Size103 Figure 4-10. Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001.

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61 IL from B15 [kA] 0246810 IL from B30 [kA] 0 2 4 6 8 10 1999 2000 2001 IL(30 m) = -0.10 + 1.44 IL(15 m) R2 = 0.83 Sample Size = 97 Figure 4-11. Dart leader current inferred using Ampere’s Law for magnetostatics from measured magnetic fields measured at 30 m vs. that at 15 m in 1999, 2000, and 2001.

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62 IL from dE/dt [kA] 024681012 IL from B15 [kA] 0 2 4 6 8 10 12 1999 2000 2001 IL(Ampere’s Law) = 1.23 + 0.32 IL(dE/dt)R2 = 0.51 Sample Size = 39 IL(dE/dt) [kA] IL(Amperes Law) [kA] Mean 3.51 2.36 StDev 2.39 1.07 Figure 4-12. Dart leader current inferred using Ampere’s Law for magnetostatics from magnetic fields measured at 15 m vs. leader current inferred from dE/dt measurements [Kodali et al. 2005] in 1999, 2000, and 2001.

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63 IL from dE/dt [kA] 0246810 IL from B30 [kA] 0 2 4 6 8 10 1999 2000 2001 IL(Ampere’s Law) = 3.6 + 0.44 IL(dE/dt) R2 = 0.56 Sample Size = 6 IL(dE/dt) [kA] IL(Amperes Law) [kA] Mean 4.98 5.86 StDev 2.90 1.71 Figure 4-13. Dart leader current inferred using Ampere’s Law for magnetostatics from magnetic fields measured at 30 m vs. leader current inferred from dE/dt measurements [Kodali et al. 2005] in 1999, 2000, and 2001.

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64 Distance 5 m, 1997 Return-Stroke Peak Current [kA] 048121620242832 Number 0 1 2 3 4 Distance 10 m, 1997 Return-Stroke Peak Current [kA] 048121620242832 Number 0 1 2 3 4 Distance 20 m, 1997 Return-Stroke Peak Current [kA] 048121620242832 Number 0 1 2 3 4 5 Distance 30 m, 1997 Return-Stroke Peak Current [kA] 048121620242832 Number 0 1 2 3 4 5 (a)(b) (c) (d)Mean 11.0 kA St Dev 5.95 kA Min 3.33 kA Ma x 19.0 k A GM 9.37 kA Sample Size 7Mean 10.5 kA St Dev 4.44 kA Min 3.69 kA Max 17.0 kA GM 9.57 kA Sample Size 9Mean 9.13 kA St Dev 3.83 kA Min 4.03 kA Max 14.4 kA GM 8.42 kA Sample Size 7Mean 9.91 kA St Dev 4.57 kA Min 4.34 kA Max 15.9 kA GM 8.97 kA Sample Size 6 Figure 4-14. Return-stroke peak currents infe rred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997.

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65 Distance 15 m, 1999 Return-Stroke Peak Current [kA] 048121620242832 Number 0 2 4 6 8 10 12 14 (a)Mean14.5 kA St Dev6.40 kA Min4.88 kA Max28.7 kA GM13.1 kA Sample Size39 Distance 30 m, 1999 Return-Stroke Peak Current [kA] 048121620242832 Number 0 2 4 6 8 10 12 14 (b)Mean14.5 kA St Dev5.80 kA Min5.70 kA Max26.7 kA GM13.4 kA Sample Size39 Figure 4-15. Return-stroke peak currents infe rred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 1999.

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66 Distance 15 m, 2000 Return-Stroke Peak Current [kA] 048121620242832 Number 0 2 4 6 8 10 12 14 Mean12.0 kA St. Dev.6.19 kA Min3.34 kA Max31.8 kA GM10.6 kA Sample Size47(a) Distance 30 m, 2000 Return-Stroke Peak Current [kA] 048121620242832 Number 0 2 4 6 8 10 12 14 16 Mean11.8 kA St. Dev.6.91 kA Min3.09 kA Max28.9 kA GM10.5 kA Sample Size47(b) Figure 4-16. Return-stroke peak currents infe rred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 2000.

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67 Distance 15 m, 2001 Return-Stroke Peak Current [kA] 048121620242832 Number 0 1 2 3 4 5 Mean13.8 kA St. Dev.6.90 kA Min6.47 kA Max29.8 kA GM12.5 kA Sample Size11(a) Distance 30 m, 2001 Return-Stroke Peak Current [kA] 048121620242832 Number 0 1 2 3 4 5 Mean14.3 kA St. Dev.6.57 kA Min6.45 kA Max28.6 kA GM13.1 kA Sample Size11(b) Figure 4-17. Return-stroke peak currents infe rred using Ampere’s Law for magnetostatics from measured magnetic fields at (a) 15 m and (b) 30 m in 2001.

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68 Distance 15 m, 1 999, 2000, & 2001 Return-Stroke Peak Current [kA] 048121620242832 Number 0 5 10 15 20 25 30 1999 n = 30 Mean = 14.5 kA St. Dev. = 6.40 kA 2000 n = 47 Mean = 12.0 kA St. Dev. = 6.19 kA 2001 n = 11 Mean = 13.8 kA St. Dev. = 6.90 kA Mean13.2 kA St. Dev.6.41 kA Min3.34 kA Max31.8 kA GM11.7 kA Sample Size97 Figure 4-18. Return-stroke peak currents infe rred using Ampere’s Law for magnetostatics from measured magnetic fields at 15 m in 1999, 2000, and 2001.

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69 Distance 30 m, 1999, 2000, 2001 & 1997 Return-Stroke Peak Current [kA] 048121620242832 Number 0 5 10 15 20 25 30 35 1999 n = 39 Mean = 14.9 kA St. Dev. = 6.30 kA 2000 n = 47 Mean = 11.8 kA St. Dev. = 6.91 kA 2001 n = 11 Mean = 14.3 kA St. Dev. = 6.57 kA 1997 n = 6 Mean = 9.90 kA St. Dev. = 4.60 kA Mean13.0 kA St. Dev.6.00 kA Min3.09 kA Max28.9 kA GM11.7 kA Sample Size103 Figure 4-19. Return-stroke peak currents infe rred using Ampere’s Law for magnetostatics from measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001.

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70 IRS from B15 [kA] 05101520253035 IRS from B30 [kA] 0 5 10 15 20 25 30 35 1999 2000 2001 IRS(30 m) = 0.99 + 0.93 IRS(15 m)R2 = 0.97 Sample Size = 97 Figure 4-20. Return-stroke peak current infe rred using Ampere’s Law for magnetostatics from measured magnetic fields at 30 m vs. that inferred from measured magnetic fields at 15 m in 1999, 2000, and 2001.

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71 Measured IRS [kA] 0510152025303540 IRS from B15 [kA] 0 5 10 15 20 25 30 35 40 1999 2000 2001 IRS(Ampere’s Law) = 0.08 + 0.83 IRS(Meas.) R2 = 0.86 Sample Size = 71 IRS(Meas.) [kA]IRS(Amperes Law) [kA] Mean 15.3 13.2 St. Dev. 6.70 6.10 Figure 4-21. Return-stroke peak current infe rred using Ampere’s Law for magnetostatics from measured magnetic fields at 15 m vs. measured return-stroke peak current in 1999, 2000, and 2001.

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72 Measured IRS [kA] 0510152025303540 IRS from B30 [kA] 0 5 10 15 20 25 30 35 40 1999 2000 2001 1997 IRS(Ampere’s Law) = 0.36 + 0.83 IRS(Meas.) R2 = 0.90 Sample Size = 76 IRS(Meas.) [kA] IRS(Ampere’s Law) [kA] Mean 15.4 13.1 St. Dev. 6.87 5.97 Figure 4-22. Return-stroke peak current infe rred using Ampere’s Law for magnetostatics from measured magnetic fields at 30 m vs. measured return-stroke peak current in 1997, 1999, 2000, and 2001.

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73 IRS from B15 [kA] 05101520253035 IL from B15 [kA] 0 1 2 3 4 5 6 7 8 9 1999 2000 2001 IL(15 m) = 0.16 + 0.13 IRS(15 m) R2 = 0.68 Sample Size = 97 Figure 4-23. Leader vs. return-stroke cu rrents inferred using Ampere’s Law for magnetostatics from magnetic fields measured at 15 m in 1999, 2000, and 2001.

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74 IRS from B30 [kA] 05101520253035 IL from B30 [kA] 0 1 2 3 4 5 6 7 8 9 1999 2000 2001 IL(30 m) = -0.29 + 0.21 IRS(30 m) R2 = 0.72 Sample Size = 97 Figure 4-24. Leader vs. return-stroke cu rrents inferred using Ampere’s Law for magnetostatics from magnetic fields measured at 30 m in 1999, 2000, and 2001.

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75 IRS from (BL+BRS)15m [kA] 0510152025303540 IRS from (BL+BRS)30m [kA] 0 5 10 15 20 25 30 35 40 IRS from (BL+BRS)30m = 0.53 + 1.01 IRS from (BL+BRS)15m R2 = 0.98 Sample size = 97 Figure 4-25. Comparison of IRS from (BL+BRS)30m and IRS from (BL+BRS)15m for 1999, 2000, and 2001.

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76 Measured IRS [kA] 01020304050 IRS from (BL+BRS)15m [kA] 0 10 20 30 40 50 1999 2000 2001 IRS from (BL+BRS)15m = 0.07 + 0.95 IRS(Meas.) R2 = 0.87 Sample Size = 71 Figure 4-26. Comparison of IRS from (BL+BRS)15m inferred using Ampere’s Law for magnetostatics vs. IRS measured at channel base in 1999, 2000, and 2001.

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77 Measured IRS [kA] 01020304050 IRS from (BL+BRS)30m [kA] 0 10 20 30 40 50 1999 2000 2001 1997 IRS from (BL+BRS)30m = -0.02 + 1.01 IRS(Meas.) R2 = 0.89 Sample Size = 76 Figure 4-27. Comparison of IRS from (BL+BRS)30m inferred using Ampere’s Law for magnetostatics vs. IRS measured at channel base in 1997, 1999, 2000, and 2001. 4.3 Discussion and Summary From the statistical analysis of 97 records obtained in 1999, 2000, and 2001 the mean dart-leader current (at the time of its attachment to ground) inferred from leader magnetic fields measured at 15 m is 1.87 kA and standard deviation is 1.01 kA. The minimum and maximum dart-lead er currents are 0.38 and 5.40 kA, respectively. From

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78 magnetic fields measured at 30 m (103 reco rds obtained in 1997, 1999, 2000, and 2001), the mean leader current is 2.58 kA and sta ndard deviation is 1.57 kA. The minimum and maximum dart-leader currents are 0.40 and 8.63 kA, respectively. Typically leader currents are in the range of a few kiloampere s. Idone and Orville (1985) estimated dartleader peak currents for 22 leaders in two rocket-triggered flashes using the relation between return-stroke peak current IR and return-stroke peak relative light intensity LR in each of two flashes {LR = 1.5 (IR)1.6 and LR = 6.4(IR)1.1} to the dart leader relative light intensities in those flashes. The mean dart -leader current was 1.8 kA and the range was 0.1 to 6.0 kA. Results of this study are in reasonably good agreement with those of Idone and Orville (1985). Return-stroke peak currents estimated from magnetic fields (as the global magnetic field peak minus the leader contribution) measured at 15 m in 1999, 2000, and 2001 have a mean value of 13.2 kA and the standard devi ation is 6.4 kA. For the individual years the mean return-stroke current varies from 14.5 kA in 1999 to 12.0 kA in 2000 and 13.8 kA in 2001. Return stroke peak currents estimated from magnetic fields measured at 30 m in 1997, 1999, 2000, and 2001 have a mean value of 13.0 kA and the standard deviation is 6.0 kA. For the individual years the mean retu rn-stroke peak current varies from 9.9 kA in 1997, to 14.9 kA in 1999, to 11.8 kA in 2000, and to 14.3 kA in 2001. These inferred return-stroke peak currents are slightly lowe r than the directly measured return-stroke peak currents whose mean is 15.3 kA and st andard deviation is 7.5 kA. Depasse (1994) reported an arithmetic mean of 14.3 kA (max imum value of 60 kA, st andard deviation of 9 kA) for 305 peak current values directly m easured at the Kennedy Space Center (KSC), Florida and an arithmetic mean of 11 kA (maximum value 49.9 kA, and standard

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79 deviation of 5.6 kA) for 54 values directly measured at Saint-Privat d’Allier, France. Rakov et al. (1998), Crawford (1998), and Uman et al. (2000) reported an arithmetic mean of 15.1 kA (sample size = 37, maximum = 44.4 kA, and st. dev. = 9 kA), 12. 8 kA (sample size = 11, maximum = 22.6 kA, and st. dev. = 5.6 kA), and 14.8 kA (sample size = 25, maximum = 33.2 kA, and st. dev. = 7 kA ) from direct current measurements at Camp Blanding in 1993, 1997, and 1998, respectively. The return-stroke peak currents obtained using Ampere’s law for magnestotatics and (BL+BRS), where BL and BRS are the leader and return-stroke contributions to the total magnetic field (as done, for example, by Schoe ne et al. (2003)), measured at 15 m are about 14 % higher than those obtained from BRS alone (excluding the leader contribution). The return-stroke peak cu rrents obtained using Ampere’s law for magnestotatics and (BL+BRS) measured at 30 m are about 20 % higher than those obtained from BRS alone. Dart-leader current to return-stroke curre nt ratio obtained fr om magnetic fields measured at 15 m has a mean of 0.14 a nd the correlation coefficient between these currents is 0.82. Leader to return-stroke curr ent ratio obtained from magnetic fields at 30 m has a mean of 0.20 and the correlation coe fficient is 0.85 (note that the determination coefficient, R2, given in Figure 4-23 a nd Figure 4-24 is the square of the correlation coefficient, R). Idone and Orv ille (1985) obtained the ratio of dart leader to return-stroke current for 22 events having a mean of 0.17. Results of this study are consistent with those of Idone and Orville (1985).

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80 CHAPTER 5 DISPLACEMENT CURRENT ASSOCIATED WITH LEADER/RETURN STROKE SEQUENCES IN TRIGGERED LIGHTNING Maxwell’s integral equation relating azimu thal magnetic field to its sources has been used to investigate the relative c ontributions of conduc tion and displacement currents to the total ground level azimuthal ma gnetic field at 15 and 30 m from the base of a triggered lightning stroke. The analysis is based on a comparison of channel base current and corresponding magnetic fields measur ed at 15 and 30 m. It is concluded that Ampere’s law for magnetostatics, which negl ects the displacement current contribution, is inadequate for presentation of the tota l magnetic field due to lightning strokes at distances beyond approximately 30 m. 5.1 Displacement Current Estimates from Measured Magnetic Fields and ChannelBase Currents The following simple expression (same as Eq. (2.1)) based on Ampere’s law for magnetostatics is used here to estimate the azimuthal magnetic field intensity at the ground due to nearby lightning: (,)()/2 HrtItr (5.1) where I(t) is the channel current, assumed to be the same in all contributing channel sections, H(r,t) is the magnetic field intensity, and r is the radial distance from the channel termination point on ground. This re lationship has been found to describe measured magnetic fields quite closely, in both magnitude and waveshape, at distances up to 15 meters from the triggered-lightning channel base. Over the period from 1999 to 2001, magnetic field measurements have been made for nearly 70 return strokes in

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81 Florida at a distance of 30 m from the triggered-lightning st rike point. It is found that amplitudes of the measured fields at both 15 and 30 m are somewhat lower then predicted by Eq. 5.1, and the early portions of their waveforms exhibit slow fronts not seen in measured current waveforms. Figure 5-1. Superposition of measured magnetic field and channel-base current for Flash S9903, stroke 3. In order to examine the discrepancy, we consider as a starting point Maxwell’s integral equation relating the azimuthal magne tic field to its arbitrary, time-varying sources, ...o lSSE HdlJdSdS t .o SE I dS t = Ic + Id (5.2)

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82 where Ic and Id are the channel-base conduction current and displacement current respectively. As already described by Eq. 2.4 in section 2.6, the first term on the right side of Eq. 5.2 corresponds to I(t) in Eq. 5. 1. The second term is the displacement current whose density is normal to the integrati on surface S bounded by the integration path l, on the left-hand side of Eq. 5.2. When applied to a lightning stroke to earth with S being defined as flat, circular area of integration lying on the surface of the ground and centered at the strike point, the first term accounts for the eff ect of conduction current flowing normally through the integration surface. Th e second term on right side of Eq. 5.2 accounts for the effects of time variation of the vertical electric fiel d associated with the changing charge density di stribution along the lightning channel during both the approach of the leader and the resultant return stroke. Equivalently Eq. 5.2 can be written as 2dmeasmeas I rHI (5.3) where Imeas and Hmeas are measured channel-base current and measured magnetic field at distance r. In order to investigate the peak displ acement current, the following procedure was used. As a first step, the measured magnetic field converted to current using Eq. 5.1. and the measured conduction current, Imeas, at the channel base were superimposed. Then the difference between the current obtained from magnetic field using Eq. 5.1 and directly measured current was interpreted as the di splacement current. Th e displacement current appears to increase with time and has nega tive polarity up to the onset of the return stroke. Upon initiation of the return stroke, the total displacement current at that point changes polarity (becomes positive) and attains a peak of a few kA.

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83 This is illustrated in Figure 5-2. Figure 5-2. Displacement current for S9903 RS 3 as inferred, using Eq. 5.3, from Imeas and Hmeas at 30 m. As seen in Fig. 5.2, the shape of the inferred displacement current waveform resembles the shape of the electric field deri vative (see Fig 3-13). Prior to the returnstroke, while no conduction current is flow ing at ground level, the effect of the displacement current is apparent in the initia l slow front of the measured magnetic field. After the start of the return stroke, an abrupt increase in the slope of the magnetic field takes place. Further effects of the displacem ent current component on the total magnetic field are the reduction in amplitude of th e peak of the magnetic field waveform. Figures 5.3 – 5.6 show histograms of pos itive peak displacement currents (during the return-stroke stage) fo r the years 1999, 2000, and 2001, estimated from waveforms

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84 similar to that shown in Fig. 5-2. Simila rly figures 5.7 – 5.10 show histograms of negative peak displacement curren ts during the leader stage. Distance 15 m, 1999 Return-Stroke Peak Displacement Current [kA] 03691215 Number 0 2 4 6 8 10 12 (a)Mean6.09 kA St. Dev.3.29 kA Min1.10 kA Max15.0 kA GM5.25 kA Sample Size23 Distance 30 m, 1999 Return-Stroke Peak Displacement current [kA] 03691215 Number 0 2 4 6 8 10 (b)Mean6.41 kA St. Dev.3.11 kA Min2.70 kA Max15.0 kA GM5.76 kA Sample Size23 Figure 5-3. Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999.

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85 Distance 15 m, 2000 Return-Stroke Peak Displacement Current [kA] 03691215 Number 0 2 4 6 8 10 12 14 16 (a)Mean3.91 kA St. Dev.2.15 kA Min1.40 kA Max9.80 kA GM3.43 kA Sample Size31 Distance 30 m, 2000 Return-Stroke Peak Displacement Current [kA] 03691215 Number 0 2 4 6 8 10 12 14 16 18 (b)Mean4.93 kA St. Dev.2.65 kA Min1.69 kA Max12.0 kA GM4.33 kA Sample Size31 Figure 5-4. Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2000.

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86 Distance 15 m, 2001 Return-Stroke Peak Displacement Current [kA] 03691215 Number 0 1 2 3 4 5 (a)Mean4.07 kA St. Dev.1.55 kA Min2.30 kA Max6.60 kA GM3.82 kA Sample Size8 Distance 30 m, 2001 Return-Stroke Peak Displacement Current [kA] 03691215 Number 0 1 2 3 4 5 6 (b)Mean5.08 kA St. Dev.1.86 kA Min2.40 kA Max7.70 kA GM4.76 kA Sample Size8 Figure 5-5. Return-stoke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2001.

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87 Distance 15 m Return-Stroke Peak Displacement Current [kA] 03691215 Number 0 5 10 15 20 25 30 1999 n = 23 Mean = 6.09 kA St. Dev = 3.29 kA 2000 n = 31 Mean = 3.91 kA St. Dev = 2.15 kA 2001 n = 8 Mean = 4.07 kA St. Dev = 1.55 kA (a)Mean4.74 kA St. Dev.2.75 kA Min1.10 kA Max15.0 kA GM4.07 kA Sample Size62 Distance 30 m Return-Stroke Peak Displacement Current [kA] 03691215 Number 0 5 10 15 20 25 30 35 1999 n = 23 Mean = 6.41 kA St. Dev. = 3.11 kA 2000 n = 31 Mean = 4.93 kA St. Dev. = 2.65 kA 2001 n = 8 Mean = 5.08 kA St. Dev. = 1.86 kA (b)Mean5.50 kA St. Dev.2.80 kA Min1.69 kA Max15.0 kA GM4.87 kA Sample Size62 Figure 5-6. Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999, 2000, and 2001.

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88 Distance 15 m, 1999 Leader Peak Displacement Current [kA] 0246810 Number 0 2 4 6 8 10 12 14 (a)Mean2.42 kA St. Dev.1.37 kA Min0.50 kA Max6.50 kA GM2.08 kA Sample Size23 Distance 30 m, 1999 Leader Peak Displacment Current [kA] 0246810 Number 0 2 4 6 8 10 12 (b)Mean3.07 kA St. Dev.1.60 kA Min0.50 kA Max7.50 kA GM2.66 kA Sample Size23 Figure 5-7. Leader peak displacement cu rrent estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999.

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89 Distance 15 m, 2000 Leader Peak Displacement Current [kA] 0246810 Number 0 5 10 15 20 (a)Mean2.15 kA St. Dev.1.70 kA Min0.30 kA Max9.30 kA GM1.73 kA Sample Size31 Distance 30 m, 2000 Leader Peak Displamement Current [kA] 0246810 Number 0 5 10 15 20 25 (b)Mean1.99 kA St. Dev.1.26 kA Min0.50 kA Max5.50 kA GM1.70 kA Sample Size31 Figure 5-8. Leader peak displacement cu rrent estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2000.

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90 Distance 15 m, 2001 Leader Peak Displacement Current [kA] 0246810 Number 0 1 2 3 4 5 6 (a)Mean1.92 kA St. Dev.0.67 kA Min1.10 kA Max3.00 kA GM1.82 kA Sample Size8 Distance 30 m, 2001 Leader Peak Displacement Current [kA] 0246810 Number 0 1 2 3 4 5 (b)Mean1.96 kA St. Dev.0.54 kA Min1.30 kA Max3.00 kA GM1.90 kA Sample Size8 Figure 5-9. Leader peak displacement cu rrent estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 2001.

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91 Figure 5-10. Leader peak displacement cu rrent estimated, using Eq. 5.3, from Imeas and Hmeas at (a) 15 m and (b) 30 m in 1999, 2000, and 2001.

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92 5.2 Displacement Current Estimates fr om dE/dt Signatures at 15 and 30 m Although variation of dE/dt as a function of radial distance from the lightning channel is needed for estimating displacemen t current, a rough estimate of this current can be obtained using dE/dt waveforms measur ed only at two distances, 15 and 30 m. In the following, we will use two approximations to the expected distance dependence of dE/dt, the latter bei ng shown by a dashed line in Fig. 5-11. In the first approximation, the dE/dt inside the circle of radius 15 m centered at the channel attachment point is assumed to be c onstant and approximately equal to that at 15 m, and the dE/dt between 15 and 30 m is assumed to be constant and approximately equal to that at 30 m. Clearly, this step-wis e approximation of dE/dt distance dependence (illustrated in Fig. 5-11) results in an underestimation of the displacement current. Figure 5-11. Distance dependences of dE/dt used in evaluating displacement current within 30 m of the lightning channel base d on measured dE/dt at 15 and 30 m. The dE/dt waveform has a characteristic sh ape which is negative until the onset of the return stroke. At the start of the retu rn stroke, the polarity is reversed and its Step-wise approximation 15 m 30 m dE dt Expected variation of dE dt Distance from the channel Linear approximation Measuredat 30 m dE dt Measuredat 15 m dE dt

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93 magnitude increases rapidly. This characterist ic waveshape is seen both at 15 and 30 m. At 30 m, the magnitude of dE/dt is smalle r than at 15 m. Assuming that the dE/dt waveform is similar at different distances ranging from 15 to 30 m from the lightning channel, the next step was to determine the value of dE/dt at 30 m corresponding to dE/dt peak at 15 m. Propagation over a dist ance of 15 m corresponds to 15/(3108) = 510-8 s = 50 ns. dE/dt waveforms were digitized at 250 MH z. Since the sampling interval is 4 ns at a rate of 250 MHz, the peak at 30 m will be observed after a delay of about 12 samples after the occurrence of peak at 15 m. Thus the dE/dt value at 30 m corresponding to the peak at 15 m is 12 samples prior to the peak at 30 m. This gives us the dE/dt values at 15 and 30 m at the same instant on time but at di fferent locations. The dE/dt values at 30 m corresponding to dE/dt at 15 m along with p eak dE/dt values at both 15 and 30 m are given in Table 5-1. Now, the displacement current based on the step-wise approximation of dE/dt distance dependence can be estimated as d I = .o SE dS t 1530 015(15)(30) 22oo rrEmEm rdrrdr tt 222(15)(30) 2(15/2)2(30/215/2)ooEmEm tt (5.4) Note that the displacement current estimated using Eq. 5.4 corresponds to the time of peak dE/dt at 15 m. Displacement currents estimated in a manner described above are summarized in Table 5-1, which also contains estimates obtained using peak values of dE/dt at both 15 and 30 m (that is, without propagation delay taken into account). The second approximation to the distance depe ndence of dE/dt, which has been used here, is a linear approximation (also illustrated in Fig. 5-11),

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94 d I = .o SE dS t 30 0(15) (15)2o rEm mrrdr t 232(15) 2(30/2)(30/3)(15).(30/2)oEm mm t (5.5) where (15)(30) 1530 EmEm tt m is the slope of the slante d line shown in Fig. 5-11 for linear approximation. Displacement current va lues calculated using Eq. 5.5 are given in the last column of Table 5-1. Figures 5.12 – 5.13 are the histograms of the displacement currents at the time of dE/dt peak at 15 m, estimated using Eq. 5.4, for 1999, 2000 and 2001. Figures 5.14 – 5.15 are the histograms of the displacement cu rrents, estimated using Eq. 5.4 and peak values of dE/dt at both 15 and 30 m, that is, without accounting for propagation delay. Figures 5.16 – 5.17 are histograms of the disp lacement currents, estimated using Eq. 5.5 and peak values of dE/dt at both 15 and 30 m.

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95 Table 5-1 Displacement currents estimated us ing Eq. 5.4 (step-wise approximation of dE/dt distance dependence) and Eq. 5. 5 (linear approximations of dE/dt distance dependence). Flash and stroke ID Peak dE/dt at 15m [kV/m/s] Peak dE/dt at 30m [kV/m/s] dE/dt at 30 m corresponding to peak at 15 m [kV/m/s] Id at the time of peak dE/dt at 15 m, step-wise approx. [kA] Id using peak values of dE/dt at both 15 and 30 m, step-wise approx. [kA] Id using peak values of dE/dt at both 15 and 30 m, linear approx. [kA] S9901 RS2 423 145273.155.36 8.26 S9901 RS3 172 55141.342.11 3.33 S9901 RS4 280 90703.063.44 5.42 S9915 RS4 198 74341.882.63 3.92 S9918 RS1 450 140834.375.44 8.67 S9918 RS2 235 80151.752.97 4.59 S9918 RS4 426 118724.014.88 8.09 S9918 RS6 362 96473.154.06 6.84 S9932 RS1 418 1111034.554.70 7.89 S9932 RS2 307 80322.523.42 5.79 S9935 RS1 330 104122.294.01 6.37 S9935 RS3 300 92102.063.60 5.77 S9935 RS4 72 23130.690.88 1.39 S9935 RS5 250 7731.623.01 4.81 S9935 RS6 330 10402.064.01 6.37 S0006 RS1 182 73702.452.51 3.64 S0006 RS4 80 26230.930.99 1.55 S0006 RS5 50 16120.540.61 0.97 S0008 RS3 250 78572.633.03 4.82 S0008 RS4 495 166824.636.21 9.64 S0008 RS5 347 126112.384.53 6.84 S0008 RS6 258 8281.763.15 4.99 S0008 RS7 673 2352017.988.62 13.2 S0012 RS1 545 200764.837.16 10.8 S0013 RS1 161 48431.811.91 3.08 S0013 RS3 336 105543.114.07 6.48 S0013 RS4 520 1651115.336.35 10.0 S0013 RS5 345 107412.934.16 6.64 S0013 RS6 447 138764.225.38 8.60

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96 Table 5-1(Contd.) Displacement currents estimated using Eq. 5.4 (step-wise approximation of dE/dt distance de pendence) and Eq. 5.5 (linear approximations of dE/dt distance dependence). Flash and stroke ID Peak dE/dt at 15m [kV/m/s] Peak dE/dt at 30m [kV/m/s] dE/dt at 30 m corresponding to peak at 15 m [kV/m/s] Id at the time of peak dE/dt at 15 m, step-wise approx. [kA] Id using peak values of dE/dt at both 15 and 30 m, step-wise approx. [kA] Id using peak values of dE/dt at both 15 and 30 m, linear approx. [kA] S0015 RS2 264 9180.43.163.36 5.16 S0015 RS4 456 166313.435.96 8.99 S0015 RS5 204 58201.652.36 3.88 S0015 RS6 349 113763.614.30 6.76 S0016 RS1 520 2061305.697.12 10.4 S0016 RS5 227 95181.763.20 4.58 S0022 RS1 228 80732.792.93 4.47 S0022 RS2 406 130333.164.98 7.85 S0022 RS3 334 11262.204.19 6.50 S0023 RS1 339 111112.334.20 6.58 S0023 RS2 559 207434.307.38 11.0 S0023 RS3 656 216885.758.15 12.7 S0025 RS1 397 122914.194.77 7.64 S0025 RS3 229 67251.902.69 4.38 S0027 RS1 217 64392.092.56 4.15 S0027 RS2 355 120232.654.47 6.92 S0027 RS3 413 127273.094.96 7.94 S0105 RS5 644 24154.128.55 12.7 S0107 RS1 638 2241416.638.19 12.5 S0123 RS2 560 1817.53.646.90 10.8 S0123 RS4 519 196614.396.92 10.3

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97 1999 Displacement Current [kA] 012345678 Number 0 1 2 3 4 5 (a)Mean2.57 kA St. Dev.1.13 kA Min0.69 kA Max4.55 kA GM2.31 kA Sample Size15 2000 Displacement Current [kA] 012345678 Number 0 2 4 6 8 10 (b)Mean3.20 kA St. Dev.1.59 kA Min0.54 kA Max7.98 kA GM2.82 kA Sample Size31 Figure 5-12. Return-stroke displacement curre nt within 30 m of the lightning channel at the time of dE/dt peak at 15 m estimat ed using step-wise approximation (with propagation delay taken into acc ount) in (a) 1999 and (b) 2000.

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98 2001 Displacement Current [kA] 012345678 Number 0 1 2 3 (a)Mean4.70 kA St. Dev.1.33 kA Min3.64 kA Max6.63 kA GM4.57 kA Sample Size4 1999, 2000, and 2001 Displacement Current [kA] 012345678 Number 0 2 4 6 8 10 12 14 1999 n = 15 Mean = 2.57 kA St. Dev = 1.13 kA 2000 n = 31 Mean = 3.20 kA St. Dev = 1.59 kA 2001 n = 4 Mean = 4.70 kA St. Dev = 1.33 kA (b)Mean3.13 kA St. Dev.1.52 kA Min0.54 kA Max7.98 kA GM2.76 kA Sample Size50 Figure 5-13. Return-stroke displacement curre nt within 30 m of the lightning channel at the time of dE/dt peak at 15 m estimat ed using step-wise approximation (with propagation delay taken into account) in (a) 2001 and (b) 1999, 2000, and 2001.

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99 1999 Displacement Current [kA] 0123456789 Number 0 1 2 3 4 5 6 (a)Mean3.63 kA St. Dev.1.23 kA Min0.88 kA Max5.44 kA GM3.37 kA Sample Size15 2000 Displacement Current [kA] 0123456789 Number 0 2 4 6 8 10 12 (b)Mean4.40 kA St. Dev.2.01 kA Min0.61 kA Max8.62 kA GM3.85 kA Sample Size31 Figure 5-14. Return-stroke displacement cu rrent within 30 m of the lightning channel estimated using peak values of dE/d t at both 15 and 30 m estimated using step-wise approximation (without propagation delay taken into account) in (a) 1999 and (b) 2000.

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100 2001 Displacement Current [kA] 0123456789 Number 0 1 2 3 4 5 (a)Mean7.64 kA St. Dev.0.86 kA Min6.90 kA Max8.55 kA GM7.55 kA Sample Size4 1999, 2000, and 2001 Displacement Current [kA] 0123456789 Number 0 2 4 6 8 10 12 14 16 1999 n = 15 Mean = 3.63 kA St. Dev. = 1.23 kA 2000 n = 31 Mean = 4.40 kA St. Dev. = 2.01 kA 2001 n = 4 Mean = 7.64 kA St. Dev. = 0.86 kA (b)Mean4.43 kA St. Dev.2.00 kA Min0.61 kA Max8.62 kA GM3.91 kA Sample Size50 Figure 5-15. Return-stroke displacement cu rrent within 30 m of the lightning channel estimated using peak values of dE/d t at both 15 and 30 m estimated using step-wise approximation (without taki ng propagation delay into account) in (a) 2001 and (b) 1999, 2000, and 2001.

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101 1999 Displacement Current [kA] 02468101214 Number 0 1 2 3 4 5 6 (a)Mean5.83 kA St. Dev.2.02 kA Min1.39 kA Max8.67 kA GM5.38 kA Sample Size15 2000 Displacement Current [kA] 02468101214 Number 0 2 4 6 8 10 12 (b)Mean6.81 kA St. Dev.3.05 kA Min0.97 kA Max13.2 kA GM6.00 kA Sample Size31 Figure 5-16. Return-stroke displacement cu rrent within 30 m of the lightning channel estimated using peak values of dE/d t at both 15 and 30 m estimated using linear approximation (without propagati on delay taken into account) in (a) 1999 and (b) 2000.

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102 2001 Displacement Current [kA] 02468101214 Number 0 1 2 3 4 5 (a)Mean11.6 kA St. Dev.1.21 kA Min10.3 kA Max12.7 kA GM11.5 kA Sample Size4 1999, 2000, and 2001 Displacement Current [kA] 02468101214 Number 0 2 4 6 8 10 12 14 16 1999 n = 15 Mean = 5.83 kA St. Dev. = 2.02 kA 2000 n = 31 Mean = 6.81 kA St. Dev. = 3.05 kA 2001 n = 4 Mean = 11.6 kA St. Dev. = 1.21 kA (b)Mean6.90 kA St. Dev.3.02 kA Min0.87 kA Max13.2 kA GM6.12 kA Sample Size50 Figure 5-17. Return-stroke displacement cu rrent within 30 m of the lightning channel estimated using peak values of dE/d t at both 15 and 30 m estimated using linear approximation (without taking propaga tion delay into acc ount) in (a) 2001 and (b) 1999, 2000, and 2001.

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103 Figure 5-18 shows the scatter plot compar ing displacement currents obtained using Imeas and Hmeas (Eq. 5.3) vs. those obtained using dE /dt at 15 and 30 m at the time of peak value of dE/dt at 15 m (s tep-wise approximation). Displacement current from measured channel base current and associated magnetic field [kA] 02468101214 Displacement current from dE/dt [kA] 0 2 4 6 8 10 12 14 1999 2000 2001 Id(dE/dt) = 1.4 + 0.37 Id(Imeas and Hmeas) R2 = 0.43 Sample size = 21 Id(dE/dt) [kA] Id(Imeas and Hmeas) [kA] Mean 3.13 4.65 St. Dev. 1.52 2.50 Figure 5-18. Scatter plot showing displacement current estimates from dE/dt measured at 15 and 30 m from the lightning channel (step-wise approximation) vs. those estimated from measured channel base current and associated magnetic field. In the former case, the estimate corresponds to the time of pe ak value of dE/dt at 15 m.

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104 Figure 5-19 is similar to Figur e 5-18, but displacement cu rrents on the vertical axis are estimated using peak values of dE/dt at both 15 and 30 m (ste p-wise approximation), that is, without taking into account propagation delay from 15 to 30 m. Displacement current from measured channel base current and associated magnetic field [kA] 02468101214 Displacement current from dE/dt [kA] 0 2 4 6 8 10 12 14 1999 2000 2001 Id(dE/dt) = 2.67 + 0.38 Id(Imeas and Hmeas) R2 = 0.31 Sample size = 21 Id(dE/dt) [kA] Id(Imeas and Hmeas) [kA] Mean 4.43 4.65 St. Dev. 2.00 2.50 Figure 5-19. Scatter plot showing displacement current estimates from dE/dt measured at 15 and 30 m from the lightning channel (step-wise approximation) vs. those estimated from measured channel base current and associated magnetic field. In the former case, the estimate is obtaine d using peak values of dE/dt at both 15 and 30 m.

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105 Figure 5-20 is similar to Figur e 5-19, but displacement cu rrents on the vertical axis are estimated using linear approximation (see Fig. 5-11). Displacement current from measured channel base current and associated magnetic field [kA] 02468101214 Displacement current from dE/dt [kA] 0 2 4 6 8 10 12 14 1999 2000 2001 Id(dE/dt) = 4.22 + 0.57 Id(Imeas and Hmeas) R2 = 0.32 Sample size = 21 Id(dE/dt) [kA] Id(Imeas and Hmeas) [kA] Mean 6.90 4.65 St. Dev. 3.02 2.50 Figure 5-20. Scatter plot showing displacemen t current from dE/dt measured at 15 and 30 m from the lightning channe l (linear approximation) vs. those estimated from measured channel base current and asso ciated magnetic field. In the former case, the estimate is obtained using peak values of dE/dt at both 15 and 30 m.

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106 5.3 Discussion and Summary The displacement current waveform rese mbles the electric field derivative waveform. The displacement current has negati ve polarity up to the onset of the returnstroke. Upon initiation of the return-stroke, th e total displacement current at that point changes polarity (becomes positive) and attains a peak of a few kiloamperes. The return-stroke peak displacement current inferred from channel-base currents, Imeas, and associated magnetic fields, Hmeas, measured at 15 m in 1999, 2000, and 2001 has a mean value of 4.7 kA and standard de viation of 2.7 kA, while return-stroke peak displacement current from Imeas and Hmeas at 30 m has a mean value of 5.5 kA and standard deviation of 2.8 kA. The sample size for both 15 m and 30 m data is 62. The leader peak displacement current from Imeas and Hmeas at 15 m has a mean of 2.2 kA and standard deviation of 1.5 kA, whereas for 30-m measurements the mean is 2.4 kA and standard deviation is 1.4 kA. The return-stroke stage displacement current within 30 m of the lightning channel at the time of dE/dt peak at 15 m estimat ed using step-wise ap proximation of dE/dt variation with distance from the lightning cha nnel (after taking propagation delay into account) is characterized by a mean value of 3.1 kA. The minimum and maximum values are 0.5 kA and 8.0 kA, respectively. The return-stroke displa cement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m (i.e. without taking propa gation delay into account) and st ep-wise approximation of dE/dt variation with distance from the lightning ch annel has a mean value of 4.4 kA. The minimum value is 0.6 kA, and the maximum value is 8.6 kA. The return-stroke displacement current within 30 m of the lightning channel esti mated using peak values of dE/dt at both 15 and 30 m and linear approxima tion of dE/dt variation with distance from

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107 the lightning channel has a mean value of 6. 9 kA. The minimum value is 1.0 kA, and the maximum value is 13.2 kA. Note that the displacement current during the return-stroke stage flows in the direction opposite to that of the conduction current in the lightning channel. Schnetzer et al. (1998) have obtained th e displacement current for flash 96-23, stroke 5, which had a return-stroke peak curren t directly measured at the channel base of approximately 20 kA. The return-stroke peak displacement current was 13.5 kA within 50 m of the lightning channel and 0.7 kA w ithin 10 m of the lightning channel. Our results match reasonably well those ob tained by Schnetzer et al. (1998). The correlation coefficient of 0.66 is obtained between displacement current estimates obtained from dE/dt measured at 15 and 30 m from the li ghtning channel (using step-wise approximation and at the time of peak value of dE/dt at 15 m) and those obtained from measured channel base currents and associated magnetic fields at 30 m.

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108 CHAPTER 6 SUMMARY From the statistical analysis of 97 records obtained in 1999, 2000, and 2001 the mean dart-leader current (at the time of its attachment to ground) inferred from leader magnetic fields measured at 15 m is 1.87 kA and standard deviation is 1.01 kA. The minimum and maximum dart-lead er currents are 0.38 and 5.40 kA, respectively. From magnetic fields measured at 30 m (103 reco rds obtained in 1997, 1999, 2000, and 2001), the mean leader current is 2.58 kA and sta ndard deviation is 1.57 kA. The minimum and maximum dart-leader currents are 0.40 and 8.63 kA, respectively. Typically leader currents are in the range of a few kiloampere s. Idone and Orville (1985) estimated dartleader peak currents for 22 leaders in two rocket-triggered flashes using the relation between return-stroke peak current IR and return-stroke peak relative light intensity LR in each of two flashes {LR = 1.5 (IR)1.6 and LR = 6.4(IR)1.1} to the dart leader relative light intensities in those flashes. The mean dart -leader current was 1.8 kA and the range was 0.1 to 6.0 kA. Results of this study are in reasonably good agreement with those of Idone and Orville (1985). Return-stroke peak currents estimated from magnetic fields (as the global magnetic field peak minus the leader contribution) measured at 15 m in 1999, 2000, and 2001 have a mean value of 13.2 kA and the standard devi ation is 6.4 kA. For the individual years the mean return-stroke current varies from 14.5 kA in 1999 to 12.0 kA in 2000 and 13.8 kA in 2001. Return stroke peak currents estimated from magnetic fields measured at 30 m in 1997, 1999, 2000, and 2001 have a mean value of 13.0 kA and the standard deviation is

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109 6.0 kA. For the individual years the mean retu rn-stroke peak current varies from 9.9 kA in 1997, to 14.9 kA in 1999, to 11.8 kA in 2000, and to 14.3 kA in 2001. These inferred return-stroke peak currents are slightly lowe r than the directly measured return-stroke peak currents whose mean is 15.3 kA and st andard deviation is 7.5 kA. Depasse (1994) reported an arithmetic mean of 14.3 kA (max imum value of 60 kA, st andard deviation of 9 kA) for 305 peak current values directly m easured at the Kennedy Space Center (KSC), Florida and an arithmetic mean of 11 kA (maximum value 49.9 kA, and standard deviation of 5.6 kA) for 54 values directly measured at Saint-Privat d’Allier, France. Rakov et al. (1998), Crawford (1998), and Uman et al. (2000) reported an arithmetic mean of 15.1 kA (sample size = 37, maximum = 44.4 kA, and st. dev. = 9 kA), 12. 8 kA (sample size = 11, maximum = 22.6 kA, and st. dev. = 5.6 kA), and 14.8 kA (sample size = 25, maximum = 33.2 kA, and st. dev. = 7 kA ) from direct current measurements at Camp Blanding in 1993, 1997, and 1998, respectively. The return-stroke peak currents obtained using Ampere’s law for magnestotatics and (BL+BRS), where BL and BRS are the leader and return-stroke contributions to the total magnetic field (as done, for example, by Schoe ne et al. (2003)), measured at 15 m are about 14 % higher than those obtained from BRS alone (excluding the leader contribution). The return-stroke peak cu rrents obtained using Ampere’s law for magnestotatics and (BL+BRS) measured at 30 m are about 20 % higher than those obtained from BRS alone. Dart-leader current to return-stroke curre nt ratio obtained fr om magnetic fields measured at 15 m has a mean of 0.14 a nd the correlation coefficient between these currents is 0.82. Leader to return-stroke curr ent ratio obtained from magnetic fields at 30

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110 m has a mean of 0.20 and the correlation co efficient is 0.85. Idone and Orville (1985) obtained the ratio of dart leader to return-s troke current for 22 events having a mean of 0.17. The displacement current waveform rese mbles the electric field derivative waveform. The displacement current has negati ve polarity up to the onset of the returnstroke. Upon initiation of the return-stroke, th e total displacement current at that point changes polarity (becomes positive) and attains a peak of a few kiloamperes. The return-stroke peak displacement current inferred from channel-base currents, Imeas, and associated magnetic fields, Hmeas, measured at 15 m in 1999, 2000, and 2001 has a mean value of 4.7 kA and standard de viation of 2.7 kA, while return-stroke peak displacement current from Imeas and Hmeas at 30 m has a mean value of 5.5 kA and standard deviation of 2.8 kA. The sample size for both 15 m and 30 m data is 62. The leader peak displacement current from Imeas and Hmeas at 15 m has a mean of 2.2 kA and standard deviation of 1.5 kA, whereas for 30-m measurements the mean is 2.4 kA and standard deviation is 1.4 kA. The return-stroke stage displacement current within 30 m of the lightning channel at the time of dE/dt peak at 15 m estimat ed using step-wise ap proximation of dE/dt variation with distance from the lightning cha nnel (after taking propagation delay into account) is characterized by a mean value of 3.1 kA. The minimum and maximum values are 0.5 kA and 8.0 kA, respectively. The return-stroke displa cement current within 30 m of the lightning channel estimated using peak values of dE/dt at both 15 and 30 m (i.e. without taking propa gation delay into account) and st ep-wise approximation of dE/dt variation with distance from the lightning ch annel has a mean value of 4.4 kA. The

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111 minimum value is 0.6 kA, and the maximum value is 8.6 kA. The return-stroke displacement current within 30 m of the lightning channel esti mated using peak values of dE/dt at both 15 and 30 m and linear approxima tion of dE/dt variation with distance from the lightning channel has a mean value of 6. 9 kA. The minimum value is 1.0 kA, and the maximum value is 13.2 kA. Note that the displacement current during the return-stroke stage flows in the direction opposite to that of the conduction current in the lightning channel. Schnetzer et al. (1998) have obtained th e displacement current for flash 96-23, stroke 5, which had a return-stroke peak curren t directly measured at the channel base of approximately 20 kA. The return-stroke peak displacement current was 13.5 kA within 50 m of the lightning channel and 0.7 kA w ithin 10 m of the lightning channel. Our results match reasonably well those ob tained by Schnetzer et al. (1998). The correlation coefficient of 0.66 is obtained between displacement current estimates obtained from dE/dt measured at 15 and 30 m from the li ghtning channel (using step-wise approximation and at the time of peak value of dE/dt at 15 m) and those obtained from measured channel base currents and associated magnetic fields at 30 m.

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112 CHAPTER 7 RECOMMENDATIONS FOR FUTURE RESEARCH Additional data are needed to verify the findings presented here. In future measurements, magnetic field records should be synchronize d to better than 40-50 ns with return stroke current records, so that the onset of return stroke current can be accurately identified in the magnetic field waveform. This will allow one to better distinguish the leader and re turn-stroke parts of the magnetic field waveform and hence obtain more accurate estimates of the dart-l eader current. Additional measurements of dE/dt waveforms are needed and at more distances from the lightning channel. This will give a better approximation of dE/dt variation with distan ce and, as a result, more accurate estimates of the di splacement current. Data collected during 1997, 1999, 2000, and 2001 should be analyzed further to infer additional properties of rocket-triggered lightning. For example, multiple-station electric and magnetic field measurements can be used for estimating distributions of char ge and current along th e lightning channel.

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113 APPENDIX DISPLACEMENT CURRENT GRAPHS In this appendix, the displacement curre nt waveforms inferred from measured channel-base currents, Imeas, and associated magnetic fields, Hmeas, measured at 15 and 30 m for strokes in lightning flashes triggere d in 1999 (23 strokes), 2000 (31 strokes), and 2001 (8 strokes) are shown. The displacement currents were estimated as 2dmeasmeas I rHI

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144 LIST OF REFERENCES Ben Rhouma, A., Auriol, A.P., Eybert-Berar d, A., Berlandis, J.-P., and Bador, B.; "Nearby Lightning Electromagnetic Fields," in Proc. of the 11th Int. Zurich Symp. on Electromagn. Compat., Zurich Switzerland, 1995, pp. 423-428 Byrne, C.J., Few, A.A., and Weber, M.E.; "I n situ Balloon Electric Field Measurements," Geophys. Res. Lett., 10:39-42, 1983 Crawford, D.E.; "Multiple-Station Measurem ents of Triggered Lightning Electric and Magnetic Fields," Master’s thesis University of Florida; 1998 Crawford, D.E., Rakov, V.A., Uman, M.A., Schnetzer, G.H., Rambo K.J., Stapleton, M.V., and Fisher, R.J.; "The Close Light ning Electromagnetic Environment: DartLeader Electric Field Change Versus Distance," J. Geophys. Res., 106, 14,90914,917, 2001 Depasse, P., "Statistics on Artificially Tr iggered Lightning," J. Geophys. Res., 99, 18,515 – 18,522, 1994 Idone, V.P., Orville, R.E.; "Correlated peak relative light intensity and peak current in triggered lightning subsequent return strokes," J. Geophys. Res., 90, 6159– 6164, 1985 Jordan, D.M., Rakov, V.A., Besley, W.H., and Uman, M.A.; "Luminosity Characteristics of Dart Leaders and Return Strokes in Natural Lightning," J. Geophys. Res., 102, 22,025-22,032, 1997 Kodali, V.; "Characterization and Analysis of Close Lightning Electromagnetic Fields," Master’s thesis, University of Florida; 2003 Krehbiel, P.R.; The Earth’s Electrical Environment ; National Academy Press, Washington DC; 1986 MacGorman, D.R., and Rust, W.D.; The Electrical Nature of Thunderstorms ; Oxford University Press, New York; 1998 Rakov, V.A.; "Some Inferences on the Propaga tion Mechanisms of Dart Leaders and Return Strokes," J. Geophys. Res., 103, 1879-1887, 1995

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145 Rakov, V.A., Uman, M.A., Rambo, K.J., Ferna ndez, M.I., Fisher, R.J., Schnetzer, G.H., Thottappillil, R., Eybert-Berard, A., Be rlandis, J.P., Lala nde, P., Bonamy, A., Laroche, P., and Bondiou-Clergerie, A.; New Insights into Lightning Processes Gained from Triggered-Lightning Experi ments in Florida and Alabama," J. Geophys. Res., 103, 14,117-14,130, 1998 Rakov, V.A.; "Lightning Disc harges Triggered using Rock et-and-Wire Techniques," J. Geophys. Res., 100, 25,711-25,720, 1999 Rakov, V.A., Uman, M.A., Wang, D., Rambo, K.J., Crawford, D.E., and Schnetzer, G.H.; "Lightning Properties from Tr iggered-Lightning Experime nts at Camp Blanding, Florida (1997-1999)," in Pr oc. of the 25th Int. Conf. on Lightning Protection, Rhodes, Greece, 2000, pp. 54-59 Rakov, V.A.; "Characterization of Light ning Electromagnetic Fields and Their Modeling," in Proc. of the 15th Int. Zurich Symp. on EMC, Zurich, Switzerland, 2001, pp. 545-550 Rakov, V.A, Uman, M.A., Crawford, D.E., Schoene, J., Jerauld, J., Rambo, K.J., Schnetzer, G.H., DeCarlo, B.A., and Miki M.; "Close Lightning Electromagnetic Environment: Triggered-Lightning E xperiments," in Proc. of the 15th Int. Zurich Symp. on EMC, Zurich, Switzerland, 2003, pp. 545-550 Rakov, V.A., and Uman, M.A.; Lightning: Physics and Effects ; Cambridge University Press, Cambridge, UK; 2003 Rakov, V.A.; EEL 5490 "Lightning," class notes; University of Florida, Spring Term 2005 Schnetzer, G.H., Fisher, R.J., Rakov, V.A., and Uman, M.A.; "The Magnetic Field Environment of Nearby Light ning," in Proc. of the 24t h Int. Conf. on Lightning Protection, Birmingham, United Kingdo m, September 14-18, 1998, pp. 346-349 Schoene, J.; "Analysis of Parameters of Rocket-Triggered Lightning Measured During the 1999 and 2000 Camp Blanding Experime nt and Modeling of Electric and Magnetic Field Derivatives using the Tran smission Line Model," Master’s thesis, University of Florida, 2002 Schoene, J., Uman, M.A., Rakov, V.A., Koda li, V., Rambo, K.J., Schnetzer, G.H.; "Statistical Characteristics of the Elec tric and Magnetic Fields and Their Time Derivatives 15 m and 30 m from Triggere d Lightning," J. Geophys. Res., 108, D6, 4192, 10.1029/2002JD002698, 2003 Simpson, G. and Scrase, F.J.; "The Distri bution of Electricity in the Thunderclouds," Proc. R. Soc. London Ser. A, 161, 309-352, 1937 Thottappillil, R., and Rakov, V.A.; "On Differ ent Approaches to Calculating Lightning Electric Fields," J. Geophys. Res., 106, 14,191-14,205, 2001

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146 Uman, M.A.; The Lightning Discharge ; Academic Press, San Diego, California; 1987 Uman, M.A., Rakov, V.A., Rambo, K.J., Vaught T.W., Fernandez, M.I., Cordier, D.J, Chandler, R.M., Bernstein, R., and Gold en, C.; "Triggered-Lightning Experiments at Camp Blanding, Florida (1993-1995)," Tr ans. of IEE Japan, Special Issue on Artificial Rocket Triggered Light ning, 117-B, No. 4, 446-452, 1997 Uman, M. A.; The Lightning Discharge ; Dover, Mineola, New York; 2001 Uman, M.A., Schoene, J., Rakov, V.A., Rambo, K.J., and Schnetzer, G.H.; "Correlated Time Derivatives of Current, Electric Fi eld Intensity, and Magnetic Flux Density for Triggered Lightning at 15 m," J. Geophys. Res., 107, D13, 4160, 10.1029/2000JD000249, 2002 Wang, D., Rakov, V.A., Uman, M.A., Fernand ez, M.I., Rambo, K.J., Schnetzer, G.H., and Fisher, R.J.; "Charact erization of the Initial Stage of Negative RocketTriggered Lightning," J. Geophys. Res., 104, 4213-4222, 1999 Wang, D., Rakov, V.A., Uman, M.A., Takagi, N., Watanabe, T., Crawford, D.E., Rambo, K.J., Schnetzer, G.H., Fisher, R.J., and Kawasaki, Z.I.; "Attachment Process in Rocket-Triggered Lightning Stroke s," J. Geophys. Res., 104, 2141-2150, 1999

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147 BIOGRAPHICAL SKETCH Ashwin Jhavar was born in Akola, India, in 1979. He graduate d with a bachelor’s degree in electrical and electronics engin eering from Birla Institute of Technology and Science, India, in 2002. In 2003, he went to the USA to pursue gra duate studies at the University of Florida.


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Title: Triggered-Lightning Properties Inferred from Measured Currents and Very Close Magnetic Fields
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Copyright Date: 2008

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Holding Location: University of Florida
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Permanent Link: http://ufdc.ufl.edu/UFE0013160/00001

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Title: Triggered-Lightning Properties Inferred from Measured Currents and Very Close Magnetic Fields
Physical Description: Mixed Material
Copyright Date: 2008

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Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
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TRIGGERED-LIGHTNING PROPERTIES INFERRED FROM MEASURED
CURRENTS AND VERY CLOSE MAGNETIC FIELDS















By

ASHWIN B. JHAVAR


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2005

































Copyright 2005

by

Ashwin B. Jhavar















ACKNOWLEDGMENTS

I would like to thank Dr. Vladimir A. Rakov for his infinite patience, guidance, and

support throughout my graduate studies at the University of Florida. I would like to thank

Dr. Martin A. Uman and Dr. Douglas M. Jordan for their valuable suggestions during the

weekly lightning meetings. I sincerely thank Jens Schoene, Jason Jerauld, Rob Olsen,

Brian DeCarlo, and Vinod Jayakumar for helping me with the data and software, and for

other innumerable favors (without which I would not have been able to complete my

thesis). Research in my thesis was funded in part by National Science Foundation. The

data analyzed in the thesis were originally acquired with NSF and FAA funding.
















TABLE OF CONTENTS



A C K N O W L E D G M E N T S ................................................................................................. iii

LIST OF TABLES .................................................................... ........ vi

L IST O F F IG U R E S .... ...... ................................................ .. .. ..... .............. vii

A B S T R A C T .......................................... ..................................................x iii

CHAPTER

1 INTRODUCTION ............... ..................................................... 1

2 LITERA TURE REVIEW .......................................................... ..............3

2 .1 C u m u lonim bu s ........................................................................... 3
2.2 Cloud Charge D istribution........................................................... ............... 4
2.3 Mechanisms of Cloud Electrification.......................................... ..............6
2.3.1 Convection M echanism ........................................ ......................... 7
2.3.2 Graupel-ice Mechanism................................................. 7
2.4 Downward Negative Lightning Discharges to Ground ....................................10
2.5 Artificial Initiation (Triggering) of Lightning Using the Rocket-and-Wire
T e c h n iq u e ................................................... ................. ................ 1 5
2.5.1 C classical Triggering......................................................... ............... 16
2.5.2 A altitude Triggering...................................................... .......................... 18
2.6 Previous Studies of Displacement Current Associated with Triggered
L ig h tn in g .................................................................................................. .... 19
2.6.1 Theory ....................... ................................. ....................19
2.6.2 Estimation of Displacement Current Contribution at 50 m........................21

3 CHARACTERIZATION OF EXPERIMENTAL DATA USED IN THIS STUDY .25

3.1 M agnetic Field M easuring Techniques ........................................ .....................25
3 .2 E xperim mental Setup ...................................................................... ...................27
3.2.1 IC LR T O verview ................................................ ............................ 27
3 .2 .2 1997 E xperim ents .......................................................................... ... ... 29
3.2.3 1999 Experim ents ................ ... ... ...... ..................... .................. 30
3.2.3.1 Instrumentation for Current Measurements ...................................32
3.2.3.2 Instrumentation for Electric Field Measurements...............................33









3.2.3.3 Instrumentation for Electric Field Derivative Measurement............33
3.2.4 2000 Experiments ......... ............. ........................ 33
3.2.5 2001 E xperim ents .......... .................. ......... ............... ............... 35
3.3 D ata Presentation ........ ..... .... .................... ........ ........ ...... .......... .... 36
3.3.1 G general Inform ation ............................................................................36
3.3.2 Channel-base current ........... .. ......... ................... 40
3.3.3 M magnetic Field............... ................................................ ........ .. ...... .. 42
3.3.4 Electric field derivative (dE/dt) ............................................. .. ............. 47

4 ESTIMATION OF LEADER AND RETURN-STROKE CURRENTS FROM
MEASURED MAGNETIC FIELDS...... .................. ...............51

4.1 Introduction ...................................................................... .......... 51
4.2 Estimation of Currents Using Ampere's Law ...............................................51
4.3 Discussion and Sum m ary .................................. .....................................77

5 DISPLACEMENT CURRENT ASSOCIATED WITH LEADER/RETurN
STROKE SEQUENCES IN TRIGGERED LIGHTNING............... .....................80

5.1 Displacement Current Estimates from Measured Magnetic Fields and
Channel-B ase Currents ............................................. ...... ........................80
5.2 Displacement Current Estimates from dE/dt Signatures at 15 and 30 m ............92
5.3 D iscu ssion and Sum m ary ........................................................ ..................... 106

6 SU M M A R Y ......... .. ...... .... .. ...... ........................................................ 108

7 RECOMMENDATIONS FOR FUTURE RESEARCH ........................ 112

APPENDIX DISPLACEMENT CURRENT GRAPHS......... ..... .............. 113

LIST OF REFEREN CE S ................ .......... ............................ ....... ..................... 144

BIOGRAPHICAL SKETCH ............................. ............................. ............... 147















LIST OF TABLES


Table p

2-1 Displacement currents Id estimated from measured electric field data at times
prior to and at the onset of a 20 kA peak stroke current. .......................................22

3-1 Summary of mean, standard deviation, GM (geometric mean), and sample sizes
of measured peak current, peak magnetic field and electric field derivative ..........37

5-1 Displacement currents estimated using eq. 5.4 (step-wise approximation of dE/dt
distance dependence) and eq. 5.5 (linear approximations of dE/dt distance
dependence)............ ............. ......................... ............ ......... 95

5-1 (Contd.) Displacement currents estimated using eq. 5.4 (step-wise
approximation of dE/dt distance dependence) and eq. 5.5 (linear approximations
of dE/dt distance dependence)....................... ..... ............................. 96
















LIST OF FIGURES


Figure page

2-1 An isolated thundercloud in central New Mexico, with a rudimentary indication
of how electric charge is thought to be distributed inside and around the
thundercloud, as inferred from the remote and in situ observations..........................

2-2 Balloon measurements of corona current and the inferred vertical electric field E
versus altitude and air temperature inside a small storm in New Mexico on 16
August 1981, which produced no lightning. ........................................ ..................6

2-3 Illustration of the convection mechanism of cloud electrification ............................8

2-4 Charge transfer by collision in the graupel-ice mechanism of cloud
electrification. It is assumed that the reversal temperature TR is -15 C and that
it occurs at a height of 6 km ........................................................... .....................9

2-5 A vertical triple representing the idealized gross charge structure of a
thundercloud such as that shown in Figure 2-1; the negative screening layer
charges at the cloud top and the positive corona space charge produced at
grou n d are ig n ored h ere........................................... ........................................... 10

2-6 Various processes comprising a negative cloud-to-ground lightning flash. ............11

2-7 Sequence of events in classical triggered lightning. The upward positive leader
and initial continuous current constitute the initial stage.........................................16

2-8 Sequence of events in altitude-triggered lightning leading to the establishment of
a relatively low-resistance connection between the upward-moving positive
leader tip and the ground. The processes that follow the sequence shown, an
initial continuous-current and possibly one or more downward-leader--upward-
return-stroke sequences, are similar to their counterparts in classical triggered
2 -1
lightning. The rocket speed is of the order of 102 m S ..................... ..................18

2-9 Qualitative illustration of the shape of the time derivative of the ground level
vertical electric field of a nearby return stroke Since displacement current
density is simply related to the derivative of electric field by a constant, it has
the sam e waveshape.. .................................. .... ......... ...............24









2-10 From top to bottom, magnetic field measured at 50 m during stroke 5 of Flash
96-23, the corresponding field according to Ampere's law for magnetostatics, as
applied to the measured channel-base current, and the difference between the
tw o ............... ................... ............................................. ...... 24

3-1 Thevenin equivalent circuit of a loop antenna ............................... ............... .25

3-2 Norton equivalent circuit for a loop antenna.............. ............................................26

3-3 An overview of the ICLRT at Camp Blanding, Florida, 1999-2001. Not all test
objects are show n. ............................................. ................... ........ 28

3-4 Photograph of lightning flash S0012 triggered from the underground launcher. ....28

3-5 Locations of different instrumentation stations for 1997 multiple station
experim ent. .......................................................................... 30

3-6 Data acquisition system used in the 1997 multiple-station experiment .................31

3-7 Experimental setup (placement of electric and magnetic field antennas) used in
SA TTLIF for 2000.. .................... .................. ... .... ..................34

3-8 Setup of strike rod and ring mounted over launch tubes in 2000...........................35

3-9 Measured channel-base current, Flash S9901, Stroke 3................ .................. 37

3-10 M agnetic field at 15 m, Flash S9901, Stroke 3. ... ......................... ...............38

3-11 M agnetic field at 30 m, Flash S9901, Stroke 3 ................................. ............... 38

3-12 Electric field derivative (dE/dt) at 15 m, Flash S9901, Stroke 3. ............................39

3-13 Electric field derivative (dE/dt) at 30 m, Flash S9901, Stroke 3. ............................39

3-14 Return-stroke peak currents in (a) 1997, (b) 1999, (c) 2000, and (d) 2001. ............40

3-15 Return-stroke peak currents in 1997, 1999, 2000 and 2001...............................41

3-16 Peak magnetic fields measured at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in
19 9 7 .............................................................................................4 2

3-17 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1999 .........................43

3-18 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 2000 .........................44

3-19 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 2001 .........................45

3-20 Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1997, 1999, 2000 and
2 0 0 1 ..................................................... ..................... ................ 4 6









3-21 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999. ..............................47

3-22 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 2000. ..............................48

3-23 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 2001. ..............................49

3-24 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999, 2000 and 2001. .....50

4-1 A straight current channel of infinite length and B at a distance r...........................51

4-2 A streaked-image diagram of a dart leader-return-stroke sequence in a rocket-
triggered lightning flash ................................................ ............................... 52

4-3 M agnetic field at 15 m, Flash S9901, Stroke 3...................... ..... .............. 54

4-4 Magnetic field at 30 m, Flash S9901, Stroke 3 ...........................................54

4-5 Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997......55

4-6 Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at (a) 15 m and (b) 30 m in 1999 .................................56

4-7 Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at (a) 15 m and (b) 30 m in 2000 .................................57

4-8 Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at (a) 15 m and (b) 30 m in 2001.............. .....................58

4-9 Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at 15 m in 1999, 2000, and 2001 ................. ............ 59

4-10 Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001..........................60

4-11 Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields measured at 30 m vs. that at 15 m in 1999, 2000, and
200 1 .............. ........ ............................................... ........................... 6 1

4-12 Dart leader current inferred using Ampere's Law for magnetostatics from
magnetic fields measured at 15 m vs. leader current inferred from dE/dt
measurements in 1999, 2000, and 2001. ...................................... ............... 62

4-13 Dart leader current inferred using Ampere's Law for magnetostatics from
magnetic fields measured at 30 m vs. leader current inferred from dE/dt
measurements in 1999, 2000, and 2001. ...................................... ............... 63









4-14 Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in
19 9 7 .................................................................................64

4-15 Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at (a) 15 m and (b) 30 m in 1999 .........................65

4-16 Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at (a) 15 m and (b) 30 m in 2000 .........................66

4-17 Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at (a) 15 m and (b) 30 m in 2001 .........................67

4-18 Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 15 m in 1999, 2000, and 2001 ..........................68

4-19 Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001 ................69

4-20 Return-stroke peak current inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 30 m vs. that inferred from measured
magnetic fields at 15 m in 1999, 2000, and 2001. ................................................70

4-21 Return-stroke peak current inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 15 m vs. measured return-stroke peak current
in 1999, 2000, and 200 1 ........................... .................................. ...... ............7 1

4-22 Return-stroke peak current inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 30 m vs. measured return-stroke peak current
in 1997, 1999, 2000, and 2001 ...... .....................................................................72

4-23 Leader vs. return-stroke currents inferred using Ampere's Law for
magnetostatics from magnetic fields measured at 15 m in 1999, 2000, and 2001...73

4-24 Leader vs. return-stroke currents inferred using Ampere's Law for
magnetostatics from magnetic fields measured at 30 m in 1999, 2000, and 2001...74

4-25 Comparison of IRS from (BL+BRS)30m and IRS from (BL+BRS)15m for 1999, 2000,
and 2001. .............................................................................75

4-26 Comparison of IRs from (BL+BRS)15m inferred using Ampere's Law for
magnetostatics vs. IRS measured at channel base in 1999, 2000, and 2001.............76

4-27 Comparison of IRS from (BL+BRS)30m inferred using Ampere's Law for
magnetostatics vs. IRS measured at channel base in 1997, 1999, 2000, and 2001...77

5-1 Superposition of measured magnetic field and channel-base current for Flash
S 9 9 0 3 strok e 3 ........................................................................................... ... ........8 1









5-2 Displacement current for S9903 RS3 as inferred, using Eq. 5.3, from Imeas and
H m eas a t 3 0 m .............................................................................................................8 3

5-3 Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and
Hmeas at (a) 15 m and (b) 30 m in 1999. ...................................... ............... 84

5-4 Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and
Hmeas at (a) 15 m and (b) 30 m in 2000. ...................................... ............... 85

5-5 Return-stoke peak displacement current estimated, using Eq. 5.3, from Imeas and
Hmeas at (a) 15 m and (b) 30 m in 2001. ...................................... ............... 86

5-6 Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas and
Hmeas at (a) 15 m and (b) 30 m in 1999, 2000, and 2001....................................... 87

5-7 Leader peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas
at (a) 15 m and (b) 30 m in 1999 ............................ ... ............. ............ 88

5-8 Leader peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas
at (a) 15 m and (b) 30 m in 2000 ............................................................................ 89

5-9 Leader peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas
at (a) 15 m and (b) 30 m in 2001 ................................................... ............... 90

5-10 Leader peak displacement current estimated, using Eq. 5.3, from Imeas and Hmeas
at (a) 15 m and (b) 30 m in 1999, 2000, and 2001. ............................................ 91

5-11 Distance dependence of dE/dt used in evaluating displacement current within
30 m of the lightning channel based on measured dE/dt at 15 and 30 m................92

5-12 Return-stroke displacement current within 30 m of the lightning channel at the
time of dE/dt peak at 15 m estimated using step-wise approximation (with
propagation delay taken into account) in (a) 1999 and (b) 2000. ..........................97

5-13 Return-stroke displacement current within 30 m of the lightning channel at the
time of dE/dt peak at 15 m estimated using step-wise approximation (with
propagation delay taken into account) in (a) 2001 and (b) 1999, 2000, and 2001...98

5-14 Return-stroke displacement current within 30 m of the lightning channel
estimated using peak values of dE/dt at both 15 and 30 m estimated using step-
wise approximation (without propagation delay taken into account) in (a) 1999
and (b) 2000. .........................................................................99

5-15 Return-stroke displacement current within 30 m of the lightning channel
estimated using peak values of dE/dt at both 15 and 30 m estimated using step-
wise approximation (without taking propagation delay into account) in (a) 2001
and (b) 1999, 2000, and 200 1 ........................................................................ ... 100









5-16 Return-stroke displacement current within 30 m of the lightning channel
estimated using peak values of dE/dt at both 15 and 30 m estimated using linear
approximation (without propagation delay taken into account) in (a) 1999 and
(b) 2000. ........................................................................... 10 1

5-17 Return-stroke displacement current within 30 m of the lightning channel
estimated using peak values of dE/dt at both 15 and 30 m estimated using linear
approximation (without taking propagation delay into account) in (a) 2001
and (b) 1999, 2000, and 200 1 ........................................................................ ... 102

5-18 Scatter plot showing displacement current estimates from dE/dt measured at 15
and 30 m from the lightning channel (step-wise approximation) vs. those
estimated from measured channel base current and associated magnetic field. In
the former case, the estimate corresponds to the time of peak value of dE/dt at
15 m ...................... ............ .. ..........................................103

5-19 Scatter plot showing displacement current estimates from dE/dt measured at 15
and 30 m from the lightning channel (step-wise approximation) vs. those
estimated from measured channel base current and associated magnetic field. In
the former case, the estimate is obtained using peak values of dE/dt at both 15
an d 3 0 m .......................................................................... 104

5-20 Scatter plot showing displacement current from dE/dt measured at 15 and 30 m
from the lightning channel (linear approximation) vs. those estimated from
measured channel base current and associated magnetic field. In the former case,
the estimate is obtained using peak values of dE/dt at both 15 and 30 m..............105















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

TRIGGERED-LIGHTNING PROPERTIES INFERRED FROM MEASURED
CURRENTS AND VERY CLOSE MAGNETIC FIELDS

By

Ashwin B. Jhavar

December 2005

Chair: Vladimir A. Rakov
Cochair: Martin A. Uman
Major Department: Electrical and Computer Engineering

Very close magnetic fields produced by rocket-triggered lightning measured in

1997, 1999, 2000, and 2001 at Camp Blanding, Florida, are examined. The leader and

return stroke contributions to the total magnetic field are estimated and used to infer

leader and return-stroke currents. The statistical characteristics of these inferred currents

are examined. The return-stroke currents inferred from measured magnetic fields are

compared with directly measured ones. Leader currents inferred from measured magnetic

fields are compared with those estimated using dE/dt measurements. The statistics of the

ratio of leader to return stroke currents are compiled. Current estimates from measured

magnetic fields are in reasonable agreement with independent measurements and

theoretical predictions found in the literature. From the statistical analysis of 97 records

obtained in 1999, 2000, and 2001 the mean leader current inferred from magnetic field at

15 m is 1.87 kA and standard deviation is 1.01 kA. For magnetic fields at 30 m (103

records obtained in 1997, 1999, 2000, and 2001), the mean leader current is 2.58 kA and









the standard deviation is 1.57 kA. Typically leader currents are in the range of few

kiloamperes.

Displacement current associated with leader/return stroke sequences in triggered

lightning is estimated using (1) measured channel-base current and current inferred from

measured magnetic field and (2) dE/dt measurements at 15 and 30 m. The displacement

currents found using the above two approaches are compared. Return-stroke

displacement current within 30 m of the lightning channel at the time of peak dE/dt at 15

m, estimated using step-wise approximation of dE/dt variation with distance from the

lightning channel (after taking propagation delay into account) is characterized by a mean

value of 3.1 kA. The minimum value is 0.5 kA and maximum is 8.0 kA.














CHAPTER 1
INTRODUCTION

Lightning discharges are the cause of many deaths and injuries. Electromagnetic

fields generated by lightning can have deleterious effects on sensitive electronic devices.

A detailed knowledge of electromagnetic fields generated by close lightning is needed for

developing adequate lightning protection schemes.

A review of the lightning literature is presented in Chapter 2. Cloud electrical

structure and mechanisms of cloud electrification are discussed. Salient properties of both

natural and triggered lightning are given with focus on triggered lightning. Both classical

and altitude rocket-triggered lightning discharges are considered.

Chapter 3 presents the characteristics of measured current, magnetic field, and

electric field derivative (dE/dt) waveforms due to rocket-triggered lightning. It also

contains a description of the instrumentation used to measure these quantities in 1997,

1999, 2000 and 2001.

Leader and return-stroke currents inferred from measured magnetic fields are

presented in Chapter 4. These are compared with the directly measured return-stroke

currents and with the leader currents inferred from close electric field derivative (dE/dt)

measurements.

Chapter 5 deals with the displacement currents associated with leader/return stroke

sequences in triggered lightning. Displacement currents are estimated from measured

magnetic fields and current records using Maxwell's equations. Also included is an

estimation of peak displacement currents from dE/dt signatures measured at 15 and 30 m.






2


Chapter 6 summarizes the data and analysis of the leader and return-stroke currents

and the displacement currents associated with triggered lightning.

Recommendations for future research are given in Chapter 7.

The Appendix has the waveforms of the displacement currents.














CHAPTER 2
LITERATURE REVIEW

2.1 Cumulonimbus

The primary source of lightning is the cloud type termed cumulonimbus or

thundercloud. A thundercloud develops from a small fair-weather cloud called a cumulus,

which is formed when parcels of warm, moist air rise and cool by adiabatic expansion,

that is, without the transfer of heat or mass across the boundaries of the air parcels. When

the relative humidity in a rising and cooling parcel exceeds saturation, moisture

condenses on airborne particulate matter within it to form the many small water particles

that constitute the visible cloud. The height of the condensation level, which determines

the height of the visible cloud base, increases with decreasing relative humidity at the

ground. This is why cloud bases in Florida are generally lower than in arid locations,

such as New Mexico or Arizona. Parcels of warm, moist air can only continue to rise to

form a cumulus and eventually a cumulonimbus if the atmospheric temperature lapse

rate, that is, the decrease in temperature with increasing height, is larger than the moist-

adiabatic lapse rate, about of 0.6 C per 100 m.

The convection of buoyant moist air is usually confined to the troposphere, the

layer of the atmosphere that extends from the Earth's surface to the tropopause. The

height of tropopause varies from approximately 18 km in the tropics in the summer to 8

km in high latitudes in the winter. The tropopause is a narrow layer that separates the

troposphere from the next layer of the atmosphere, the stratosphere, which extends from

tropopause to a height of 50 km. In the troposphere the temperature decreases with









increasing altitude, while in the stratosphere the temperature at first becomes roughly

independent of altitude and then increases with altitude. A zero or positive temperature

gradient in the stratosphere serves to suppress convection and, therefore, hampers the

penetration of cloud tops into the stratosphere.

Lightning is usually associated with convective cloud systems ranging from 3 to 20

km in vertical extent. The horizontal dimensions of active air-mass thunderstorms range

from about 3 km to >50 km.

2.2 Cloud Charge Distribution

The distribution and motion of thunderstorm electric charges, most resides on

hydrometeors but some of which is free ions, is complex and changes continuously as the

cloud evolves. Hydrometeors whose motion is predominantly influenced by gravity (with

fall speeds > 0.3 m s-) are called precipitation particles. All other hydrometeors are

called cloud particles. The basic features of the cloud charge structure include a net

positive charge near the top, a net negative charge below it, and an additional positive

charge at the bottom of the cloud. These features are illustrated in Figure 2-1.

In-situ measurements of electric fields inside the cloud have been made using free

balloons carrying instruments to measure those fields. In situ measurements are superior

to remote measurements in that a relatively accurate charge height can be determined.

However, since the balloon can sense the field only along a more or less straight vertical

path and it samples different portions of that path at different times, the charge magnitude

can be estimated only if assumptions regarding the size and shape of individual charge

regions and the charge variation with time are made. The average volume charge density,

pv, in the cloud is generally found by assuming that the charge (i) is horizontally uniform

and (ii) does not vary in time.

































Figure 2-1. An isolated thundercloud in central New Mexico, with a rudimentary
indication of how electric charge is thought to be distributed inside and around
the thundercloud, as inferred from the remote and in situ observations.
Adapted from Krehbiel (1986).

Then according to Gauss's law in point form pv = So(dEz/dz), that is, pv is

proportional to the rate at which the vertical electric field Ez increases or decreases with

increasing altitude z as the balloon ascends. Figure 2-2 shows the results of a vertical

sounding of the electric field in a small New Mexico storm that produced no lightning.

This electric field profile was obtained up to a height of 10 km above mean sea level

using a balloon-borne instrument that measured the corona current from a 1-m-long

vertical wire. The corona current and the corresponding vertical electric field reversed

sign twice, between 6 and 7 km and above 9 km. The charge structure in Figure 2-2, a

negative charge between -5 and -15 C with positive charges above and below it, appears

to be consistent with the "classical" tripolar charge structure.











10 16 August 1981

I I
I I


1 Pos




I 7 --10
o I


4 I
t I I I

1 I Pos


E -50 -25 +25 +50 (kVIm) -0


Cloud Base





-4 -2 0 2 4
Corona Current, pA

Figure 2-2. Balloon measurements of corona current and the inferred vertical electric
field E versus altitude and air temperature inside a small storm in New
Mexico on 16 August 1981, which produced no lightning. Adapted from
Byrne et al. (1983)

2.3 Mechanisms of Cloud Electrification

Any cloud electrification mechanism involves (i) a small-scale process that

electrifies individual hydrometeros and (ii) a process that spatially separates these

charged hydrometeors by their polarity, the resultant distances between the charged cloud

regions being of the order of kilometers. Since most charges reside on hydrometeors of

relatively low mobility, the cloud is a relatively good electrical insulator and leakage


~~_~__~_









currents between the charged regions are thought to have a small effect on the charge

separation process.

2.3.1 Convection Mechanism.

In this mechanism the electric charges are supplied by external sources: fair-

weather space charge and corona near the ground and cosmic rays near the cloud top.

Organized convection provides large-scale separation. According to this mechanism,

illustrated in Figure 2-3, warm air currents (updrafts) carry positive fair-weather space

charge to the top of the growing cumulus. Negative charge, produced by cosmic rays

above the cloud, is attracted to the cloud's boundary by the positive charges within it.

The negative charge attaches, within a second or so, to cloud particles to form a negative

screening layer. These charged cloud particles carry much more charge per unit volume

of cloudy air than is carried by precipitation particles. Downdrafts, caused by cooling and

convective circulation, assumed to carry the negative charge down the sides of the cloud

toward the cloud base, this negative charge serving to produce positive corona at the

Earth's surface. Corona generates additional positive charge under the cloud and, hence,

provides a positive feedback to the process. The convective mechanism results in a

positive cloud-charge dipole, although it seems unlikely that the negative charge region

formed by this mechanism would lie in a similar temperature range for different types of

thunderstorms, as suggested by observations. Note that in convection model there is no

role for precipitation in forming the dipole charge structure.

2.3.2 Graupel-ice Mechanism.

In this mechanism the electric charges are produced by collisions between

precipitation particles (graupel) and cloud particles (small ice crystals). Precipitation

particles are generally larger than cloud particles, although there is no absolute











(a) (b) (c) -- -

++ + + -
--++ ++ + + +
++
F e + + +++ ++--
+ -+++- + --
+ + + + + + +- +
+ + + Far Weather Large Positive
Positive Space Charge
Space Charge + + + ++--h
S + + SpaceCharge ++++ ++4 ++ + + ++ +_ .Produced by Corona
+ +/ + + + .+ + + + ++ -,++ + e+"+++


Figure 2-3. Illustration of the convection mechanism of cloud electrification. Adapted
from MacGorman and Rust (1998)

demarcation in size to distinguish precipitation particles, which are falling out of the

cloud, from cloud particles, which remain essentially suspended or move upward in

updrafts. The large-scale separation of charged particles is provided by the action of

gravity. In the graupel-ice mechanism, which appears to be capable of explaining the

"classical" tripolar cloud charge structure, the electrification of individual particles

involves collisions between graupel particles and ice crystals in the presence of water

droplets. The presence of water droplets is necessary for significant charge transfer, as

shown by the laboratory experiments. A simplified illustration of this mechanism is given

in Figure 2-4.

The heavy graupel particles (two of which are shown in Figure 2-4) fall through a

suspension of smaller ice crystals (hexagons) and supercooled water droplets (dots). The

droplets remain in a supercooled liquid state until they contact an ice surface, whereupon

they freeze and stick to the surface in a process called riming. Laboratory experiments

show that when the temperature is below a critical value called the reversal temperature,

TR, the falling graupel particles acquire a negative charge in collision with the ice

particles. At temperature above TR they acquire positive charge. The charge sign reversal









temperature TR is generally thought to be between -10 and -20 C, the temperature range

characteristic of the main negative charge region found in thunderclouds.

*..0 2.''. -...-. ; *,...-


,,"- .'* -'l \ ..,- .o" Water Droplets
e 0
** \+ y \ ,,


U .o U \ i o i *.
(./-) .. I -. I e-". s, c stals
.
2-4. C -g t s y coll*io i e--c-.m
:: -. .. .

,. *o :" *. *Ij ,*e. *0
Higher "-r-(Colder)'-A 9 ,- : .'. --
Lower (Warner) "a is gw *a p. *v. (-cr)

0 ... t ." e. c
0r l f F e l b c a
.. .,* 9-E ......... : ':
"* "


0 Grapel 9 8 ,
r* I

..

F .: KIIr t:e a *.n t g p *e i s of








that it occurs at a height of 6 km. Taken from Rakov and Uman (2003).



collisions is determined by the rates at which the ice and graupel surfaces are growing.


The surface that is growing faster acquires a positive charge.

It is possible that the primary electrification mechanism changes once a storm

becomes strongly electrified. For example, collisions between ice crystals and graupel









could initiate the electrification, and then the larger convective energies of the storm

could continue it.

2.4 Downward Negative Lightning Discharges to Ground

The source of lightning is usually a cumulonimbus, whose idealized charge

structure is shown in the Figure 2-5 as three vertically stacked regions labeled P and LP

for the main positive and the lower positive charge regions and N for the main negative

charge region.





-- Qp= 40 C

~= -40 C


Hp= 12 km H =7 km Q 3C
!2Nin 7kin &.
Hp= 2 km



Figure 2-5. A vertical triple representing the idealized gross charge structure of a
thundercloud such as that shown in Figure 2-1; the negative screening layer
charges at the cloud top and the positive corona space charge produced at
ground are ignored here.

Downward negative lightning discharges, that is, discharges that are initiated in the

cloud, initially develop in an overall downward direction, and transport negative charge

to ground, probably account for about 90 percent of all cloud-to-ground discharges. The

overall cloud-to-ground lightning discharge, termed a flash, is composed of a number of

processes, some of which involve channels that emerge from the cloud while others

involve channels that are confined to the cloud volume. Only processes occurring in the

channels outside the cloud render themselves to optical observations that can be used to











determine channel geometry, extension speed and other pertinent features of those


channels. The sequence of the processes involved in a typical negative downward


lightning flash is shown in Figure 2-6.


CLOUD CHARGE
DISTRIBUTION


t=0


PRELIMINARY
BREAKDOWN


1.00 ms


STEPPED
LEADER


1.10 ms


1.15 ms


19 ms


/ DRT


Figure 2-6. Various processes comprising a negative cloud-to-ground lightning flash.
Adapted from Uman (1987, 2001)

The stepped leader is preceded by an in-cloud process called the preliminary or


initial breakdown. There is no consensus on the mechanism of this process. It may be a


discharge bridging the main negative and the lower positive charge regions, as shown in


Figure 2-5. The initial breakdown may last from a few milliseconds to some tens of


milliseconds and serves to provide conditions for the formation of the stepped leader. The


latter is a negatively charged plasma channel extending toward the ground at an average


speed of 2 x 105 m s- in a series of discrete steps. From high-speed time resolved


1.20 ms









20.20 ms





SECOND
RETURN
I c nv=


ms









photographs, each step is typically 1 [ts in duration and tens of meters in length, the time

interval between steps being 20 to 50 [as. The peak value of the current pulse associated

with an individual step has been inferred to be 1 kA or greater. The stepped leader serves

to form a conducting path or channel between the cloud charge source and ground.

Several coulombs of negative charge are distributed along this path, including downward

branches. Thus the leader may be viewed as a process removing negative charge from the

source and depositing this charge onto the downward extending channel. The stepped-

leader duration is typically some tens of milliseconds, and the average leader current is

some hundreds of amperes.

The electric potential difference between a downward-moving stepped-leader tip

and ground is probably some tens of megavolts which is comparable to or a considerable

fraction of that between the cloud charge source and ground. The magnitude of the

potential difference between two points, one at the cloud charge source and the other on

ground, is the line integral of the electric field intensity between those points.

The upper and lower limits for the potential difference between the lower boundary

of the main negative charge region and ground can be estimated by multiplying,

respectively, the typical observed electric field in the cloud, 105 V m-1, by the height of

the lower boundary of the negative charge center above ground, 5 km or so. The resultant

range is 50 to 500 MV. As the leader approaches ground, the electric field at the ground

surface, particularly at objects or relief features protruding above the surrounding terrain,

increases until it exceeds the critical value for the initiation of one or more upward-

connecting leaders. The initiation of an upward connecting leader from ground in

response to the descending stepped leader marks the beginning of the attachment process.









This process ends when contact is made between the downward and upward moving

leaders, probably some tens of meters above ground (more above a tall structure),

whereafter the first return stroke begins. The return stroke serves to neutralize the leader

charge, in other words, to transport the negative charges stored on the leader channel to

the ground. It is worth noting that the return-stroke process may not neutralize all the

leader charge or may deposit some excess positive charge onto the leader channel and

into the cloud charge source region. The final stage of the attachment process and the

initial stage of the return-stroke process are complex. The net result of those stages is a

fully formed return stroke, which is somewhat similar to the potential discontinuity that

would travel upward along a vertical, negatively charged transmission line if the lower

end of the line were connected to the ground. The first return-stroke current measured at

ground rises to an initial peak of about 30 kA in some microseconds and decays to half-

peak value in some tens of microseconds while exhibiting a number of subsidiary peaks,

probably associated with the branches. The return stroke effectively lowers to ground the

several coulombs of charge originally deposited on the stepped-leader channel, including

that on all the branches.

The high-current return-stroke wave rapidly heats the channel to a peak

temperature near or above 30 000 K and creates a channel pressure of 10 atm or more,

resulting in channel expansion, intense optical radiation, and an outward propagating

shock wave that eventually becomes the thunder (sound wave) we hear at a distance.

When the first return stroke, including any associated in-cloud discharge activity, ceases,

the flash may end. In this case, the lightning is called a single-stroke flash. However,

more often the residual first-stroke channel is traversed downwards by a leader that









appears to move continuously, a dart leader. During the time interval between the end of

the first return stroke and the initiation of a dart leader, J (for junction) and K processes

occur in the cloud. K-process can be viewed as transients occurring during the slower J-

process. The J-processes amount to a redistribution of cloud charge on a time scale of

tens of milliseconds, in response to the preceding return stroke. The J-process is often

viewed as a relatively slow positive leader extending from the flash origin into the

negative charge region, the K-process then being a relatively fast "recoil streamer" that

begins at the tip of the positive leader and propagates toward the flash origin. Both the J-

process and the K-process in cloud-to-ground flashes serve to transport additional

negative charge into and along the existing channel, although not all the way to the

ground. In this respect, K-process may be viewed as attempted dart leaders. The

processes that occur after the only stroke in single stroke flashes and after the last stroke

in multiple-stroke flashes are sometimes termed F (final) processes. These are similar, if

not identical, to J-processes.

The dart leader progresses downward at a typical speed of 107 m s1, typically

ignores the first stroke branches and deposits along the channel a total charge of the order

of 1 C. The dart-leader current peak is about 1 kA. Some leaders exhibit stepping near

ground while propagating along the path traversed by the preceding return stroke, these

leaders being termed dart-stepped leaders. When a dart leader or dart-stepped leader

approaches the ground, an attachment process similar to that described for the first stroke

takes place, although it probably occurs over a shorter distance and consequently takes

less time, the upward connecting-leader length being of the order of some meters. Once

the bottom of the dart or the dart-stepped leader channel is connected to the ground, the









second return-stroke wave is launched upward and again serves to neutralize the leader

charge. The subsequent return-stroke current at ground typically rises to a peak value to

10 to 15 kA in less than a microsecond and decays to half-peak value in a few tens of

microseconds. The upward propagation speed of such a subsequent return stroke is

similar to that of the first return stroke, although due to the absence of branches the speed

variation along the channel does not exhibit abrupt drops.

The impulsive component of the current in a subsequent return stroke is often

followed by a continuing current that has a magnitude of tens to hundreds of amperes and

duration up to hundreds of milliseconds. Continuing currents with a duration in excess of

40 ms are traditionally termed long continuing currents. The source for the continuing

current is the cloud charge, as opposed to the charge distributed along the leader channel,

the latter charge contributing to at least the initial few hundred microseconds of the

return-stroke current observed at ground. The time interval between successive return

strokes in a flash is usually several tens of milliseconds, although it can be as large as

many hundreds of milliseconds if a long continuing current is involved and as small as

one millisecond or less. The total duration of a flash is typically some hundreds of

milliseconds, and the total charge lowered to ground is some tens of coulombs.

2.5 Artificial Initiation (Triggering) of Lightning Using the Rocket-and-Wire
Technique

Two techniques for triggering lightning with a small rocket that extends a thin wire

in the gap between a thundercloud and the ground are "classical" triggering and

"altitude" triggering. These descriptions primarily apply to triggering negative lightning.

These two techniques are discussed in the next two sections. Figure 2.7 and Figure 2.8

show the sequence of events for these two techniques.










2.5.1 Classical Triggering

The most effective technique for triggering lightning involves the launching of a

small rocket trailing a thin grounded wire toward a charged cloud overhead. This

triggering method is usually called classical triggering and is illustrated in Figure 2-7.





Natural
channel /

~ 10sm/s -



wire trace
+300m /
Copper Wire-
2xlO2M/sJ 300 channel 1O8m/s



1-2s (hundreds (tens of ms)
I I of ms)
Ascending Upward Initial No-current Downward Upward
rocket positive continuous interval negative return
leader current leader stroke


Figure 2-7. Sequence of events in classical triggered lightning. The upward positive
leader and initial continuous current constitute the initial stage. Adapted from
Rakov et al. (1998)

The triggering success rate is generally relatively low during very active periods of

thunderstorms, one reason being that during such periods the electric field is more likely

to be reduced by a natural lightning discharge before the rocket rises to a height sufficient

for triggering.

When the rocket, ascending at about 200 m s-, is about 200 to 300 m high, the

enhanced field near the rocket tip results in a positively charged leader that propagates

upward toward the cloud. This upward positive leader (UPL) vaporizes the trailing wire,

bridges the gap between the cloud and ground, and establishes an initial continuous

current (ICC) with a duration of some hundreds of milliseconds that effectively transports









negative charge from the cloud charge source to the triggering facility. The ICC can be

viewed as a continuation of the UPL when the latter has reached the main negative

charge region in the cloud. At that time the upper extremity of the UPL is likely to

become heavily branched. The UPL and ICC constitute the initial stage (IS) of a classical

triggered-lightning discharge. After cessation of the initial continuous current, one or

more downward dart-leader--upward-return-stroke sequence may traverse the same path

to the triggering facility. The dart leaders and the following return strokes in triggered

lightning are similar to dart-leader return-stroke sequences in natural lightning,

although the initial processes in natural downward and in classical triggered lightning are

distinctly different. In summer, the triggering success rate for positive lightning is

apparently lower than for the negative lightning.

There is contradictory information regarding whether the height H of the rocket at

the time of lightning triggering depends on the electric field intensity E at ground at the

time of launching the rocket. A strong correlation (with correlation coefficient 0.82)

between H and E for triggered lightning in New Mexico was given by H = 3900E-1.33

where H is in meters and E in kV m1.

In Florida it was found that lightning can be initiated with grounded triggering

wires approximately 400 m long when the ambient fields aloft are as small as 13 kV m1.

When lightning occurred, ambient potentials with respect to earth at the triggering-rocket

altitude were 3.6 MV (negative with respect to earth). These potentials are referred to as

triggering potentials. The first measurable current pulses at the bottom of the triggering

wires were observed at similar fields aloft but at wire heights only about half as large, the

corresponding potential being 1.3 MV.









2.5.2 Altitude Triggering

A stepped leader followed by a first return stroke in natural downward lightning

can be reproduced to some degree by triggering lightning via a metallic wire not attached

to the ground. This ungrounded-wire technique is usually called altitude triggering. In

this type of lightning, illustrated in Figure 2-8, a bidirectional (positive charge up and

negative charge down) leader process is involved in initiating the first return stroke from

ground.


(105l-16)m/sf|f

~ 10s5mss +


4 +

liot+ +
1 lOVsf/ -+ + +

102m/s ~ 102m/s
150m Copper ~1.2km
wire
a 105m/s
SKevlar
400m cable
2 x 02ms Copper (10-10)m/s
50m wire
3s 6ms -1ims (10-100)ps
Ascending Upward Bi-directional Upward Upward
rocket positive leader return positive
leader stroke leader

Figure 2-8. Sequence of events in altitude-triggered lightning leading to the establishment
of a relatively low-resistance connection between the upward-moving positive
leader tip and the ground. The processes that follow the sequence shown, an
initial continuous-current and possibly one or more downward-leader--
upward-return-stroke sequences, are similar to their counterparts in classical
triggered lightning. The rocket speed is of the order of 102 m s-1. Adapted
from Rakov et al. (1998)

Note that the "gap", in this case, the length of the insulating Kevlar cable, between

the bottom end of the upper (triggering) wire and the top end of the grounded









(intercepting) wire is some hundreds of meters. Altitude triggering can also be

accomplished without using an intercepting wire, whose only function is to increase the

probability of lightning attachment to instrumented rocket-launching facility.

2.6 Previous Studies of Displacement Current Associated with Triggered Lightning

Schnetzer et al. (1998) in a study reported only in a conference proceeding, carried

out a numerical evaluation of Maxwell's integral equation relating azimuthal magnetic

field to its sources to investigate the relative contributions of conduction and

displacement currents to the total ground level azimuthal magnetic field at a distance of

50 m from the base of a triggered lightning stroke. The results revealed differences

between observed magnetic fields measured at 50 m from expectations based on

Ampere's law for magnetostatics. It is concluded that Ampere's law for magnetostatics,

which neglects displacement current contributions, provides an inadequate representation

of the total magnetic field due to a lightning ground stroke at distances beyond

approximately 30 m. The rest of this section contains an overview of Schnetzer et al.

(1998), which is the only publication, as of today, on the subject of displacement current

in triggered lightning.

2.6.1 Theory

The following simple expression based on Ampere's law for magnetostatics is

often used to estimate the azimuthal magnetic field intensity at the ground due to nearby

lightning:

H(r,t)=I(t)/27r (2.1)

where I(t) is the channel current, H(r,t) is the magnetic field intensity, and r is the radial

distance from the strike point on the earth. Schnetzer et al. (1998) observed that beyond

30 m, peak amplitudes of the measured magnetic fields are somewhat lower than their









counterparts predicted by equation (2.1) when measured currents are substituted in it. To

understand the sources of this observed behavior, a first-order numerical evaluation was

carried out using as a starting point Maxwell's integral equation relating the azimuthal

magnetic field to its arbitrary, time-varying sources,


(f, dJ = fj -dS+f aoE -dS
at


=I+ ,Eo- dS (2.2)


Here the first term on the right corresponds to I(t) in Eq. 2.1. The second term

constitutes the contribution to the azimuthal magnetic field due to displacement current

through the integration surface S bounded by /. When applied to a lightning stroke to

earth with S being defined as a flat, circular area of integration lying on the surface of the

ground and centered at the strike point, the first terms accounts for the effects of

conduction currents flowing normally through the designated surface. These would

include corona and upward leader currents prior to the attachment of the descending

leader, and the return-stroke current after that time. The second term accounts for the

effects of time variations of the vertical electric field associated with the changing charge

density distribution along the lightning channel during both the approach of the leader

and the resultant return stroke.

On the basis of circular symmetry considerations,


H(t) =() + f F(rt).dS (2.3)
2'rr 2rrt s at

aE
To the degree that an average can be treated as constant over the area of integration,
at


H can be approximated as










H(t) = I(t)+ r dE(t) H, + Hd (2.4)
2 rr 2 dt

where He and Hd are the contribution to the total magnetic field H from conduction and

displacement current, respectively. Alternately, average values of dEz/dt can be defined

for different ring-shaped parts of S, in which case the second term on the right side of Eq.

2.4 becomes the sum of all individual contributing subareas of S. The first term on the

right of Eq. 2.4 is recognized as corresponding to Ampere's law for magnetostatics, and

therefore any effects due to the current variation with height and radiation field must be

accounted for by the second, displacement current term. Since the descending leader does

not penetrate the surface of integration, during the leader phase I(t) is approximately zero,

except for assumed-to-be-negligibly-small corona or upward leader currents emitted from

the prospective attachment point. During that time, therefore, the magnetic field intensity

is related solely to the displacement current. Commencing with the onset of the return

stroke, both terms contribute. However, close to the channel, where r -- 0, the

displacement current contribution tends to zero, and the total field is dominated by the

contribution from the channel conduction current term.

2.6.2 Estimation of Displacement Current Contribution at 50 m

In order to investigate the distance at which the conduction current term alone

ceases to provide an adequate representation of the total magnetic field, Schnetzer et al

(1998) carried out a numerical evaluation of the relative contributions of both terms in

Eq. 2.4 for a typical 20-kA stroke using available recorded channel-base current and

associated magnetic field at 50 m and electric field data at two distances, 5 and 20 m,

from the strike point. The first step was to derive estimates of the displacement current

for r ranging from 0 to 10 m and from 10 to 50 m from electric fields measured at 5 and








20 m, respectively. Because electric fields were not recorded beyond 20 m, estimates of

the displacement current contributed by the annular area between 10 and 50 m were

obtained by assuming that the electric field over that area was, on average, the same as

the value measured at 20 m. Electric field waveforms were numerically differentiated to

obtain dEz/dt waveforms to be substituted in Eq. (2.4). The resulting estimated

amplitudes of displacement currents calculated at four time points prior to and at the

return-stroke onset are listed in Table 2.1.

Table 2-1. Displacement currents Id estimated from measured electric field data at times
prior to and at the onset of a 20 kA peak stroke current. Taken from Schnetzer
et al. (1998).


Tie d for Id toe Total I
Bf Area Aem for Area
fowithin within within 50 m
S 10 m 10to 0m I(A
(s) (A) (A)

-4.5 -5.01 -318 -323

-2.5 -16.7 -848 -865

-1.5 -42.3 -1130 -1172

-0.5 *303 -2090 -2393

0.0 +716 +12800 +13516


A qualitative representation of the electric field derivative is given in Figure 2-9.

According to Table 2-1, prior to the return stroke, while there is no appreciable

conduction current flowing through the integration surface at ground level, the

magnitudes of displacement currents out to 10 m at the various time steps are negligible

relative to the prospective returns stroke peak current of 20 kA. On the other hand, during









that same period the displacement current contribution from the area between 10 and 50

m becomes increasingly significant in comparison to 20 kA. Consistent with Figure 2-10,

the displacement current increases in amplitude with time and is negative in polarity up to

the point of onset of the return stroke. Upon initiation of the return stroke, the local

electric field abruptly changes sign and its derivative reaches its peak. The corresponding

magnitude of the total displacement current at that point becomes comparable to that of

the channel current, which then begun to flow but has not reached its peak.

Contribution of the displacement current in addition to the return-stoke channel

conduction current contribution clearly alters both the waveshape and amplitude of the

return-stroke portion of the total magnetic field compared to that predicted by Ampere's

law for magnetostatics. This is demonstrated in Figure 2-10. Here, the magnetic field

measured at 50 m (labeled Measured) during stroke 5 of flash 96-23 is plotted along with

the magnetic field (labeled Ampere's Law) that would be predicted by Eq. 2.1 when

applied to the recorded channel-base current of that stroke. Finally, the difference

between the two, which is qualitatively consistent with the results of Table 2-1 and

apparently represents the contribution due to the displacement current term of Eq. 2.4, is

also plotted. As can be seen in Figure 2-10, the shape of the difference curve corresponds

well to the anticipated shape of the electric field derivative, and hence of displacement

current density, illustrated in Figure 2-9. Prior to the return stroke, while no channel

current is flowing at ground level, the effect of the displacement current is apparent in the

initial ramp of the measured magnetic field. Further effects of the displacement current

component on the total field are the rounding and reduction in amplitude of the peak of

the magnetic field waveform.


















LEADER




.io -S 4 .24 I 0 2 4 10
TIME(Its


Figure 2-9. Qualitative illustration of the shape of the time derivative of the ground level
vertical electric field of a nearby return stroke Since displacement current
density is simply related to the derivative of electric field by a constant, it has
the same waveshape. Taken from Schnetzer et al. (1998).




MEASURED




AMPERWS LAW
-


Figure 2-10. From top to bottom, magnetic field measured at 50 m during stroke 5 of
Flash 96-23, the corresponding field according to Ampere's law for
magnetostatics, as applied to the measured channel-base current, and the
difference between the two. Taken from Schnetzer et al. (1998).














CHAPTER 3
CHARACTERIZATION OF EXPERIMENTAL DATA USED IN THIS STUDY

3.1 Magnetic Field Measuring Techniques

To measure the magnetic field from lightning a loop of wire can be used as an

antenna. According to Faraday's Law a changing magnetic field passing through an open

circuited loop of wire will induce a voltage at the terminals of the wire. The voltage at the

terminals of the wire is

dBn
Vo =A
dt

where A is the area of the antenna and B is the magnetic flux density passing through the

loop, perpendicular to the plane of the loop. Since the output voltage is proportional to

the time derivate of the magnetic field, this voltage will have to be integrated to obtain

the signal proportional to the field. The Thevenin equivalent circuit of a loop antenna is


the open circuit source voltage A- in series with the source impedance (primarily
dt

inductive). The Thevenin equivalent is shown in Figure 3-1.


Figure 3-1. Thevenin equivalent circuit of a loop antenna









A Norton equivalent circuit model for the antenna can be derived from the

Vth Aj/cB AB
Thevenin equivalent with I Vh coB AB. The Norton equivalent circuit is
jcoL jcoL L

shown in Figure 3-2


Antenna Integrator
........ ...............................








................... ....... .. .. .. .... ........... ........ I


Figure 3-2. Norton equivalent circuit for a loop antenna.

Since the loop antenna has an inductance L associated with it, the impedance of the

antenna will change with frequency. In the frequency domain that impedance is coL

where co is the angular frequency. This frequency-dependent impedance will cause

distortion in the derivative signal. To eliminate the distortion a resistor can be placed in

series with the antenna with the resistive impedance R much higher than the inductive

impedance coL of the antenna at the highest frequency of interest. The decay time

constant of the overall circuit in Figure 3-1 and Figure 3-2 will be T = RC as long as R is

much smaller then the input resistance of the recorder and C is much larger then the input

capacitance of the recorder, both conditions being usually met. In the frequency domain

the output voltage across the capacitor is


A(jcoB)( )
Vout =- -

ja>C
R + ji~L 1










If we choose R >> jcoL and R >> for the highest and lowest frequencies of
jcoC

AB
interest respectively, as discussed above, then Vout = In this way magnetic field from
RC

lightning can be measured from a loop antenna. Using the output voltage, Vout, area of the

loop antenna A, and choosing appropriate resistance R the magnetic field B can be

estimated.

3.2 Experimental Setup

3.2.1 ICLRT Overview

In this section, an overview of International Center for Lightning Research and

Testing (ICLRT) is presented. The ICLRT is located at Camp Blanding, Florida, at

coordinates 29056' N, 820 02' W, 8 km east of Starke. It was constructed by Power

Technologies in 1993 to study the effect of lightning on power lines. It has been operated

by the University of Florida since 1994. The rocket-and-wire technique (e.g., Rakov et

al., 1998) was used to artificially initiate (trigger) lightning from natural thunderclouds.

An overview of the ICLRT during the 1999, 2000, and 2001 experiments is found in

Figure 3-3 and a photograph of Flash S0012, triggered in 2000, in Figure 3-4. Flash

S0012 was triggered using the underground launcher. The triggered-lightning

experiments are usually conducted from May through September. As can be seen from

Figure 3-3, the ICLRT includes a tower launcher 11 m in height. Other launchers placed

at different positions on the site were also used in different years. Apart from the

launchers, the ICLRT includes test overhead power lines, under-ground cables, four

instrumentation stations, a test house, test runway, other test objects and systems and

various office and storage trailers.









OFFICE TRAILER


SATTLIF
TRAILER


BURIED
METAL
GRID


CONTROL
TRAILER
TEST POWER LINE
TOWER LAUNCHER ef r





Figure 3-3. An overview of the ICLRT at Camp Blanding, Florida, 1999-2001. Not all
test objects are shown.


Figure 3-4. Photograph of lightning flash S0012 triggered from the underground launcher
(see Figure 3-3).









3.2.2 1997 Experiments

In this section, a brief discussion of instrumentation used in the 1997 multiple

station experiment is discussed. The multiple station experiment involved a 5 m rocket

launcher located at northeast corner of the ICLRT and grounded through three 8 foot

(2.43 m) galvanized steel rods driven into sandy soil. Seven field measuring stations were

located (see Figure 3-5) south of the rocket launcher with distances ranging from 5 to 500

m. Each station had electric field and magnetic field antennas. The lightning channel base

current was measured using 0.5 milliohm CVR (Current Viewing Resistor) located at the

launcher. Three digitizing systems (see Figure 3-6) were used in this experiment, two

were provided by the University of Florida and were located at SATTLIF trailer (see

Figure 3-5) and launch control, the third digitizing system was provided by Sandia and

was located at SATTLIF trailer. When the current measured by the CVR located at

SATTLIF launcher exceeded 4 kA a digital pulse was generated by a current threshold

triggering circuit, which triggered all three digitizing systems. The digitizing system at

SATTLIF trailer consisted of a single Nicolet Multipro 150 digitizer and five LeCroy

model RM9400 digital oscilloscopes. Nicolet Multipro consisted of 8 data acquisition

cards of 4 channels each, but for this experiment only two cards were used of which one

was faulty. Each channel had 12-bit resolution with a sampling rate of 10 MHz for a total

record length of 51.2 ms. The LeCroy oscilloscopes were segmented for multiple triggers

and provided 8-bit resolution with a sampling rate of 25 MHz for a total record length of

100 ps.

At launch control five Nicolet model pro90 digital oscilloscopes were used. Pro90

consists of 4 channels; channels 1 and 2 had 8-bit resolution and a sampling rate up to

200 MHz, and channels 3 and 4 had 12-bit resolution and a sampling rate up tolO MHz.









The first channel had a pretrigger delay of 2 ms and second channel had a 23.6 ms

pretrigger delay that allowed continuous recording of the same quantity for 51.2 ms.

Nicolet Isobe 3000 fiber optic links were used to transmit analog data from antennas to

digitizing systems. More detailed description of 1997 instrumentation can be found in

Chapter 4 of David E. Crawford's thesis (Crawford 1998).


M ANTE SATTLIF
S.A LAUNCHER
OFFICE AND \
STORAGE SATTLIF
TRASTIRAGE RAL ANTEN FIELD


UF LAUNCH N
CONTROL \
T TRAILER wE
100m S
-uI TEST POWERLINE UF TOWER LAUNCHER




Figure 3-5. Locations of different instrumentation stations for 1997 multiple station
experiment. Taken from Crawford (1998).

3.2.3 1999 Experiments

The rocket launcher consisted of six metallic tubes aligned vertically from which

rockets were launched. The rocket launcher was mounted on insulating fiberglass legs

and placed underground, with the top of the launcher flush with ground, in a 4 m x 4 m x

4 m pit. The pit and the launcher were located in the center of a 70 m x 70 m buried

metallic grid (see Figure 3-3) intended to simulate a perfectly conducting ground. This

configuration eliminates ground surface arcing (e.g., Rakov et al., 1998) and minimizes

field propagation effects due to a finite ground conductivity. The low frequency, low

current grounding resistance of the buried grid was measured to be 6 Q. A hollow metal

rod with an outside diameter of 3.8 cm and a wall thickness of 0.6 cm protruding 1 m












SATTLIF


..... _, _, T...... _,LA U N C H
LEGEND: CONTROL
SATTLIF
ELECTRIC FIELD LAUNCHER
ANTENNA (.155 m2)
ANTENNA (.155 2) CHANNEL BASE CURRENT SHUNT TRIGGER
MAGNETIC FIELD GEN.
ANTENNA (.27 m2) ANTENNAS (4 kA Thresh.)

DSO = Digital Storage 5m LECROY
Oscilloscope REC 10 m DSOs TRIG I
fro Crw 4 Ksamples/seg
e fsp es tn 1 25 Msamples/sec
oe w fru c8 bit reset





















Forthe ethri field, magnetic- field, aimns producasused in
30 m fr r r l ANALOG
MAG TAPE
UF LAUNCH CONTROL \REC IN RECORDER
ANALOG FIELD DATA

NICOLET 50m 0 1 NICOLET
TRIga DSO g RECd 110mad s r DIGITIZERe
launcher detected a magneticChannels eld that corresponded to a current of4 Channelst 5 kA (using
256 Ksamples/ch CIN 512 Ksamples/ch
10 Msamples/sec 500 m 10 Msamples/sec
12 bit res 12 bit res
ANALOG FIELD DATA
--------------------------- TR LOUT------



Figure 3-6. Data acquisition system used in the 1997 multiple-station experiment. Taken
from Crawford (1998).

above the ground surface was used as the strike object for flashes S9901-S9918 in 1999.

For the other flashes triggered in 1999 (flashes S9925 S9935), a 2 m rod was used in

order to increase the probability of lightning attachment to the rod. During 1999, the

underground launcher was connected via four metal straps to the buried grid and the base

of the launcher was connected via two metal straps to a 16.5 m long vertical ground rod

whose low frequency, low current grounding resistance was measured to be 40 Q.

The electric field, magnetic field, and their time derivatives produced by lightning

strokes were measured 15 and 30 m from the strike rod. A TTL-level digital pulse trigger

signal was generated when the magnetic field sensor located 15 m from the rocket

launcher detected a magnetic field that corresponded to a current of at least 5 kA (using









Ampere's law of magnetostatics). The TTL signal was transmitted to the external trigger

input of the oscilloscopes located in the SATTLIF trailer (see Figure 3-3) to trigger the

digitizing system. The oscilloscopes for the field and current measurements had a pre-

trigger (stored data recorded prior to the trigger pulse) that ranged from 10% to 50% of

the total record length. Fiber optic transmitters (FOT) converted the analog output signals

from the antennas to optical signals and transmitted those signals via fiber optic cables to

fiber optic receivers (FOR). Meret and Nanofast fiber optic links (FOL) were used in the

experiment. The bandwidth of the Meret and Nanofast FOL was dc to 35 MHz and 5 Hz

to 175 MHz, respectively. The FOT were powered with 12 V dc lead-acid batteries. RG-

58 or RG-223 coaxial cables (both 50 Q) connected the FOT to the antennas, which were

located in metal boxes near the antennas. The FORs in the SATTLIF trailer were

powered with 120 V ac uninterruptible power supplies (UPS). RG-58 or RG-223 coaxial

cables connected the FOR to the digitizing system. The optical fibers transmitting the

signal from the FOT to the FOR were 200 [tm glass, Kevlar-reinforced, duplex cables.

3.2.3.1 Instrumentation for Current Measurements

Six P110A current transformers (CTs) with a lower frequency response of 1 Hz and

an upper frequency response of 20 MHz were used to measure the current at the lightning

channel base, two measured the current flow to the vertical ground rod, and four

measured the current flow to the buried grid. The current amplitude range of each sensor

is from a few amperes to approximately 20 kA. A passive combiner summed the two

signals from the ground rod CTs to obtain a total ground rod current, and another one

summed the four signals from the buried grid CTs to obtain a total grid current. The total

ground rod current signal and the total grid current signal were then each transmitted via









separate Meret FOL (35 MHz bandwidth) to the SATTLIF trailer. Both signals were

filtered with a 20 MHz, 3 dB anti-aliasing filters and then digitized at 50 MHz. The total

current at the lightning channel base was obtained by numerically summing the ground

rod current and the buried-grid current.

3.2.3.2 Instrumentation for Electric Field Measurements

Electric fields were measured using flat plate antennas with an area of 0.16 m2. The

output of each electric field antenna was connected to an integrating capacitor of value

105 nF at 15 m and 55 nF at 30 m. The input impedance of the fiber optic transmitter was

about 1 MQ. Meret fiber optic links with a bandwidth of 35 MHz were used to transmit

the signal to the SATTLIF trailer where the 15-m electric field signals were filtered using

10 MHz, 3 dB anti-aliasing filters and digitized at 25 MHz, and the 30-m electric field

signals were filtered using 20 MHz, 3 dB anti-aliasing filters and digitized at 25 MHz.

3.2.3.3 Instrumentation for Electric Field Derivative Measurement

Electric field derivatives were measured using flat plate antennas with an area of

0.16 m2. The output of each electric field derivative antenna was terminated using 50 Q,

and the input impedance of the fiber optic transmitter was about 1 MQ. Meret fiber optic

links with a bandwidth of 35 MHz were used to transmit the 15-m signal, and a Nanofast

FOL was used to transmit the 30-m signal to SATTLIF trailer. Signals of dE/dt at 15 and

30 m were filtered using 20 MHz, 3 dB anti-aliasing filters and digitized at 250 MHz.

3.2.4 2000 Experiments

The strike object was a 2 m vertical rod surrounded by a 3 m diameter horizontal

ring elevated to 1.5 m height and electrically connected to the base of the rod (see Figure

3-8). Most of the 2000 instrumentation was the same as the 1999 instrumentation except

for the two major changes made in 2000 and listed below: (1) The triggering signal was









generated when the current measured at the strike rod base exceeded 3 kA. (2) Current at

the channel base was measured simultaneously by two different methods (a) the total

lightning current was measured using a single current viewing resistor installed just

below the strike object (new measurement), and (b) the current components flowing to

the vertical ground rod and to the buried grid were measured individually and added

numerically to obtain the total lightning current. The current to the ground rod was

measured as in 1999, while the currents to the buried grid were measured with two

current viewing resistors in the two connections rather than with the four current

transformers and four connections used in 1999. Electric field and electric field derivative

instrumentation in 2000 was the same as in 1999.

03 Camrnrder
Edge of M-B30 a 3
Ground h(30)
Screen30)
\]IVI-E30
sh(15) M-B15-E30

\ / 3 M-E15

E(5)
SATTLIF k l Pit &
Pockep Launch Tubes
id Cell sh(3)
Video & dE(1 \
35-mm / B(15)
Cameras B(15)
/ dB(15) E(15)
dE(30) / \(\
d (B(30)
1 5dB(30) E(30
15 / 15 C mcorder


Figure 3-7 Experimental setup (placement of electric and magnetic field antennas) used
in SATTLIF for 2000 [Courtesy G. Schnetzer].




































Figure 3-8 Setup of strike rod and ring mounted over launch tubes in 2000.

3.2.5 2001 Experiments

The experiment set-up was the same as in 2000, except for the strike ring and the

ground rod connection were removed. Additionally, the 2 m strike rod was replaced with

4.5 m section of gas pipeline for the experiments on August 18, 2001. The pipeline was

mounted directly onto the base of the incident current CVR (current viewing resistor) and

nylon fishing line was used to support the structure. The pipeline consisted of four

sections of different diameters, the sections being connected by three different insulating

joints. Current was measured in the same way as in 2000, but was digitized at 25 MHz

(instead of 50 MHz as in 1999 and 2000). The electric field and electric field derivative

instrumentation in 2001 was the same as in 1999 and 2000.









3.3 Data Presentation

3.3.1 General Information

In this section the statistical distributions of measured peak magnetic fields, return-

stroke peak currents and peak dE/dt fields are presented. Corresponding waveforms are

shown in Figures 3-9 to 3-13.

For measured return-stroke current which are not saturated the sample size is 88.

For 1997, 1999, 2000, and 2001 data combined, the mean value of peak current is 15.3

kA and standard deviation is 7.50 kA.

The magnetic fields are used in Chapter 4 to estimate the leader and return-stroke

currents. For measured peak magnetic fields which are not saturated at 15 m for 1999,

2000 and 2001 the mean value is 201 [tWb/m2 and the standard deviation is 96.8

[tWb/m2. At 30 m for 1997, 1999, 2000 and 2001 the mean value is 104 [tW/m2 and the

standard deviation is 49.2 atW/m2. The sample size for 15 m data is 97, and for 30 m data

the sample size is 103. Histograms are shown in Figures 3.17-3.22.

For measured dE/dt waveforms which are not saturated the sample size is 50 for

both 15 and 30 m. At 15 m for 1999, 2000 and 2001 the mean value is 355 kV/m/tas and

the standard deviation is 154 kV/m/[ts. At 30 m for those three years the mean value is

118 kV/m/tas and the standard deviation is 56 kV/m/ats.

Table 3-1 summarizes the mean, standard deviation, geometric mean and sample

sizes for 1999, 2000 and 2001 combined.









Table 3-1. Summary of mean, standard deviation, GM (Geometric Mean), and sample
sizes of measured peak current, peak magnetic field and electric field
derivative


Parameter


Mean


Peak current, kA


15.3


Peak magnetic field at
15 m, aWb/m2
Peak magnetic field at
30 m, aWb/m2
Peak dE/dt field at 15 m,
kV/m/ts
Peak dE/dt field at 30 m,
kV/m/ts


St. Dev.

7.5


96.8

49.2


GM

13.4

179

92.9

315

103


Sample
size
88


S9901 RS3 I-measured


10 20 30 40 50
t[l.s]


60 70 80 90 100


Figure 3-9. Measured channel-base current, Flash S9901, Stroke 3.










S9901 RS3 B15


20 40 60 80
t [Ls]


Figure 3-10. Magnetic field at 15 m, Flash S9901, Stroke 3.

S9901 RS3 B30


20 40 60 80
t [p.s]


Figure 3-11. Magnetic field at 30 m, Flash S9901, Stroke 3.











S9901 RS3 dE15/dt


200



150



100



50 -
SsoJ



0



-50
-5


0 6


t [ls]

Figure 3-12. Electric field derivative (dE/dt) at 15 m, Flash S9901, Stroke 3.


S9901 RS3 dE30/dt


60
G~-


50


40
--7
1 30


S20
LU
10


0


-10
-5


0 6
t [kIs]


Figure 3-13. Electric field derivative (dE/dt) at 30 m, Flash S9901, Stroke 3.














3.3.2 Channel-base Current


4
() Mean 13.1 kA
St. Dev. 5.60 kA
Min 5.70 kA
3 -Max 23.0 kA
GM 12.1 kA
Sample Size 11

2



1- --





0 4 8 12 16 20 24 28 32 36 40
Return-Stroke Peak Current [kA]


2000
12
(C) Mean 13.2kA
SSt. Dev. 6.90 kA
10
Min 1.10 kA
Max 36.8 kA
8 GM 11.3 kA

Sample Size 40
6-


4-


2-



0 4 8 12 16 20 24 28 32 36 40
Return-Stroke Peak Current [kA]


1999
8 -
(b) Mean 16.7 kA
S St. Dev. 6.80 kA
Min 2.80 kA
6 -- Max 30.0 kA

GM 15.1kA
Sample Size 24





2 -





0 4 8 12 16 20 24 28 32 36 40
Return-Stroke Peak Current [kA]





2001

(d) Mean 21.1kA
St. Dev. 9.30 kA
Min 9.20 kA
Max 38.9 kA
GM 19.3 kA
Sample Size 13





1 -



0 r -- -- ----- --- --- -- -- -- --
0 4 8 12 16 20 24 28 32 36 40

Return-Stroke Peak Current [kA]


Figure 3-14. Return-stroke peak currents in (a) 1997, (b) 1999, (c) 2000, and (d) 2001.







41




1997, 1999, 2000, & 2001


Mean
St. Dev.
Min


15.3 kA
7.54 kA
1.05 kA


Max 38.9 kA
GM 13.4 kA
Sample Size 88















0 4 8 12 16 20 24 28 32 36 40

Return-Stroke Peak Current [kA]


1999
2000
2001
1997


Mean
Mean
Mean
Mean


16.7 kA
13.2 kA
21.1 kA
13.1 kA


St. Dev.
St. Dev.
St. Dev.
St. Dev.


S6.80 kA
:6.90 kA
S9.30 kA
= 5.60 kA


Figure 3-15. Return-stroke peak currents in 1997, 1999, 2000 and 2001.












3.3.3 Magnetic Field


Distance 5 m, 1997

(a) Mean 511 tWb/m2
St. Dev. 274 tWb/m2
Min 176 tWb/m2
Max 916 tWb/m2
GM 443 aWb/m2
Sample Size 7


0 200 400 600
Peak Magnetic Field [RWb/m2]




Distance 20 m, 1997


0 50 100 150 200 250
Peak Magnetic Field [tWb/m2]


Distance 10 m, 1997

(b) Mean 247 Wb/m2
St. Dev. 101 pWb/m2
Min 100 pWb/m2
Max 395 pWb/m2
GM 227 pWb/m2
Sample Size 9


800 1000 0 100 200 300 400
Peak Magnetic Field [pWb/m2]


Distance 30 m, 1997


25 50 75 100
Peak Magnetic Field [RtWb/m2]


125 150


Figure 3-16. Peak magnetic fields measured at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m
in 1997.


(C) Mean 111 Wb/m2
St. Dev. 47.3 pWb/m2
Min 51.3 tWb/m2
Max 183 pWb/m2
GM 103 pWb/m2
Sample Size 7







43




Distance 15 m, 1999


12


10


8-


_ 6-


4



2-


0






12


10


8


Peak Magnetic Field [[tWb/m2]


Distance 30 m, 1999


0 25 50 75 100 125 150 175
Peak Magnetic Field [iWb/m2]


200 225 250


Figure 3-17. Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1999.


0 50 100 150 200 250 300 350 400 450 500







44




Distance 15 m, 2000


Mean
St. Dev.
Min
Max
GM
Sample Size


0 50 100 150 200 250 300 350
Peak Magnetic Field [[tWb/m2]


180 gWb/m2
92.0 gWb/m2
49.5 gWb/m2
467 gWb/m2
159 gWb/m2
47


400 450


Distance 30 m, 2000


0 25


C.

6


4


2


0





12


10 -


8 -


I I I I 1
50 75 100 125 150 175
Peak Magnetic Field [itWb/m2]


93.1 gWb/m2
47.2 gWb/m2
25.4 gWb/m2
235 gWb/m2
82.5 gWb/m2
47


200 225


Figure 3-18. Peak magnetic fields measured at (a) 15 m and (b) 30 m in 2000.


Mean
St. Dev.
Min
Max
GM
Sample Size









Distance 15 m, 2001


0 50 100 150 200 250 300 350
Peak Magnetic Field [[tWb/m2]


Mean
St. Dev.
Min
Max
GM
Sample Size


400 450 500


Distance 30 m, 2001


113 gWb/m2
56.7 gWb/m2
48.8 gWb/m2
248 gWb/m2
102 gWb/m2
11


1 __ 11______


0 25


50 75 100 125 150 175
Peak Magnetic Field [tWb/m2]


200 225


Figure 3-19. Peak magnetic fields measured at (a) 15 m and (b) 30 m in 2001.


(a) Mean 212 gWb/m2
St. Dev. 107 gWb/m2
Min 97.6 gWb/m2
Max 470 gWb/m2
GM 192 gWb/m2
Sample Size 11






-r














Distance 15 m (1999, 2000, & 2001)

(a) Mean 201 gWb/m2
St. Dev. 96.8 gWb/m2
Min 49.5 gWb/m2
Max 470 gWb/m2
GM 179 gWb/m2
Sample Size 97


0 5 1
0 50 100 150


200 250 300 350 400 450 500


Peak Magnetic Field [pWb/m2]

1999 n = 39 Mean = 223 Wb/m2 St. Dev. = 96.5 Wb/m2
S 2000 n = 47 Mean = 180 LWb/m2 St. Dev. = 92.0 LtWb/m2
I 2001 n = 11 Mean = 212 gtWb/m2 St. Dev. = 107 LWb/m2


Distance 30 m (1997, 1999, 2000, and 2001)


Mean 104 tWb/m2
St. Dev. 49.2 gWb/m2
Min 25.4 tWb/m2
Max 248 gWb/m2
GM 92.9 gWb/m2
Sample Size 103


0 25 50 75 100 125 150 175 200 225 250
Peak Magnetic Field [pWb/m2]

1999 n = 39 Mean =118 Wb/m2 St. Dev.= 48.2 Wb/m2
2000 n = 47 Mean = 93.1 Wb/m2 St. Dev.= 47.2 Wb/m2
I 2001 n= 11 Mean = 112 gWb/m2 St. Dev.= 56.7 gWb/m2
1997 n = 6 Mean = 79.8 Wb/m2 St. Dev. = 33.7 Wb/m2


Figure 3-20. Peak magnetic fields measured at (a) 15 m and (b) 30 m in 1997, 1999, 2000
and 2001.


15 -


701










3.3.4 Electric Field Derivative (dE/dt)


Distance 15 m, 1999


0 100 200 300 400 500 600 700
Peak dE/dt [kV/m/ps]



Distance 30 m, 1999


50 75 100 125 150
Peak dE/dt [kV/m/ps]


175 200 225 250


Figure 3-21. Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999.


304 kV/m/ts
107 kV/m/is
72.0 kV/m/ps
450 kV/m/ts
280 kV/m/ts
15


Mean
St Dev
Min
Max
GM
Sample Size


92.6 kV/m/ps
31.0 kV/m/ls
23.0 kV/m/gs
145 kV/m/ps
86.1 kV/m/gs
15


Mean
St Dev
Min
Max
GM
Sample Size


4 +


0 25







48




Distance 15 m, 2000


0 100 200 300 400 500 600 700 800
Peak dE/dt [kV/m/ps]


Distance 30 m, 2000


0 25 50 75 100 125 150
Peak dE/dt [kV/m/ps]


175 200 225 250


Figure 3-22. Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 2000.













Distance 15 m, 2001

Mean
St Dev
Min
Max
GM
Sample Size


0 100 200 300 400 500
Peak dE/dt [kV/m/ps]


600 700 800


Distance 30 m, 2001


0 25 50 75 100 125 150 175 200 225 250
Peak dE/dt [kV/m/is]


Figure 3-23 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 2001.


4 -




3 -

-c













0
S -


590 kV/m/gs
61.0 kV/m/ps
519 kV/m/gs
644 kV/m/gs
579 kV/m/gs
4


t + +








50




Distance 15 m (1999, 2000, & 2001)


355 kV/m/is
154 kV/m/is
50.0 kV/m/ls
673 kV/m/ts
315 kV/m/is
50


0 100 200 300 400 500 600 700 800
Peak dE/dt [kV/m/ts]


Mean = 304 kV/m/tgs
Mean = 350 kV/m/tgs
Mean = 590 kV/m/|gs


St. Dev. = 107 kV/m/gs
St.Dev. =156 kV/m/gs
St. Dev. = 61.0 kV/m/gs


Distance 30 m (1999,2000, & 2001)


Mean 118 kV/m/is
St Dev 56.0 kV/m/is
Min 16.0 kV/m/is
Max 241 kV/m/ls
GM 103 kV/m/ls
Sample Size 50


0 25 50 75 100 125 150 175 200 225 250
Peak dE/dt [kV/m/ts]


Mean = 92.6 kV/m/tgs
Mean = 118 kV/m/tgs
Mean =211 kV/m/gs


St. Dev. = 31.0 kV/m/gs
St. Dev. = 56.0 kV/m/gs
St. Dev. = 27.0 kV/m/gs


Figure 3-24 Peak dE/dt fields measured at (a) 15 m and (b) 30 m in 1999, 2000 and 2001.


I 1999
S 2000
S 2001


n=15
n=31
n=4


I 1999
S 2000
S 2001


n=15
n=31
n=4














CHAPTER 4
ESTIMATION OF LEADER AND RETURN-STROKE CURRENTS FROM
MEASURED MAGNETIC FIELDS

4.1 Introduction

Magnetic fields measured at 15 and 30 m are available for 1999, 2000, and 2001.

In 1997, magnetic field records were measured at 5, 10, 20, and 30 m.

4.2 Estimation of Currents Using Ampere's Law

According to Ampere's law for magnetostatics, f B dl = toleno, the line integral

of magnetic flux density, B, around a closed path is proportional to the enclosed current,

Ienc. The constant of proportionality ,o is the permeability of free space. In SI units ,o =

47 x 107 H/m.

For a straight wire of infinite length the magnetic flux density external to the wire

at a distance r from its axis is given by


B ~ ol (4.1)
27tr












dl

Figure 4-1. A straight current channel of infinite length and B at a distance r.






52

Here we have used the fact that the magnetic field is constant and tangential at any point

on the circular integration path. Equation (4.1) is essentially the same as equation (2.1).

If we assume that earth is a perfect conductor, and consider a very close

observation point (a distance 15 or 30 m compared to the lightning channel of some

kilometers) (4.1) will apply to a lightning channel above ground. Thus, knowing the

magnetic field at distance r, from the lightning channel and using (4.1) one can estimate

the current flowing in the channel if the magnetostatic approximation is valid.

Typical magnetic field waveforms with respect to time are shown in Figures 3.10

and 3.11. They usually exhibit a relatively slow initial front followed by a fast rise to

peak and then decay, as discussed below.


Downward leader


Lightning terminus .
level [ I-- --
-1200 -800 400


Return stroke


Ground Attachment


400
400


Time, ns


Figure 4-2. A streaked-image diagram of a dart leader-return-stroke sequence in a
rocket-triggered lightning flash


=__.i









As the downward leader tip approaches ground surface the magnetic field on

ground associated with the leader current increases with time. When the leader attaches to

the ground, return stroke is initiated. Hence the current increases abruptly and there is a

fast rise in magnetic field.

The initial rising portion (up to the peak) of each magnetic field record can be

divided into two parts: a slow rise part corresponding to leader and steep rise part

corresponding to the return stroke. The division is illustrated in Figures 4-3 and 4-4,

where the magnitude of the leader part is labeled BL and that of the return stroke part BRS.

For each part the corresponding current was estimated using equation 4.1. It is important

to note that the leader current corresponds to the final stage of the dart-leader process,

when leader channel attaches to the ground, and the return-stroke current represents the

peak value based on the assumption that the leader current continues to flow in the

channel during the return-stroke process. Thus, the total peak current flowing in the

channel during the return-stroke stage is the sum of leader current inferred from BL and

return stroke current estimated from BRS.

Using this approach, leader and the return stroke currents for the years of 1997,

1999, 2000 and 2001 are evaluated. The histograms showing the statistics of leader and

return-stroke currents for 1997, 1999, 2000 and 2001 are shown in Figure 4-5 through

Figure 4-9.

The scatter plots (see Figures 4-13 and 4-14) show comparisons of leader currents

obtained from dE/dt (Kodali et al. 2005) vs. those obtained from magnetic fields (BL) and

of measured return stroke currents (see section 3.3) vs. those obtained from magnetic

fields (BRS).







54


S9901 RS3 B15


2 4 6 8
t [p.s]


Figure 4-3 Magnetic field at 15 m, Flash S9901, Stroke 3.

S9901 RS3 B30


2 4 6 8
t [ps]


Figure 4-4. Magnetic field at 30 m, Flash S9901, Stroke 3.


0

-20

-40

-60

-80

-100

-120

-140

-160

-180


0

-10

-20


E
i-40

m -50

-60

-70

-80

-90

0












Distance 10 m, 1997


6


5-


4 -


S3-


2-


1 -























2-


1


0
5-


U F i F i I I
0 1 2 3 4 5 6 7 8 9
Leader Current [kA]


Distance 30 m, 1997

(d) Mean 2.06 kA

St Dev 0.72 kA
Min 1.34 kA
Max 3.11kA
GM 1.95 kA
Sample Size 6












0 1 2 3 4 5 6 7 8 9


Leader Current [kA]


Figure 4-5. Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in 1997.


(a) Mean 1.80 kA

St Dev 1.08 kA
Min 0.94 kA
Max 3.95 kA
GM 1.58kA
Sample Size 7


(b) Mean 1.80 kA

St Dev 0.70 kA
Min 1.05 kA
Max 2.84 kA
GM 1.69 kA
Sample Size 9


0 1 2 3 4 5 6 7 8 9
Leader Current [kA]


Distance 20 m, 1997

(c) Mean 2.02 kA
St Dev 1.00 kA
Min 1.10kA
Max 3.93 kA
GM 1.84kA
Sample Size 7












1 2 3 4 5 6 7 8 9
Leader Current [kA]


Distance 5 m, 1997










Distance 15 m, 1999


0 1 2 3 4 5
Leader Current [kA]
Distance 30 m, 1999


0 1 2 3 4 5
Leader Current [kA]


6 7 8 9


6 7 8 9


Figure 4-6. Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at (a) 15 m and (b) 30 m in 1999.












20




15 -

--


5 10-




5


u


57


Distance 15 m, 2000

(a) Mean 1.53 kA
St. Dev. 0.82 kA
Min 0.38 kA
Max 3.83 kA
GM 1.32 kA
Sample Size 47


0 1 2 3 4 5 6 7 8
Leader Current [kA]
Distance 30 m, 2000


0 1 2 3 4 5
Leader Current [kA]


6 7 8


Figure 4-7. Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at (a) 15 m and (b) 30 m in 2000.


Mean
St. Dev.
Min
Max
GM
Sample Size


2.13 kA
1.30 kA
0.40 kA
6.36 kA
1.80 kA
47


(b)










Distance 15 m, 2001


(a) Mean 2.03 kA
St. Dev. 1.28 kA
4 Min 0.85 kA
Max 5.45 kA
GM 1.76 kA
3 Sample Size 11




2



1


0 1 2 3 4 5
Leader Current [kA]
Distance 30 m, 2001


0 1 2 3 4 5
Leader Current [kA]


6 7 8


6 7 8 9


Figure 4-8. Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at (a) 15 m and (b) 30 m in 2001.






59


Distance 15 m, 1999,2000,&2001


Mean
St. Dev.
Min
Max
GM
Sample Size


1.87 kA
1.01 kA
0.38 kA
5.40 kA
1.62 kA
97


0 1 2 3 4


5 6 7 8
5 6 7 8


Leader Current [kA]


1999
2000
2001


n = 39
n = 47
n= 11


Mean = 2.25 kA St. Dev. = 1.02 kA
Mean = 1.53 kA St. Dev. = 0.82 kA
Mean = 2.03 kA St. Dev. = 1.28 kA


Figure 4-9. Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at 15 m in 1999, 2000, and 2001.


I I






60


Distance 30 m, 1997, 1999, 2000, and 2001


Mean
St. Dev.
Min
Max
GM
Sample Size


2.58 kA
1.57 kA
0.40 kA
8.63 kA
2.17 kA
103


0 1 2 3 5 6 7 8
0 1 2 3 4 5 6 7 8 9


Leader Current [kA]


Mean = 3.21 kA
Mean = 2.13 kA
Mean = 2.57 kA
Mean = 2.10 kA


Dev. = 1.61 kA
Dev. = 1.30 kA
Dev. = 2.18 kA
Dev. = 0.70 kA


Figure 4-10. Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001.


n


1999
2000
2001
1997


n = 39
n = 47
n= 11
n=6







61





10

IL(30 m) -0.10 + 1.44 IL(15 m)
R2 = 0.83
Sample Size =97

8-





6 -

0

E *
0



0 *


2 *
S* 1999
2000
S2001





IL from B1 [kA]


Figure 4-11. Dart leader current inferred using Ampere's Law for magnetostatics from
measured magnetic fields measured at 30 m vs. that at 15 m in 1999, 2000,
and 2001.











































0 2 4 6 8 10


IL from dE/dt [kA]


IL(dE/dt) [kA]
3.51
2.39


IL(Amperes Law) [kA]
2.36
1.07


Figure 4-12. Dart leader current inferred using Ampere's Law for magnetostatics from
magnetic fields measured at 15 m vs. leader current inferred from dE/dt
measurements [Kodali et al. 2005] in 1999, 2000, and 2001.


Mean
StDev













10





8





6


o
E
0
4-
- 4





2





0


0 2 4 6 8


IL from dE/dt [kA]


IL(dE/dt) [kA]
4.98
2.90


IL(Amperes Law) [kA]
5.86
1.71


Figure 4-13. Dart leader current inferred using Ampere's Law for magnetostatics from
magnetic fields measured at 30 m vs. leader current inferred from dE/dt
measurements [Kodali et al. 2005] in 1999, 2000, and 2001.


Mean
StDev












Distance 10 m, 1997


Distance 5 m, 1997


0 4 8 12 16 20 24 28 32
Return-Stroke Peak Current [kA]



Distance 20 m, 1997

(c) Mean 9.13 kA

St Dev 3.83 kA
Min 4.03 kA
Max 14.4 kA
GM 8.42 kA
Sample Size 7


0 4 8 12 16 20 24
Return-Stroke Peak Current [kA]


Mean
St Dev
Min
Max
GM
Sample Size


10.5 kA
4.44 kA
3.69 kA
17.0 kA
9.57 kA
9


u I
0 4 8 12 16 20 24 28 3;

Return-Stroke Peak Current [kA]


Distance 30 m, 1997
5
(d) Mean 9.91 kA

St Dev 4.57 kA
4 Min 4.34 kA
Max 15.9 kA
GM 8.97 kA
3" Sample Size 6



2-



1 -



0 -- i


28 32 0 4 8 12 16 20 24
Return-Stroke Peak Current [kA]


28 32


Figure 4-14. Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at (a) 5 m, (b) 10 m, (c) 20 m, and (d) 30 m in
1997.










Distance 15 m, 1999


0 4 8 12 16 20
Return-Stroke Peak Current [kA]


24 28 32


Distance 30 m, 1999


0 4 8 12 16 20
Return-Stroke Peak Current [kA]


24 28 32


Figure 4-15. Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at (a) 15 m and (b) 30 m in 1999.


(b) Mean 14.5 kA
St Dev 5.80 kA
Min 5.70 kA
Max 26.7 kA
GM 13.4 kA
Sample Size 39


i + i i i







66


Distance 15 m, 2000


(a) Mean 12.0 kA
St. Dev. 6.19 kA
Min 3.34 kA
Max 31.8 kA
GM 10.6 kA
Sample Size 47












0 4 8 12 16 20 24 28 3


Return-Stroke Peak Current [kA]

Distance 30 m, 2000


0 4 8 12 16 20 24 28 32


Return-Stroke Peak Current [kA]

Figure 4-16. Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at (a) 15 m and (b) 30 m in 2000.







67


Distance 15 m, 2001


0 4 8 12 16 20 24 28 3:

Return-Stroke Peak Current [kA]

Distance 30 m, 2001

(b) Mean 14.3 kA
St. Dev. 6.57 kA
Min 6.45 kA
Max 28.6 kA
GM 13.1 kA
Sample Size 11


0 4


8 12 16 20 24 28


Return-Stroke Peak Current [kA]

Figure 4-17. Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at (a) 15 m and (b) 30 m in 2001.


Mean
St. Dev.
Min
Max
GM
Sample Size


13.8 kA
6.90 kA
6.47 kA
29.8 kA
12.5 kA
11







68



Distance 15 m, 1999, 2000, & 2001


Mean 13.2 kA
St. Dev. 6.41 kA
Min 3.34 kA
Max 31.8 kA
GM 11.7 kA
Sample Size 97


0 4 8 12 16 20 24 28 32


Return-Stroke Peak Current [kA]


Mean = 14.5 kA St.
Mean = 12.0 kA St.
Mean= 13.8 kA St.


Dev. = 6.40 kA
Dev. = 6.19 kA
Dev. = 6.90 kA


Figure 4-18. Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 15 m in 1999, 2000, and 2001.


1999
2000
2001


m
M
r-- -


n = 30
n = 47
n = 11


I


I









Distance 30 m, 1999, 2000, 2001 & 1997


Mean
St. Dev.
Min
Max
GM
Sample Size


13.0 kA
6.00 kA
3.09 kA
28.9 kA
11.7 kA
103


0 4 8 12 16 20 24 28 32

Return-Stroke Peak Current [kA]


Mean = 14.9 kA
Mean = 11.8 kA
Mean = 14.3 kA
Mean = 9.90 kA


St. Dev. = 6.30 kA
St. Dev. = 6.91 kA
St. Dev. = 6.57 kA
St. Dev. = 4.60 kA


Figure 4-19. Return-stroke peak currents inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 30 m in 1997, 1999, 2000, and 2001.


I-I
m
m


1999
2000
2001
1997


n = 39
n = 47
n= 11
n=6


7







70





35

IRS(30 m) = 0.99 + 0.93 IRS(15 m)
R2 = 0.97
30 Sample Size = 97

2*
*
25












10 -



5O 1999
S* 2000
O6 2001



0 5 10 15 20 25 30 35

IRS from B15 [kA]


Figure 4-20. Return-stroke peak current inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 30 m vs. that inferred from measured
magnetic fields at 15 m in 1999, 2000, and 2001.







71





40


IRS(Ampere's Law) = 0.08 + 0.83 IRS(Meas.)
35 R2 = 0.86
Sample Size = 71

30 *


S*
25-


m
20

2. 1***
4--

15 -



10 -

Se 0 1999
5- 2000
5 2001



0 5 10 15 20 25 30 35 40

Measured IRS [kA]


IRS(Meas.) [kA] IRS(Amperes Law) [kA]
Mean 15.3 13.2
St. Dev. 6.70 6.10

Figure 4-21. Return-stroke peak current inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 15 m vs. measured return-stroke peak
current in 1999, 2000, and 2001.











































0 5 10 15 20 25 30 35 40


IRS(Meas.) [kA]
15.4
6.87


Measured IRS [kA]


IRS(Ampere's Law) [kA]
13.1
5.97


Figure 4-22. Return-stroke peak current inferred using Ampere's Law for magnetostatics
from measured magnetic fields at 30 m vs. measured return-stroke peak
current in 1997, 1999, 2000, and 2001.


Mean
St. Dev.







73







IL15 m) 0.16 + 0.13 IRS(15m)
8 R = 0.68
Sample Size = 97

7 -


6 -


m
m- 5-

E *
o 4 *


3 *
3 g


2 -

S 1999
1 0 y 2000
** 2001



0 5 10 15 20 25 30 35

IRS from B15 [kA]


Figure 4-23. Leader vs. return-stroke currents inferred using Ampere's Law for
magnetostatics from magnetic fields measured at 15 m in 1999, 2000, and
2001.







74








IL30 m) = -0.29 + 0.21 IRS(30 m)
R = 0.72 *
Sample Size = 97




6 -



ICO 4 *
5-


S4-
2* *



3 0 **




2001
0 *

0 5 10 15 20 25 30 35
IRS frm 3 [kA]

magnetostatics from magnetic fields measured at 30 in 1999, 2000, and
2001. 2001
0 5 10 15 20 25 30 35

IRS from B30 [kA]


Figure 4-24. Leader vs. return-stroke currents inferred using Ampere's Law for
magnetostatics from magnetic fields measured at 30 m in 1999, 2000, and
2001.













40

IRS from (BL+BRS)30m = 0.53 + 1.01 IRS from (BL+BRS)15m
R2 = 0.98
35 Sample size =97 e

*/

30



S25
0
U)
M 0*
+ 20 -

E ,
o0 *
4- 15 -


^*
10 -



5-



0 I I I I I
0 5 10 15 20 25 30 35 40

IRS from (BL+BRS)5m [kA]


Figure 4-25. Comparison of IRS from (BL+BRS)30m and IRS from (BL+BRS)15m for 1999,
2000, and 2001.







76





50

IRS from (BL+BRS)15m = 0.07 + 0.95 IRS(Meas.)
R2 = 0.87
Sample Size = 71
40



< S*

E 30-

+
G j

E
5 20 **
.- *

.6% *
**
10 1999
o 2000
2001



0
0 10 20 30 40 50

Measured IRS [kA]


Figure 4-26. Comparison of IRS from (BL+BRS)15m inferred using Ampere's Law for
magnetostatics vs. IRS measured at channel base in 1999, 2000, and 2001.













50

IRS from (BL+BRS)30m = -0.02 + 1.01 IRS(Meas.)
R2 = 0.89
Sample Size = 76

40





2 30 -



-j *


77
0 30 *







10 -
(* 1999
2000
2001
v 1997


0 10 20 30 40 50

Measured IRS [kA]


Figure 4-27. Comparison of IRS from (BL+BRS)30m inferred using Ampere's Law for
magnetostatics vs. IRS measured at channel base in 1997, 1999, 2000, and
2001.

4.3 Discussion and Summary

From the statistical analysis of 97 records obtained in 1999, 2000, and 2001 the

mean dart-leader current (at the time of its attachment to ground) inferred from leader

magnetic fields measured at 15 m is 1.87 kA and standard deviation is 1.01 kA. The

minimum and maximum dart-leader currents are 0.38 and 5.40 kA, respectively. From









magnetic fields measured at 30 m (103 records obtained in 1997, 1999, 2000, and 2001),

the mean leader current is 2.58 kA and standard deviation is 1.57 kA. The minimum and

maximum dart-leader currents are 0.40 and 8.63 kA, respectively. Typically leader

currents are in the range of a few kiloamperes. Idone and Orville (1985) estimated dart-

leader peak currents for 22 leaders in two rocket-triggered flashes using the relation

between return-stroke peak current IR and return-stroke peak relative light intensity LR in

each of two flashes {LR = 1.5 (IR)16 and LR = 6.4(IR)1.1} to the dart leader relative light

intensities in those flashes. The mean dart-leader current was 1.8 kA and the range was

0.1 to 6.0 kA. Results of this study are in reasonably good agreement with those of Idone

and Orville (1985).

Return-stroke peak currents estimated from magnetic fields (as the global magnetic

field peak minus the leader contribution) measured at 15 m in 1999, 2000, and 2001 have

a mean value of 13.2 kA and the standard deviation is 6.4 kA. For the individual years the

mean return-stroke current varies from 14.5 kA in 1999 to 12.0 kA in 2000 and 13.8 kA

in 2001. Return stroke peak currents estimated from magnetic fields measured at 30 m in

1997, 1999, 2000, and 2001 have a mean value of 13.0 kA and the standard deviation is

6.0 kA. For the individual years the mean return-stroke peak current varies from 9.9 kA

in 1997, to 14.9 kA in 1999, to 11.8 kA in 2000, and to 14.3 kA in 2001. These inferred

return-stroke peak currents are slightly lower than the directly measured return-stroke

peak currents whose mean is 15.3 kA and standard deviation is 7.5 kA. Depasse (1994)

reported an arithmetic mean of 14.3 kA (maximum value of 60 kA, standard deviation of

9 kA) for 305 peak current values directly measured at the Kennedy Space Center (KSC),

Florida and an arithmetic mean of 11 kA (maximum value 49.9 kA, and standard









deviation of 5.6 kA) for 54 values directly measured at Saint-Privat d'Allier, France.

Rakov et al. (1998), Crawford (1998), and Uman et al. (2000), reported an arithmetic

mean of 15.1 kA (sample size = 37, maximum = 44.4 kA, and st. dev. = 9 kA), 12. 8 kA

(sample size = 11, maximum = 22.6 kA, and st. dev. = 5.6 kA), and 14.8 kA (sample size

= 25, maximum = 33.2 kA, and st. dev. = 7 kA) from direct current measurements at

Camp Blanding in 1993, 1997, and 1998, respectively.

The return-stroke peak currents obtained using Ampere's law for magnestotatics

and (BL+BRs), where BL and BRs are the leader and return-stroke contributions to the total

magnetic field (as done, for example, by Schoene et al. (2003)), measured at 15 m are

about 14 % higher than those obtained from BRS alone (excluding the leader

contribution). The return-stroke peak currents obtained using Ampere's law for

magnestotatics and (BL+BRS) measured at 30 m are about 20 % higher than those

obtained from BRS alone.

Dart-leader current to return-stroke current ratio obtained from magnetic fields

measured at 15 m has a mean of 0.14 and the correlation coefficient between these

currents is 0.82. Leader to return-stroke current ratio obtained from magnetic fields at 30

m has a mean of 0.20 and the correlation coefficient is 0.85 (note that the determination

coefficient, R2, given in Figure 4-23 and Figure 4-24 is the square of the correlation

coefficient, R). Idone and Orville (1985) obtained the ratio of dart leader to return-stroke

current for 22 events having a mean of 0.17. Results of this study are consistent with

those of Idone and Orville (1985).














CHAPTER 5
DISPLACEMENT CURRENT ASSOCIATED WITH LEADER/RETURN STROKE
SEQUENCES IN TRIGGERED LIGHTNING

Maxwell's integral equation relating azimuthal magnetic field to its sources has

been used to investigate the relative contributions of conduction and displacement

currents to the total ground level azimuthal magnetic field at 15 and 30 m from the base

of a triggered lightning stroke. The analysis is based on a comparison of channel base

current and corresponding magnetic fields measured at 15 and 30 m. It is concluded that

Ampere's law for magnetostatics, which neglects the displacement current contribution,

is inadequate for presentation of the total magnetic field due to lightning strokes at

distances beyond approximately 30 m.

5.1 Displacement Current Estimates from Measured Magnetic Fields and Channel-
Base Currents

The following simple expression (same as Eq. (2.1)) based on Ampere's law for

magnetostatics is used here to estimate the azimuthal magnetic field intensity at the

ground due to nearby lightning:

H(r, t) = I(t) / 2Ir (5.1)

where I(t) is the channel current, assumed to be the same in all contributing channel

sections, H(r,t) is the magnetic field intensity, and r is the radial distance from the

channel termination point on ground. This relationship has been found to describe

measured magnetic fields quite closely, in both magnitude and waveshape, at distances

up to 15 meters from the triggered-lightning channel base. Over the period from 1999 to

2001, magnetic field measurements have been made for nearly 70 return strokes in






81


Florida at a distance of 30 m from the triggered-lightning strike point. It is found that

amplitudes of the measured fields at both 15 and 30 m are somewhat lower then predicted

by Eq. 5.1, and the early portions of their waveforms exhibit slow fronts not seen in

measured current waveforms.


S9903 RS3


t[.Ls]

Figure 5-1. Superposition of measured magnetic field and channel-base current for Flash
S9903, stroke 3.

In order to examine the discrepancy, we consider as a starting point Maxwell's

integral equation relating the azimuthal magnetic field to its arbitrary, time-varying

sources,


aE
H.dl= JJ.dS+J o-_.dS


OE
=I+S o-t .dS = Ic + Id
=I+ so---


(5.2)









where Ic and Id are the channel-base conduction current and displacement current

respectively. As already described by Eq. 2.4 in section 2.6, the first term on the right

side of Eq. 5.2 corresponds to I(t) in Eq. 5.1. The second term is the displacement current

whose density is normal to the integration surface S bounded by the integration path 1, on

the left-hand side of Eq. 5.2. When applied to a lightning stroke to earth with S being

defined as flat, circular area of integration lying on the surface of the ground and centered

at the strike point, the first term accounts for the effect of conduction current flowing

normally through the integration surface. The second term on right side of Eq. 5.2

accounts for the effects of time variation of the vertical electric field associated with the

changing charge density distribution along the lightning channel during both the

approach of the leader and the resultant return stroke.

Equivalently Eq. 5.2 can be written as

Id = 2iTrHmeas Imeas (5.3)

where Imeas and Hmeas are measured channel-base current and measured magnetic field at

distance r.

In order to investigate the peak displacement current, the following procedure was

used. As a first step, the measured magnetic field converted to current using Eq. 5.1. and

the measured conduction current, Imeas, at the channel base were superimposed. Then the

difference between the current obtained from magnetic field using Eq. 5.1 and directly

measured current was interpreted as the displacement current. The displacement current

appears to increase with time and has negative polarity up to the onset of the return

stroke. Upon initiation of the return stroke, the total displacement current at that point

changes polarity (becomes positive) and attains a peak of a few kA.







83


This is illustrated in Figure 5-2.


S9903 RS3
5

4-


3 -
Id = 4.5 kA (Return Stroke)
2 -







-1


-2 Ii = 2.4 kA (Leader)


-3 I
0 5 10 15
t[l.s]


Figure 5-2. Displacement current for S9903 RS3 as inferred, using Eq. 5.3, from Imeas and
Hmeas at 30 m.

As seen in Fig. 5.2, the shape of the inferred displacement current waveform

resembles the shape of the electric field derivative (see Fig 3-13). Prior to the return-

stroke, while no conduction current is flowing at ground level, the effect of the

displacement current is apparent in the initial slow front of the measured magnetic field.

After the start of the return stroke, an abrupt increase in the slope of the magnetic field

takes place. Further effects of the displacement current component on the total magnetic

field are the reduction in amplitude of the peak of the magnetic field waveform.

Figures 5.3 5.6 show histograms of positive peak displacement currents (during

the return-stroke stage) for the years 1999, 2000, and 2001, estimated from waveforms







84


similar to that shown in Fig. 5-2. Similarly figures 5.7 5.10 show histograms of

negative peak displacement currents during the leader stage.

Distance 15 m, 1999


3 6 9 12
Return-Stroke Peak Displacement Current [kA]

Distance 30 m, 1999


0 3 6 9 12 15
Return-Stroke Peak Displacement current [kA]

Figure 5-3. Return-stroke peak displacement current estimated, using Eq. 5.3, from Imeas
and Hmeas at (a) 15 m and (b) 30 m in 1999.


(b) Mean 6.41 kA
St. Dev. 3.11kA
Min 2.70 kA
Max 15.0 kA
GM 5.76 kA
Sample Size 23







85


Distance 15 m, 2000


0 3 6 9 12
Return-Stroke Peak Displacement Current [kA]


Distance 30 m, 2000


0 3 6 9 12
Return-Stroke Peak Displacement Current [kA]


Figure 5-4. Return-stroke peak displacement current estimated, using Eq.
and Hmeas at (a) 15 m and (b) 30 m in 2000.


5.3, from Imeas







86


Distance 15 m, 2001


0 3 6 9 12
Return-Stroke Peak Displacement Current [kA]


Distance 30 m, 2001


Return-Stroke Peak Displacement Current [kA]


Figure 5-5. Return-stoke peak displacement current estimated, using Eq. 5.3, from Imeas
and Hmeas at (a) 15 m and (b) 30 m in 2001.


(b)
(b) Mean 5.08 kA
St. Dev. 1.86 kA
Min 2.40 kA
Max 7.70 kA
GM 4.76 kA
Sample Size 8