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INTRODUCTION Physics of Lightning E. PHILIP KRIDER University of Arizona Lightning is a transient, high-current electric dis- charge that occurs in the atmospheres of the Earth and other planets and that has a total path length on the or- der of kilometers. Most lightning is produced by thun- derclouds, and well over half of all discharges occur within the cloud. Cloud-to-ground flashes (Figure 2.1), although not so frequent as intracloud flashes, are, of course, the primary lightning hazard to people or struc- tures on the ground. The continental United States re- ceives an estimated 40 million cloud-to-ground strikes each year, and lightning is among the nation's most damaging weather hazards (see Chapter 1, this vol- ume). The peak power and total energy in lightning are very large. Thus far, it has not been possible to simulate in the laboratory either the geometrical development of a lightning channel or the full extent of lightning dam- age. Lightning is a leading cause of outages in electric power and telecommunications systems, and it also is a major source of interference in many types of radio com- munications. The possible effects of lightning on ad- vanced aircraft, nuclear power plants, and sophisti- cated military systems are problems of increasing concern. Besides its many deleterious effects, lightning also has some unique benefits. The chemical effects of lightning 30 may have played an important role in the prebiotic syn- thesis of amino acids, and today lightning is still an im- portant source of fixed nitrogen, a natural fertilizer, and other nonequilibrium trace gases in the atmosphere (see Chapter 6, this volume). Also, lightning-caused fires have long dominated the dynamics of forest ecosystems throughout the world. The electromagnetic fields that are radiated by lightning can be used to study the phys- ics of radio propagation and have been used for many years in geophysical prospecting. Also, lightning-caused "whistlers" are still being employed to study the charac- teristics of the ionosphere and magnetosphere. Light- ning plays an important role in maintaining an electric charge on the earth and is therefore an important com- ponent of the global electric circuit (see Chapter 15, this volume). It is clear, therefore, that an understanding of the physics of lightning is important to further insight into our geophysical environment as well as for the de- velopment of optimum protection from the lightning's hazards. In recent years, new experimental techniques have enabled researchers to obtain a better understanding of the physics of lightning. Among these techniques have been applications of optical, acoustic, and electromag- netic sensors to measure the properties of various dis- charge processes on time scales ranging from tens of nanoseconds to several seconds. These measurements

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PHYSICS OF LIGHTNING _. I. _ . _ _ _= _ ~ ~ _ ~ . ~.t Wi. ~ ~ ~ :~ Cow _a _a have also been used to infer properties of the thunder- cloud charge distribution that is affected by lightning (see Chapter 8, this volume). Within the category of cloud-to-ground lightning, there are flashes that effectively lower negative charge to ground and those that lower positive charge. Most ground flashes are negative, but there is recent evidence that positive discharges are often unusually deleterious, and, therefore, this type is discussed separately in Chap- ter 3 (this volume). Before describing some of the recent advances in lightning research in more detail, the processes that oc- cur during a typical negative lightning flash to ground will be reviewed briefly. There are still many open ques- tions about basic lightning phenomena, such as whether or how the characteristics of individual flashes depend on the type of thunderstorm, the season, and the type of terrain that is struck. CLOUD-TO-GROUND LIGHTNING Simplified sketches of the luminous processes that oc- cur during a typical cloud-to-ground discharge are given in Figures 2.2, 2.3, and 2.4. For more detailed discussions of these phenomena, the reader is referred to Schonland (1964), Uman (1969), and Salanave (1980~. Figure 2.2a shows an assumed cloud charge-distribu- tion just before the lightning begins. Concentrations of negative charge are shown at altitudes where the ambi- ent air temperature is - 10 to - 20C, typically 6 to 8 km above mean sea level. The positive charge is more diffuse than the negative and most of it is at higher alti- tudes (see Chapter 8, this volume). Cloud-to-ground lightning almost always starts 31 FIGURE 2.1 Cloud-to-ground lightning over Tucson, Arizona. within the cloud with a process that is called the prelimi- nary breakdown. The location of the preliminary break- down is not well understood, but it may begin in the high-field region between the positive and negative charge regions, as shown in Figure 2.2b. After several tens of milliseconds, the preliminary breakdown initi- ates an intermittent, highly branched discharge that propagates horizontally and downward and that is called the steppe&-lea~er. The stepped-leader is sketched in Figures 2.2c and 2.2d, and this process effec- tively lowers negative charge toward ground. The indi- vidual steps in the stepped-leader have lengths of 30 to 90 m and occur at intervals of 20 to 100 ,usec. The direc- tion of the branches in a photograph indicates the direc- tion of stepped-leader propagation; for example, in Fig- ure 2.1 each stepped-leader propagated downward. When the tip of any branch of the stepped-leader gets close to the ground, the electric field just above the sur- face becomes very large, and this causes one or more upward discharges to begin at the ground and initiate the attachment process (see Figure 2.3~. The upward propagating discharges rise until one or more attach to the leader channel at a junction point that is usually a few tens of meters above the surface. When contact oc- curs, the first return stroke begins. The return stroke is basically an intense, positive wave of ionization that starts at or just above the ground and propagates up the leader channel at about one third the speed of light (Fig- ure 2.2e). The peak currents in return strokes range from several to hundreds of kiloamperes, with a typical value being about 40 kA. These currents carry the ground potential upward and effectively neutralize most of the leader channel and a portion of the cloud charge. The peak power dissipated by the return stroke

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32 15 km 10 5- _ 15 km 10 + + + / - - - - J ,,,/,+/: ) ~ Skm ~ 1 15t km 10 ~ _ ~a) - + + + + + J 7~ 0.040sec. ~ 5km it 15! C) ~d) km 10 15T km 10 5 0.090sec. - ~ -+-~+J 0.100 sec. f) i be) 0.101 sec. FIGURE 9. ~ Sketch of the luminous processes that form the stepped- leader and the first return stroke in a cloud-to-ground lightning flash. E. PHILIP KRIDER Is probably on the order of 108 watts per meter of chan- nel (Guo and Krider, 1982), and the peak channel tem- perature is at least 30,000 K (Orville, 1968~. The last few steps of the stepped-leader, the onset of a connecting discharge, and the beginning of a return stroke are illustrated in Figure 2.3. Here, the distance between the object that is about to be struck and the tip of the leader when the connecting discharge begins is called the striking distance (SD) and is an important concept in lightning protection. The distance to the ac- tual junction (~) between the leader and the connecting discharge is often assumed to be about half the striking distance. After a pause of 40 to 80 milliseconds, most cloud-to- ground flashes produce a new leader, the dart leader, which propagates without stepping down the previous return-stroke channel and initiates a subsequent return stroke. Most flashes contain two to four return strokes, and each of these affects a different volume of cloud charge (see also Chapter 8, this volume). Figure 2.4 shows a sketch of a dart leader and the subsequent re- turn stroke. Visually, lightning often appears to flicker because the human eye can just resolve the time inter- vals between different strokes. In 20 to 40 percent of all cloud-to-ground flashes, the dart leader propagates down just a portion of the previous return-stroke chan- nel and then forges a different path to ground. In these cases, the flash actually strikes the ground in two places, and the channel has a characteristic forked appearance that can be seen in many photographs. (See the left two flashes in Figure 2. 1. ~ IMPORTANT RESULTS OF RECENT RESEARCH Three types of research have recently provided new information about the physics of lightning. These are described briefly, and their importance is indicated. First, we discuss how remote measurements of electric and magnetic fields can be used to infer properties of lightning currents, including some implications of re- cent measurements. Next, we describe how the sources of radio-frequency (rfl noise can be used to trace the geometrical development of lightning channels as a function of time and to determine other properties of lightning. Finally, we discuss how small rockets can be used to trigger lightning artificially and give some appli- cations of this technique. Time-Domain Fields and Lightning Currents Recently, it has become clear that the electric and magnetic fields that are radiated by different lightning

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PHYSICS OF LIGHTNING .1 ]' . t Leader Steps . Return Stroke ~) ~ )[2 '\ f NI: ~,\t (a) (b) (c) (d) (e) 15t km 10 5~; 15 km 10 - 15~s .1. 15',s 1. 5'LS 1. 0.5'lS 5 FIGURE 2.3 Sketch of the luminous processes that occur during at- tachment of a lightning stepped-leader to an object on the ground. processes have different but characteristic signatures that are reproduced from flash to flash. For example, Figure 2.5 shows three of the many impulses that were radiated by a typical cloud-to-ground flash at a distance of about 50 km. These particular signatures were re- corded using a broadband antenna system and an oscil- loscope that covered all frequencies from about 1 kHz to 2 MHz. Trace (a) shows a cloud impulse that was radi- ated during the preliminary breakdown; trace (b) shows the waveform that was radiated by the first return stroke; and trace (c) shows a subsequent return stroke. The small pulses that precede the first return stroke in trace (b) were radiated by individual steps of the stepped-leader just before the attachment occurred (see Figure 2.3~. The characteristics of these newly mea- sured signatures have been put to use in the detection and location of cloud-to-ground lightning. For exam- ple, there are now large networks of magnetic direction- finders that can discriminate between the shapes of the return-stroke fields and other processes and that can provide accurate locations of the ground-strike points (see Chapters 1 and 5, this volume; Krider et al., 1980~. In a series of recent papers, Uman and co-workers have developed a theoretical model that describes the shapes of the electric and magnetic fields that are pro- duced by return strokes at various distances (Uman et al., 1975; Master et al., 1981; Uman and Krider, 1982~. One particularly important result of this work is the pre- diction that during the first few microseconds of the stroke, i.e., just after the attachment process has been 33 ~+ _+ ? ~ /-\- _ - ~ \J .~: .,) }\ ~ 5km 3: a) ~- , / 0.150sec ~ I,_ ~1 5km ~ 15- ~I. km 10 ~ 5km 151 km 10 ,~ C) + \ (, ] ,_ _- a`, \J ,,,' ' ) 0181 sec i}\ ~ 6~: 0.182sec ~ 5km 151 km 10 ~1 I ~ ~,_~ _~ ~ 5km ~ FIGURE 9.4 The development of a lightning dart-leader and a re- turn stroke subsequent to the first in a cloud-to-ground lightning flash.

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34 20 ~ 0 CY Lo 1 Lo \ (a) 1 :~ ~ (a) 1 1 1 1 1 1 1 on , I ,I , I I 0 40 80 1 20 1 60 200 MICROSECONDS FIGURE 2.5 Examples of electric-field impulses that were produced by a cloud-to-ground flash at a distance of about 50 km. Trace (a) was radiated during the preliminary breakdown, trace (b) is due to the first return stroke, and trace (c) is due to a subsequent return stroke. completed, the waveform of the distant or radiation field is proportional to the channel current, EnAD(t) = - 21l D I(t - Dlc), where E is the vertical electric field that is measured at the ground at time t, ,uO the permeability of free space, v the return stroke velocity, c the speed of light, and D the horizontal distance to the flash. A typical first return stroke will produce a peak field of about 8 V/m at a dis- tance of lOO km (tin et al., 1979~. The stroke velocity near the ground is typically on the order of 1O~ m/see (Idone and Orville, 1982~. With these values, Eq. (2.1) predicts a peak current of about 40 kA, a value that is in good agreement with currents that have been measured in direct strikes to instrumented towers (Berger et al., 1975; Garbagnati et al., 1981~. Recently, Weidman and Krider (1978, 1980) exam- ined the microsecond and submicrosecond structure of return-stroke E-field and field derivative, dE/dt, signa- tures. These investigators found that a typical first stroke produces an electric field "front" that rises in 2-8 ,usec to about half of the peak-field amplitude. This E. PHILIP KRIDER front is followed by a fast transition to peak whose mean lO-9O percent rise time is about 9O nsec (see Figure 2.6~. Subsequent stroke fields have fast transitions similar to first strokes, but fronts that last only 0.5 to 1 ,usec and that rise to only about 20 percent of the peak field. This fine structure in the initial return-stroke field is illus- trated by the waveform shown in Figure 2.7. Unfortunately, the origin of fronts in return-stroke fields is still not well understood, particularly for first strokes (Weidman and Krider, 1978~. If fronts are pro- duced by upward connecting discharges, then these dis- charges must have lengths in excess of lOO m and peak currents of JO kA or more. A front may be produced by a slow surge of current in the leader channel prior to the fast transition, but then this surge must contain currents on the order of 1O kA or more, and the associated chan- nel length must be at least 1 km. To date, the available optical data are not adequate to determine whether ei- ther of these processes (or both) does actually occur. Clearly, more research will be needed before we shall understand the physics of the important striking pro- cess. 90% 7N Breakp: ~ ~ ^~10%- 90% 305 _ N= 125 ~_ Mean= 90ns it, 20- ~.. At 1 0 O- = l l l a= 4C) ns 0 100 200 300 N anoseconds FIGURE 2.6 Histogram of the 10 to 90 percent rise times of the fast portions of return stroke fields over seawater.

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PHYSICS OF LlGHTNlNG FIRST RET: RANGE 1 9km STROKE 50 V/m~ ~ 4 ps/cl i v A 200 es/al i v FIGURE 2.7 The initial portion of a return-stroke field recorded 20 with fast time resolution. The same signal is shown on both traces, and the peaks coincide in time. The rise times of the fast field components that are radiated by return strokes are summarized in Figure 2.6. Note that the mean 10 to 90 percent value is about 90 nsec. These submicrosecond components in the field must be caused by submicrosecond components in the current, but few of the currents that have been mea sured during direct strikes to instrumented towers show components as fast as 90 nsec (Berger et al., 1975; Gar bagnati et al., 1981~. It is possible that an upward dis charge from a tall tower or the electrical characteristics of the tower itself will reduce the rise time that is mea sured from the value that would actually be present in a strike to normal terrain. Therefore, new measurements of lightning currents and fields with fast time-resolution will be necessary before we can understand the true cur rent rise times. 35 The actual current rise time is important for the de sign of lightning protection systems (see Chapter 5, this volume). For example, if a 100-nsec current interacts with a resistive load, the voltage rise time on that load will be 100 nsec. Most of the standard surge waveforms that are used to verify the performance of protectors on power and telecommunications circuits specify that open-circuit voltage should have a rise time of 0.5, 1.2, or 10 ,usec and that the short-circuit current should have a rise time of 8 or 10 ,usec (see IEEE Standard 587-80 and r FCC Docket 19528, Part 68~. These values are substan ~~ tially slower than those shown in Figure 2.6; therefore, it is probable that the degree of protection that is pro vided by devices that have been tested to the above stan dards will not be adequate for direct lightning surges. Measurements of the maximum dEIdis that are radi ated by return strokes striking seawater are summarized in Figure 2.8. Here, the average maximum dE/dt is about 33 V/m/,usec when the values are range-normal ized to 100 km using an inverse distance relation. To HE J 5 ~ At Peak /\t @ 100 k m N = 1 0 8 M as n = 3 3 V/m/,us = 1 4 V/m /,~ s o a 80 OCR for page 30
36 measure a dE/dt signature on a 10-nsec time scale, it is essential that the field propagation from the lightning source to the measuring station be entirely over saltwa- ter; otherwise there can be a significant degradation in the high-frequency content of the signal due to propaga- tion over the relatively poorly conducting earth. It is possible that strikes to saltwater contain inherently faster rise times than lightning strikes to ground, but Weidman and Krider (1978) argued that this is proba- blv not the case. If Eq. (2.1) is valid, then the dE/dt values in Figure 2.8 can be used to infer the maximum dlldt in the light- ningchannel, i.e., dl/dt 2 ~ D de/d OH (2.2) If a typical dE/dt is 33 V/m/,usec at 100 km and v is 108 m/see, then Eq. (2.2) implies that the maximum dI/dt is typically 1.5 x 10~i A/sec during a return stroke, a value that is about a factor of 20 higher than the tower mea- surements. At this point, it should be noted that, if re- turn strokes do contain large current components with dl/dt on the order of 1.5 X 10~i A/sec, then, if these currents interact with an inductive load, the overvol- tage will be substantially larger and faster than has pre- viously been assumed and the lightning hazard will be greater. (See Chapter S. this volume, for further discus- sions of lightning protection. ~ As a final point, we note that the electromagnetic fields that are produced by lightning are now known to be large and to change rapidly; hence, these fields them- selves can be deleterious. For example, Uman et al. (1982) showed that, if an object is struck directly by lightning, then the associated electromagnetic distur- bance may be substantially more severe than the electro- magnetic pulse (EMP) produced by an exoatmospheric nuclear burst at all frequencies below about 10 MHz. Also, Krider and Guo (1983) showed that the typical peak field from a return-stroke at 100 km corresponds to a peak electromagnetic power at the source of at least 20,000 megawatts. Locations of Lightning Radio Sources The radio-frequency noise that is generated by light- ning in the HE and VHF bands appears in the form of discrete bursts, and within each of these bursts there are hundreds to thousands of separate pulses. If the differ- ence in the time of arrival of each pulse is carefully mea- sured at four widely separated stations, the location of the source of each pulse can be computed, and the geo- metrical development of the If bursts can be mapped as E. PH ~ LIP KRIDER a function of time (Proctor, 1971~. Unfortunately, the physical processes that produce HE and VHF radiation in lightning are not well understood. Proctor (1981) re- ported that the pulses in most bursts are produced by a regular progression of source points, and, therefore, he suggests that bursts are produced by new ionization pro- cesses and extensions of old channels. If the source location of each rf pulse within a burst is plotted, the width of the associated "radio image" of the channel ranges from about 100 m to more than 1 km (Proctor, 1981, 1983; Rustan et al., 1980~. Figure 2.9 shows the paths of the central cores of six successive lightning discharges that were reconstructed by Proctor (1983~. By combining reconstructions such as these with measurements of the associated changes in the electric field at the ground, Proctor inferred that in-cloud chan- nels usually have a net negative charge and that the av- erage line charge density is about 0.9 C/km. Also, by dividing the length of a channel segment by the time required for that portion to develop, Proctor deter- mined that the average velocity of streamer formation ranges from 4 x 104 m/see to 8 X 105 m/see with a mean of (1.4 + 1.2) x 105 miser. If Proctor's average charge density is multiplied by the velocity of channel forma- tion, then the average current in developing channels would appear to be on the order of 100 A, a value that is in reasonable agreement with other estimates (Brook and Ogawa, 1977~. In an analysis of the locations of the first If sources in 26 lightning flashes, Proctor (1983) found that most dis- charges begin within or near precipitation, i.e., those regions of the cloud that produce a radar reflectivity greater than 25 dBZ. He also reports that all stepped- leaders begin in a narrow range of altitudes where the ambient air temperature is - 5 to - 16C. The average altitude of the initial rf sources in the flashes studied by Proctor was about 4 km above ground level (- 10C), and the standard deviation was only 440 m. The geometrical forms of intracloud discharges range from concentrated "knots" or "stars" a few kilometers in diameter to extensive branched patterns up to 90 km in length. Proctor (1983) reports that successive discharges in a storm often form an interconnected system and that some flashes seem to extend the paths of earlier dis- charges. In one case, two flashes that were separated by just 1.6 see produced tortuous channels that ran parallel to each other for almost 2 km, but the channels re- mained about 300 m apart. Although more data will be required before Proctor's results can be generalized, it is clear that time-of-arrival methods offer great promise for future research, partic- ularlv for those phases of lightning that occur within a cloud (see also Taylor, 1978; Rustan et al., 1980~. Radio

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PHYSICS OF LIGHTNING ~15 -10 Y . -A 1 , ' ! I I~ I I ~ ~I ~I ~I ~1 ,$ ~CHIT T r E6 34 ,~ X lam interferometer observations of lightning have also pro- vided interesting results (Warwick et al., 1979; Hay- enga and Warwick, 1981), and perhaps in the future interferometric methods will be developed to the point that they can provide unambiguous three-dimensional reconstructions of the discharge processes. Artificial Triggering of Lightning The last development that we describe is the artificial triggering of lightning by small rockets. This technique is particularly important because it provides, for the first time, the capability of studying both the physics of the discharge process and the interactions of lightning with structures and other objects in a partially con- trolled environment. Although rockets were first used to study atmospheric electricity in the eighteenth century, the first artificial initiation of lightning was clearly demonstrated by Newman et al. (1967~. The technique has subsequently been improved by researchers in France (Fieux et al., 1975; Fieux and Hubert, 1976; St. Privat d,Allier Research Group, 1982) and is now being used to investigate a variety of lightning problems in France, Japan, and the United States. When a thunderstorm is overhead and the electrical conditions are favorable, a small rocket is launched and carries a grounded wire aloft. If the rocket is fired when 37 5 10 her _1~ 1 , , , I , , , , I X -10 km ^: "' - 37 _30 -24 -1 6 - ` :-95 ~ 1~ _ / ~ - _ 1/, , "J ,-~-t.. I 5 10 _ 8 _ 6 4 2 GOD FIGURE 2.9 Geometrical reconstructions of six successive lightning discharges in South Africa (Proctor, 1983). The top panel shows a plane view of the channels from above, and the bottom panel shows an elevation view that is a projection of the same channels on a vertical plane parallel to the x axis. the surface electric field is 3 to 5 kV/m, then about two thirds of all launches will trigger a lightning discharge (Fieux et al., 1978~. Most triggers occur when the rocket is at an altitude of only 100 to 300 m, and the first stroke in the flash usually propagates upward into the cloud. The majority of the subsequent strokes follow the first stroke and the wire to ground; but in about one third of the cases, the subsequent strokes actually forge a differ- ent path to ground. These latter events are called "anomalous triggers" (Fieux et al., 1978~. The first stroke in a triggered discharge is not like natural light- ning, but subsequent strokes appear to be almost identi- cal to their natural counterparts. An example of lightning that was triggered by Hubert and co-workers is shown in Figure 2.10. The upward branching in this photograph was produced by a leader that propagated upward from the wire, and the bright, straight section of channel near the ground shows the path of the wire just before it exploded as a result of the lightning current. Triggered lightning is now being used to investigate the luminous development of lightning channels, the characteristics of lightning currents, the velocities of re- turn strokes, the relation between currents and fields, the mechanisms of lightning damage, the performance of lightning protection systems, and many other prob- lems (Fieux et al., 1978; Hubert and Fieux, 1981; Horii,

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38 FIGURE 2.10 An example of a rocket-trig- gered lightning flash in New Mexico. 1982; Miyachi and Horii, 1982; St. Privat d'Allier Re- search Group, 1982; Hubert et al., 1984~. Among the more important results to date have been a direct experimental verification of the existence of sub- microsecond fields and currents during return strokes and the general validity of Eq. (2.1) (Fieux et al., 1978; Djibari et al., 1981; Hubert and Fieux, 1981~. Wald- teufel et al. (1980) also reported a curious case in which a triggered discharge originated everywhere in clear air. The main benefit of the rocket triggering technique is that it can be used to cause lightning to strike a known place at a known time, thus enabling controlled experi E. PHILIP KRIDER meets to be performed. The triggering wire guides the lightning current to a point where a variety of sensors can measure the physical properties of the discharge and its deleterious effects directly. All cameras and data-re- cording equipment can be turned on and be fully opera- tional just before the rocket is fired. In most locations, the total number of triggers is limited to a few tens of events per year by the frequency of overhead storms, but the number and quality of the measurements can be made quite high to compensate for the relatively few events.

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PHYSICS OF LIGHTNING CONCLUSION We have seen that new experimental techniques now provide an opportunity to investigate many of the im- portant questions that remain unanswered about the physics of lightning. Among the more important un- knowns are the following: How is lightning initiated within a cloud? Can the initiation of lightning be suppressed or con- trolled? What are the mechanisms of stepped- and dart-leader propagation? What factors control the geometrical development of lightning? What is the physics of the attachment process? What are the currents in return strokes? How rapidly do return-stroke currents change with time? What physical processes control the propagation of return strokes? What is the energy balance of the various lightning processes? What physical phenomena occur during a cloud dis- charge? What are the characteristics of the currents in cloud discharge processes? What processes generate HF and VHF radio noise in lightning? Recent spacecraft observations have shown that light ning may be present in the atmospheres of Jupiter, Ve- nus, and Saturn, and the upcoming Galileo probe will carry a lightning detector to Jupiter (Lanzerotti et al., 1983~. Perhaps a study of lightning in atmospheres that are radically different from that of Earth will help us to better understand lightning on Earth and offer even more challenging questions for future work. REFERENCES Berger, K., R. B. Anderson, and H. Kroninger (1975). Parameters of lightning flashes, Electra 80, 23-37. Brook, M., and T. Ogawa (1977). The cloud discharge, in Lightning, Vol. 1, R. H. Golde, ea., Academic, New York, pp. 191-230. Djibari, B., J. Hamelin, C. Leteinturier, and J. Fontain (1981). Com- parison between experimental measurements of the electromag netic field emitted by lightning and different theoretical models- Influence of the upward velocity of the return stroke, Proc. Int. Conf. on EMC, March 1981, Zurich. Fieux, R., and P. Hubert (1976). Triggered lightning hazards, Nature 260, 188. Fieux, R., C. Gary, and P. Hubert (1975). Artificially triggered light ning above land, Nature 257, 212-214. Fieux, R., C. H. Gary, B. P. Hutzler, A. R. Eybert-Berard, P. L. Hubert, A. C. Meesters, P. H. Perroud, J. H. Hamelin. and J. M. Person (1978). Research on artificially triggered lightning in France, IEEE Trans. PowerAppar. Syst. PAS-97, 725-733. Garbagnati, E., F. Marinoni, and G. P. Lo Pipero (1981~. Parameters of lightning currents-Interpretation of the results obtained in Italy, PTOC. 16th Int. Conf. on Lightning Protection, July 1981, Szeged, Hungary. Guo, C., and E. P. Krider (1982~. The optical and radiation field sig- natures produced by lightning return strokes, J. Geophys. Res. 87, 8913-8922. Hayenga, C. O., and J. A. Warwick (1981). Two-dimensional inter- ferometric positions of VHF lightning sources, J. Geo phys. Res. 86, 7451-7462. Horii, K. (1982). 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