IL ~NUOVO CI,-~IENTO VOL. 5 C, N. 4 Luglio-Agosto 1982

Various Features of VLF Waves Generated by Lightning Discharge.

R. PRASAD and :R. ~ . SXNGH

Applied Physics Section, Inslitu~v of Technology Banaras Hindu University - Varanasi-221005, India

(ricevuto il 6 Aprile 1982; inanoscritto revisionato ricevuto il 17 Agosto 1982)

Summary. - - Using the well-accepted features of lightning discharge, we have studied certain aspects of electromagnetic-wave generation, frequency spectrum and polar characteristics of these radiations. The effect of conducting ground and ionospheric layer on the attenuation of VLF signal is discussed. The likely role of the verticality of cloud-to-ground discharges and tile horizontality of cloud-to-cloud discharges in launching of VLF waves and governing the occurrence and overall morphology of whistlers is discussed.

PACS. 94.30. - Physics of the magnetosphere.

1 . - I n t r o d u c t i o n .

The electromagnetic emission from lightning discharges extends from a few hertz in the E L F range to beyond the visible region. The exact physical pro-

cesses of electromagnetic-wave generation by lightning and thunder covering this extended frequency range are not yet fully understood. Extensive observa-

tions have shown that one lightning event is different from another in many dynamic respects, however, it is rather difficult to obtain the detailed features by

measurements of various parameters of the individual lightning event. Therefore,

it has not been yet possible to test empirical models for lightning parameters and the spectral details of radiated electromagnetic energy. Using various

462

VARIOUS FEATURES OF VLF WAVES GENERATED BY L I G H T N I N G DISCHARGE ~

models for l ightning discharge current, m a n y workers (1-1o) have studied certain characterist ics of generat ing sources and their r ad ia ted electromagnet ic spec- t rum. These re tu rn current and veloci ty models are not unique and fur ther ref inements in l ightning discharge models are desired to in terpre t correct ly the cloud-to-cloud and cloud-to-ground data . The effect of or ientat ion of cloud- to-cloud and cloud-to-ground discharges on the rad ia ted energy spec t rum has been studied and changes in the field s t rength and polar izat ion of r ad ia ted signals in the ex tended f requency range have been shown (11,1~). The change in the polar d iagram of rad ia ted Y L F waves arises f rom the or ientat ions of the current mo m en t s which finally govern the f rac t ion of incident VLI~ wave energy launched along the geomagnet ic field lines in the whistler mode.

Various features of ionospheric and magnetospher ic p lasma, the inter- vening electric and magnet ic fields and the l ightning-generated u waves can be derived f rom the analyses of whistlers sonograms. The s t udy of various features of recorded whistler sonograms reveals ei ther the details of V L F generat ing source or the p ropaga t ion characteris t ics of field-aligned whistlers and various features of the in tervening magnetospher ic plasma. Wi thou t the full knowledge of generat ing source characterist ics it becomes difficult to decipher reliable informat ion abou t the magnetospher ic p la sma and the likely role of the wave-par t ic le interactions. I n the present paper , the authors have studied certain features of l ightning source which are re levant to the launching, focusing and propaga t ion of whistlers along the geomagnetic-field line. I t is shown t h a t the V L F energy radia ted b y l ightning discharge is of Gaussian shape wi th the m a x i m u m appear ing a t certain f requency which changes f rom one l ightning stroke to another. Fur ther , it is shown t h a t the launching of V L F waves at the generat ing end is highly dependent on the angle of incidence of V L F waves and is dominant ly governed b y the ver t ica l i ty of c loud-to-ground and the horizontal i ty of cloud-to-cloud l ightning discharges. The effect of con- duct ing ground below and the ionospheric bounda ry above has been considered. I t is shown tha t the net effect of ground and ionosphere is to introduce an a t t enua t ion factor in the received u energy. I t is shown tha t under a given

(1) C. (2) E. (3) A. (4) D. (~) K. (6) ~/[. (7) ~ .

(s) T. (0) G. (lO) y . (11) D. (12) Ca-.

]~. R. BRUCE and R. H. GOLDE: J. Inst. Electr. Eng., 88, 487 (1941). L. ItILL: Proc. IRE, 45, 775 (1957), D. WATT and E. L. MAXWELL: Proc. 1RE, 45, 787 (1957). L. CROO~: J. Atmos. Terr. Phys., 26, 1015 (1964). ~ . L. SRIVASTAVA and B. A. P. TANTRY: Ind. J. Pure Appl. Phys., 4, 272 (1966). A. TLT~AN and D. K. McLAIN: J. Geophys. l~es., 75, 5143 (1970). A. TLT~AN, D. K. 1V[cLAIN and R. J. FISHER: J. Geophys. Res., 78, 3523 (1973). NAKAI: Radio Sci., 12, 389 (1977). H. PRICE and E. T. PIERCE: Radio Sci., 12, 381 (1977). T. LIN, 1V[. A. U~AN and R. B. STANDLER: J. Geophys. l~es., 85, 1571 (1980). A. KOHL: J. Geophys. l~es., 69, 4184 (1964). O. MARNEY and K. SI{A~T~UGHA~: J. Geophys. l~es., 76, 4198 (1971).

4 6 4 R. PRASAD and R. 2. SINGH

configuration the magni tude of V L F energy can change significantly. Fur ther , the impor tance of l ightning source characterist ics in the in terpre ta t ion of whistler sonograms and whistler da ta is discussed.

2. - R a d i a t e d e l e c t r o m a g n e t i c f i e ld f r o m l i g h t n i n g r e t u r n s t rokes .

Ini t ia l r e tu rn stroke current propagates bo th upward and downward f rom the junct ion point (where upward connecting discharge contacts the down- ward propaga t ing s tepped leader) which lies several tens of metres above the ground. Both upward and downward current waves contr ibute to radiat ion fields. I n order to s tudy the characterist ics of rad ia ted electric field, we take the widely accepted Bruce and Golde (1) model for l ightning re tu rn stroke current. The re tu rn stroke current model is wr i t ten as

0) I t ~- Io[exp [-- a t ] - exp [-- fit]],

where Io, o: and fl are constants which va ry f rom one stroke to another. The paramete rs a and fl depend on the charge densi ty and the dimension of the channel. Io determines the to ta l charge deposited on the s tepped leader channel which changes f rom one re tu rn stroke to another r e tu rn stroke.

The veloci ty of the re turn s t reamer has never been precisely measured (la). However , SRIVASTAVA (14), referring to the table given b y SCHO~LA~D (15), inferred t ha t the re turn s t reamer veloci ty is generally modified by the pre- ionization of the leader channel, therefore the veloci ty of re tu rn s t reamer will have a double-exponent ial fo rm similar to t ha t of re turn s t roke current given b y eq. (1):

(2) V~ ~- Vo[exp [ - - at] - - oxp [ - - bt]] .

The values of Vo, a and b change f rom one l ightning stroke to another. S•I- VASTAVA (14) obta ined the following values:

Vo ---- 3 .10 8 m s -1, a ---- 6.10 4 s -1 ~ b ~-- 7.10 5 s -1

to explain the shape of the recorded wave fo rm of atmospherics. I t has been shown tha t this expression for r e tu rn stroke veloci ty accounts well for the to ta l length of the l ightning discharge channel and various other features of measured re tu rn current (14). The current m o m e n t of re tu rn stroke channel

(13) C. D. WI~IDI~IAN and E. P. KRIDER: J. Geaphys. l~es., 83, 6239 (1978). (14) K. ~ . L. SRIVASTAVA: J. Geophys. Res., 71, 1283 (1966). (15) B. F. J. SCHO~LA~D: Handbuck der Physik, Vol. 22 (1956), p. 576.

VARIOUS FEATURES OF VLF WAVES GENERATED BY LIGI ITNING DISCIIARG:E ~ 5

determines the s trength and spectral features of the electromagnetic-wave radiation. The current moment is defined as

(3) Me(t) = z, f v, dt = I t S t .

We assume the re turn stroke channel to be a vertical an tenna of length S f rom the ground to the charge centre of the thunder cloud. F ro m simple dipole antenna theory, the direct component of the radiated electric field at a dis- tance r from the lightning discharge chan~el is wri t ten as

:l dM~( t ) /d t (4) Ed(r, t) : 4-~-o cZr '

where so is the permi t t iv i ty of free space. By subst i tut ing for Me(t) f rom eqs. (1)-(3) into eq. (4), the direct component of the radia ted electric field is rewri t ten as

30Io Vo sin 0 ] ( t ) , (5) Ea(r, t, O) == eabr

where 0 is the angle made by the line joining the observation point to the mean direction of the discharge channel and the factor ](t) is similar to tha t given by SRIVAS~AVA and TA~TRu (5):

(6) /(t) = (b -- a ) (a exp [-- :r -- fl exp [-- flt]) --

- - b((a + ~) exp [-- (a + ~)t] -- (a ~- fl) exp [-- (a -~ fl)t]} -~

~- a((b + a) exp [-- (b + a) t ] - - (b -~ fl) exp [-- (b + fl) t ]} .

The values of the constants in eq. (6) determine the magni tude of ](t).

The ground below the lightning re turn stroke channel is, as a first approx- imation, considered as perfect ly conducting. I t gives rise to an image con- t r ibut ion to the electromagnetic field of the re turn stroke. The image con- t r ibut ion to the electric field is given as

(7) Ei(r , t, O) ~- AEd(r , t, 0 ) ,

where A is the ground a t tenua t ion factor which depends on f requency and distance. I t is cus tomary to assume, as a first approximation, the ground at- tenuat ion factor for low-frequency waves and largo distances of observation to be almost constant and close to uni ty (16.~7). Under this approximat ion, the

(is) K . P . SPIES and J. R. WAIT: I E E E Trans. Antennas Propag., AP-14, 515 (1966). (iv) j . R. WAIT: ElectromagNetic Waves in Strati]ied Media (Oxford, 1970).

~1 - I I Nuovo Cimento C.

4~6 1~. I'RASAD and R. N. SINGH

radiated electric field including the effect of perfectly conducting ground is

expressed as (3)

(8) E(r , t, O) : E , ( r , t, O) -{- Ed(r , t, O) : 2E~(r, t, 0 ) .

The magnitude and shape of the radiated electric field are controlled by the

nature and magni tude of the return current and the velocity of the upward streamer (13). WEID~AN and KRIDER (is) have reported that large submicro-

second components in lightning re turn stroke current could produce radiative field components with submicrosecond rise time. Sn~VASTAVA and TA.~TRY (5),

while s tudying the YLF characteristics of electromagnetic radiation, chose Io ----- 22 kA, ~ ---- 1.4.104 s -1 and fl ---- 50.104 s -1. We have used eRual values

of these constants and have calculated the electric field radiated from the current source reaching a point 100 km away from the source. The variation

of computed radiated electric field arriving at a distance of 100 km and making

different angles with the chaimel orientations is shown in fig. 1. The radiated

10

6 = 9 0 ~

~ 6

= 30 ~

' ~ 2 / ~

l I I ? ! I - 2 5 10 20 5 0 100 150

time(~s)

Fig. 1. - Variation of the radiated electric field of lightning return stroke at a dis- tance r ~ 100 km.

(zs) C. D. W~.IDMAN and E. P. KRID]~R: Geophys. Res. ~ett., 7, 955 (1980).

V A R I O U S F E A T U R E S OF V L F W A V E S G E N E R A T E D B Y L I G H T N I N G D I S C H A R G E 467

electric field is max imum at an angle of 90 ~ which is consistent with the dipolar characteristics of the source. The electric field is seen to maximize after 4 ms and thereaf ter decreases with increasing t ime and finally exhibits an excur- sion to negative values. The instant at which the field peaks is governed by

the values of parameters :r and ft.

3. - F r e q u e n c y spectrum.

The frequency spectrum of the lightning discharge is obtained f rom the Fourier t ransform of the radia ted electric or magnetic fields. The magni tude of the direct radiated electric field is wri t ten as

co

(9) lEd(o))] : lEa(r, t, O) exp [-- i0)t] dt . 0

The direct electromagnetic radia ted power density is obtained from the Poyn t ing vector which, in terms of direct radia ted electric field, is wri t ten as

( lo ) -Pd(0)) = IEC~I,_,~,0),,2 ~7

and, by including the effect of perfect ly conducting ground, the electromagnetic radiated power density is wri t ten as

( :11) 2 ( 0 ) ) - ]E (0 ) )13 _ ,.~ ] .Ed(0)) ]3 _ 4 P d ( 0 ) ) ,

where ~ ( = 120z) is the impedance of the free space through which the ra- diated electromagnetic wave has been assumed to propagate. Subst i tut ing for Ed(r , t, O) f rom eqs. (5) and (6) into eq. (9), we obtain

(12) lEd(o))]- rvab ~ - - 0 ) ~ § (a -t- 003 § 0)2 -~ (b § fl)2 § 0)3]

a(b § a) 3 11" + + [ ~3 § 0)~ + (a § p)2 § 0)~ (b § : )2T ~3JJ

§ o) 2 [ I ~ ( b - - a ) b(a § fl) a(b § ~) } L ( ~ T - o -i § (a § fl)~ § 0)2 § (b § ~)3 § 0)3 --

__~fl(b--a) 3 b(a § a) a(b § fl) }]3)�89 [fl2§ § (a § ~)3 § 0)3 § (b § fl)2_~ 0)i �9

~, fl and a, b are two sets of parameters which control the nature of electro- magnetic radiations f rom lightning sources. These parameters are interrelated

~68 R. PRASAD and R. ~'. SI~GI~

a n d t h e influence of one set of pa r ame te r s on the rad ia t ion character is t ics of cur- r en t m o m e n t can be in t e rp re t ed b y keeping the o ther set of pa rame te r s cons tan t .

The forms of the empir ica l cur ren t a n d ve loc i ty expressions used b y SRIVA- STAVA (~4) h a v e been r ecen t ly modif ied b y RAI (1~). I t is shown t h a t the values

of a, fi and of a a nd b are gove rned b y t he to ta l charge of t he c loud and t he c o n d u c t i v i t y of ~he cur ren t channels. I n order to a ccoun t for these var ia t ions ,

we have c o m p u t e d the spec t ra l character is t ics of r ad i a t ed e lec t romagne t ic power

dens i ty for four sets of cons tan t s (Io, a and /5) appea r ing in eq. (12). The va- r ia t ions of r ad i a t ed power dens i ty wi th f r equency for four sets of cons tan t s

(Io, ~ and f l )have been c o m p u t e d b y us ing eq. (12) and the var ia t ions of r ad ia t ed power dens i ty wi th f r equency are shown in fig. 2. The four sets of cons tan t s are :

1) ~ = 1.4"104 S -1, fl = 50"104 s -1, Io = 22 kA ;

2) ~ = 2.1"104 s -1 , fl = 25"104 s -1, Io = 22 k A ;

3) a = 3 .5 "104 s - 1 , fl = 50 "104 s -1, Io = 26 k A ;

4) a = 3.5 "10 ~ s -1 , fi = 50 "104 s -1, Io = 22 k A .

x l 0 -

E

t.,.

1 2 4 6 8 10 20 30 50 frequency (k Hz)

Fig. 2. - Frequency spectrum of the radiated power density of lightning return stroke at an observation distance r = 100 km and an observation angle 0 -- 90 ~

(x~) j . RAx: J. Atmos. Terr. Phys., 40, 1275 (1978).

V A R I O U S F E A T U R ] ~ S O F V L F W A V E S G E N E R A T E D B Y L I G H T N I N G D I S C H A R G E 469

The four curves in fig. 2 are characterized by these constants. The radiated electromagnetic-wave power density variation with frequency has a Gaussiau shape with a rather broad peak. The values of g, fl and Io govern the shape of the Gaussian curves shown in fig. 2. Considering the half-power density points, we have estimated the band width of radiated spectrum. We find that a band of frequencies containing different ranges is emitted out from different lightning strokes. The band widths of radiated VI~F waves as obtained from curves of fig. 2 are

1) (1.7-15) kHz,

2) (2.5--18) kHz ,

3) (3.5--21) kHz

4) (3.6_2~:) kHz .

These data clearly show the lower and upper frequency limits of VLF radiation. The lower and upper frequency cut-offs observed in whistler sonograms can be used to derive approximate values of these constants. This can be clone only when simultaneous absorption data and the overall attenuation factor are available to ascertain that the cut-off is not produced by occasional excessive absorption of YLF waves or some interference effect. Since we are interested in the changes of electric field with O, we have not accounted for the changes in the power density spectrum arising from changes in the orientations of cloud-to-cloud and cloud-to-ground discharges (12).

4 . - V L F f i e ld a t t e n u a t i o n .

The simplifying assumption that A in eq. (7) is constant and equal to unity is far from reality. The varying conductivity of the ground distorts the ampli- tudes, rise times and shapes of electromagnetic radiation (s0,sl). The precise meas- urements and analysis of field data at a given point should account for the attenuation factor introduced by the conducting ground below and the iono- spheric boundary above. We have considered the practical situation in fig. 3 and find that at the reception point B(r, 0), in addition to the direct field com- ponent, two more indirect field components arrive. One component is reflected from the ground and the other one is reflected from the ionospheric boundary. The distance of the point of reception and the angles of incidence to the ground and to the ionospheric boundary determine the correct phase of the three field components and their resultant value. The angles of incidence 0g and 01 are

(20) j . R. WAIT: I E E E Trans. Antennas Propag., AP-5, 198 (1957). (~1) ~. A. U~A~, D. K. ~cLAI~ and E. P. KRID~R: Am. J. Phys., 43, 33 (1975),

470 ~. eRASAD and R. ~. 8INGII

re la ted wi th the angle of di rect obse rva t ion 0. F r o m the g e o m e t r y shown in

fig. 3~ 0g and 0, are wr i t t en as

0 3 )

r sin 0 0g -~ Sill -~ r q- (Ari-~

a n d

r s i n 0 0, = sin -1

r + ( A r ) , '

........ ~ ..~ �9 �9 ..... ,...'.'.'...." ... ...... ., ........... .... .-...,

. . . : . : . : . : . . . . . . . : . ~ f ~ , . . : . . . . : . . . . . . . . . . . . . . . . . . . . . . . : . . . . . . . . : : . . . . .

" " ' " ' " " - ' " " i i ~ ' ~ - ~ . ~ . "" ' " " " ' - " " . . . . . . " " " " - " " - " " " . . - . : . . . ' . : . : . : . . . : . : �9 . : ~ "..... -.:.:.......-...:. .:.:.:.-..-..:..-.-. . . : . - . - . : . ' . : .....: : . : . . . : . : . . . . . . . : : . . : : : :: : : . . : : : : : : : : : .:.:.:.:.:.:.:.-...:. :.....-....~: .:.:.:.:..:.-...-.:.z.-...:.......:.:................:.:.:.:.:... :.:.:.:.:.-.:.:.:.z.:[.-.-.:.:.~...~:.:.:.:.-.:.:.:.-..:.:.:.:.:.:.:.:.:.:.:.:.:..:.z..:.: .:.:. ========================= :::::." :::: '"'~i~::::"': '"".: ': ': " ' : : : ::" :::'::: :::::"'::" ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ============================= ::.! i~.~!!i!i~i~!~!~i~!~i~i~i~!~i~i~i:}~!~i~.i..<...~i~./;~i~;; ~i.ii!~!~.~ii!!~i~iii~i~

I I

B(r~O)

" / / / / / / / 4 ~ / / / / / / / / / / / / / / / / / / / / /ll/////~-///con~uc~'ng grounr~///////~/

(ar)g

Fig. 3. - Schemo showing direct and reflected components of VLF waves reaching

the observation point B(r, 0).

where (Ar), and (Ar) l are t he geometr ica l p a t h difference wi th respect to the direct

w a v e of the ground-ref lec ted a nd ionosphere-ref lected waves and depend on

t h e obse rva t ion distance. I n te rms of the ionospheric he ight h and the aver-

age channe l l eng th l', we wri te

(At), = {(r cos 0 + 2/') ~ + r 2 sin S 0}t - - r

(14) a nd

(Ar)~ = {(2h -- 21'-- r cos 0) 2 + r 2 sin 2 0}t - - r .

F r o m the g e o m e t r y shown in fig. 3, t he electric fields of the ground-ref lec ted

and ionosphere-ref lected waves E , a nd E, are wr i t t en as (5,22)

(15) E, = r~R" exp [ - - i(2~/2)(Ar),] Ed {r + (~r),}~

(23) M . DOLUEHANOV: ~rapcbgation o] Radio Waves ( M o s c o w , 1971) .

VARIOUS :FEATURES OF VLF WAVES GENERATED BY LIGHTNING DISCHARGE 471

and

(16) E~ = r2R~ exp [-- i(2~/2)(Ar)~] ]~d, { r -~- ( A t ) i } ~

where R and R~ are complex reflection coefficients for the ground and the ionosphere. The complex reflection coefficients are controlled by the electrical properties of reflecting surfaces~ angles of incidence at reflecting surfaces and the nature of polarization (23). In the case of lightning return stroke, the parallel polarization of VLF waves dominates.

The resultant electric field Ea at an instant t at a point B(r, O) is the vector sum of three field components:

(17) = Ed + + E,.

By substituting for E~ and E~, respectively, from eqs. (15) and (16) into eq. (17), the expression for [ERI is rewritten as

r~R~ exp [-- i(2re/2)(Ar)~] (is) IER] = 1 + {r + �9

The quantity within brackets is termed attenuation factor and is denoted by E. Proceeding as in sect. 3, we can express the radiated power density spec- trum of VLF waves, in the presence of the ground and of the ionosphere, as

(19)

where Pd(C0) is unattenuated VLF wave power density at point B(r, 0). Equa- tion (19) reveals that the presence of the ground and the ionosphere modifies the YLF power spectrum of the lightning return stroke significantly. To il- lustrate its quantitative effect on the VLF field at B(r, 0), we have computed the variation of IF[ with frequency for three different angles, as shown ia fig. 4. In this computation, we have taken illustrative values of eonductivities of the ground and ionospheric reflecting layer, respectively, as 10 -8 and 10 -~ mho/m, their relative permittivities, respectively, as 10 and 1, and the ionospheric height and the average channel length as 90 km and 5 km, respectively. The variation of the attenuation factor vs. frequency in the frequency range from 1 kHz to 50 kHz is shown in fig. 4. I t is obvious from this figure that the attenuation factor has maxima and minima as the frequency varies from

(ss) E. C. JORDAN and K. G. BALI~AIN: Eleetromagnetiv Waves and Radiating Systems (Bombay, 1969).

472 R. PRASAD and R. N. SINGII

1 k H z to higher values. I n this f requency range, the m a x i m u m value of the a t t enua t ion factor is seen a t the lowest f requency of 1 k I Iz . The m a x i m u m value of the a t tenuat io l t factor at 30 ~ is 2.86. As the angle of observat ion

3.0

2.5

c: .o

4::$ .3

2.0

cl

e = 30 ~

. . . . ; ' " : 0 ' ' 4'o 2 4 8 20 frequency ( k H z )

Fig. 4. - Variat ion of a t tenuat ion factor with frequency for r = 100 km.

increases, the m a x i m a of the a t t enua t ion factor shift to lower values. As the f requency increases, the a t t enua t ion fac tor decreases and passes through a m i n i m u m value. The min ima for 30 ~ 60 ~ and 90 ~ are seen, respectively, to occur a t 50 kHz, 20 k H z and (9"-10) kHz. I n a higher-frequency regime, the a t t enua t ion factors for 60 ~ and 90 ~ oscillate and create differences of abou t 36 per cent and 16 per cent, respectively, which are significantly above the sensi t ivi ty of the measur ing system.

5. - Orientation of lightning channel and imlar diagram.

I n t h e fo rego ing d e s c r i p t i o n we h a v e cons ide red t h e r e t u r n s t roke l i g h t n i n g

c h a n n e l in t h e v e r t i c a l d i r e c t i o n a n d t h e ang le 0 m a d e b y t h e r a d i u s v e c t o r is

m e a s u r e d w i t h r e s p e c t to t h e ve r t i ca l . V i sua l o b s e r v a t i o n s a n d p h o t o g r a p h s (24.~,)

h a v e m a d e i t obv ious t h a t t h e c l o u d - t o - g r o u n d r e t u r n s t r oke s a re n o t a l w a y s

v e r t i c a l . T h e v e r t i c a l i t y of t h e r e t u r n s t r o k e d e p e n d s on t h e l o c a t i o n of t h e

(24) W. H. EvAI~S and R. L. WALKER: J. Geophys. Rvs., 68, 4455 (1963). (25) :E. P. KRIDER and G. I~IARCEK: J. Geophys. ties., 77, 6017 (1972). (2e) R . E . ORVILLE, G. G. LALA and V. P. IDONE: Science, 201, 59 (1978).

VARIOUS FEATURES OF VLF WAVES GEh'ERATED :BY LIGIITNING DISCIIA-RGE ~ 7 3

centre of the charged cloud and the conduct ing region of the ground, especially the projected conducting masks. The re tu rn strokes are established between two such regions, which necessarily do not conform to a vert ical configuration. The result ing configuration of the charged cloud and the conduct ing mask changes the orientat ions of the reference axis with respect to which the meas- urements of polar angles are made. This is schematical ly depicted in fig. 5a). KRII)EIr et al. (27), ~-~ERI~MAN et al. (~8) and UMA:, ~ et al. (-'~) have studied the

cU~tnnt receiv/ng poin~

verdca! cloud.-to-ground #1 ~ . o b s c h ~ ~

n) cond.uctlng ground.

ol[stant receiv/ng pofnt

hor/zont(zL cLou~-to-cLouoL

~ # s~ant cLoucZ-to-clouoL cdscharge

////////////////////////////////,7/ conoLucUng grounc~

b)

Fig. 5. - a) Scheme showing verticality and nonvcrticality of cloud-to-ground discharge, b) scheme showing horizontality and nonhorizontality of cloud-to-cloud discharge.

(27) E. 1 ). K R I D E R , l~. C. •OGGLE and .~[. A. U~A.w: J. Appl. Meteorol., 15, 302 (1976). (2s) B.D. HERR~AN, B[. A. UMA~,', R. D. BRATL~Y and E. P. KRIDER: J. Appl. Meteorol., 15, 402 (1976). (2~) ~. A. U~A~, Y. T. LIN and E. P. KRIDER: Radio Sci., 15, 35 (1980).

4 7 4 R. PRASAD a n d R. N. SINGH

errors found in the magnetic direction caused by nonver t ical i ty of the cloud-to- ground re turn strokes. The polar diagram of the radia ted electromagnetic energy has the usual figure-of-eight shape symmetr ic along the direction of the re turn stroke channel. Wi th the changes in orientat ion of the re turn stroke from verti- cality, the polar diagram accordingly changes and gives rise to a variabil i ty of max imum radiated energy from one re tu rn stroke to another re turn stroke. The change in the frequency spectrum of radiated field due to a change in the orien- tat ions of the current channel is considered of novital significance in the process of focusing of VLF wave energy ~long the geomagnetic field. I a the light of this changing situation, it can be easily argued tha t the powerful re turn stroke channel ma y not produce radiated V L F wave energy in the desired direction for focusing and guidance, which may result in the absence of whistlers on the conjugate point. Sometimes the whistler sonograms are seen without the spherics and vice versa. The propagational features of the VLF waves and the properties of the magnetoplasma remaining the same, the orientat ion of lightning strokes seems to control the f requency of occurrence of whistlers significantly. Cloud- to-ground discharges have horizontal components of the order of kilometres (30-32). Thus we find tha t the orientat ion of lightning strokes is one of the most impor tan t parameters which controls the magnitude of the field and the frequency of radia ted VLF waves which satisfy the conditions of launching of incident VLF wave energy along the geomagnetic field and the formation of whistlers. Similarly the cloud-to-cloud discharges, generally, approximated to be hori- zontal, are not always horizontal. The direction of cloud-to-cloud discharge may change within the extreme limit of perfect horizontal to perfect vertical. In fact, the altitudes and size of charge centre of two clouds determine the orien- ta t ion of cloud-to-cloud discharges. This is schematically shown in fig. 5b). Thus we find tha t significant VLF energy radiated from cloud-to-cloud lightning discharges may be launched along the geomagnetic field giving rise to equally good sources of whistlers.

6. - R e s u l t s a n d d i s c u s s i o n .

The generation of V L F waves f rom lightning discharge has been outlined in terms of a simple radiat ion process. The well-known dipole radiat ion process gives the required low-frequency radiat ion characteristics from lightning chan- nels. I t is clear from fig. 2 tha t the varying values of various current parameters

(30) T. L. TEER and A. A. F~w: J. Geophys. Res., 79, 3435 (1974). (31) R.D. B~ANTLEY, J. A. TILL]~R and IV[. A. UMAN: J. Geophys. t~es., 80, 3402 (1975). (32) E. A. JACOBSO~r and E. P. KRID~,R: J. Atmos. Terr. :Phys., 33, 103 (1976).

V A R I O U S F E A T U R E S OF V L F W A V E S G E N E R A T E D B Y L I G H T N I N G D I S C I I A R G E 4 7 5

f rom one event to another m a y result into va ry ing rad ia ted low-frequency electromagnet ic peak power densi ty and the f requency a t which it pe~ks. The nature of the spectral var ia t ion of V L F power densi ty on the or ientat ion of the current channel has not been considered. The orientat ions of current channel m a y also produce corresponding changes in the polar diagram. Using the current model wi th suitable parameters , we find that , for reasonable var ia t ions in the chosen parameters , the peak V L F power is rad ia ted a t frequencies below 10 kHz. The or ientat ion of l ightning discharge m a y change significantly f rom one l ightning event to another . The or ientat ion of the polar d iagram of V L F radia t ion also changes and determines the necessary and sufficient conditions for controlling various propagat iona l and morphological features of V L F emis- sions. The magni tude of V L F energy a t a desired angle to the local geomagnet ic field is governed by the magni tudes and phases of three components , namely direct, reflected f rom the ground and reflected f rom the ionospheric boundary . The overall a t t enua t ion of incident V L F signal has been discussed and is shown to change with various parameters . The m a x i m u m and m i n i m u m in the at- t enua t ion factor m a y govern the occurrence f requency of whistlers and their morphological features. We find t h a t the cloud-to-cloud lightning discharge with sui table or ientat ion angle can be as good a source of whistlers as the cloud-to-ground re turn stroke is. I f such informat ion can be obta ined for each l ightning channel, it would certainly improve the diagnostic po ten t ia l i ty of whistlers bo th at low and high lati tudes. The quan t i t a t ive control of this requi rement war ran t s a co-ordinated spat ial and t empora l recording of a tmos- pherics and s imultaneous observat ions of whistlers a t the conjugate points

corresponding to low- and high-lat i tude stations.

* * *

One of us (RP) is grateflfl to Ind ian Space Research Organizat ion for the award of a Research Associateship.

�9 R I A S S U N T 0 (*)

Usando le caratr accettate della scarica del fuhnine, sono stati studiati alcuni aspetti della generazione di onde elettromagnetiche, lo spettro di frequenza e le carat- teristiche polari di queste radiazioni. Si discute l'effetto del terreno conduttore e dello strato ionosferico sull'attenuazione del segnMe VLF. Si discute il ruolo probabile della verticalit~ delle scariehe dalle nuvole alla terra e dell'orizzontalit~t delle seariche tra nuvole nel lancio di onde VLF e nel regolare il verificarsi c la morfologia globale dei sibili.

(*) Traduz ione a cura della Redazione .

4 7 6 R. PI~ASAD ~md R. N. $INGI~I

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