Long impulse currents associated with positive return strokes

\PERGAMON Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588

S9906Ð8209:87:,*See front matter Þ 0887 Published by Elsevier Science Ltd[ All rights reservedPII ] S 0 2 5 3 Ð 5 7 1 5 " 8 7 # 9 9 9 2 8 ÐX

Long impulse currents associated with positive return strokesChandima Gomes\ Vernon Cooray�

Institute of High Voltage Research\ Uppsala University\ Sweden

Received 7 April 0886 ^ accepted 09 March 0887

Abstract

Long distant electric _elds "399Ð499 km#\ generated by 15 positive cloud!to!ground ~ashes\ were analysed[ These~ashes consist of well detectable long impulse _elds subsequent to the initial peak[ These hook!shaped slow _elds are ofconsiderable amplitude and have a mean duration of 0[13 ms[ The amplitude of the long impulse _eld and the initialpeak of the _eld show an approximately linear relationship[ The long impulse current pertinent to positive return strokeswhich give rise to the measured long impulse _elds were estimated[ Flashes with these slow _elds lower a mean chargeof 49 C within the _rst 2 ms "excluding the _rst 099 ms which contains the initial peak#\ whereas the maximum chargelowered is 013 C[ The mean of the ratio between the peak of the long impulse _eld and the initial peak is 30)[ We alsoestimated the _elds that will be generated by the long impulse currents at distances of 0999 km\ 2999 km and 4999 kmfrom the strike[ The estimated peak magnetic _elds at 4999 km have a mean of 41 pT[ The peak magnetic _elds observedat distances of about 4999 km from positive lightning ~ashes\ which were associated with red sprites\ are in the samerange as the peak magnetic _elds that we have calculated for the above 15 ~ashes[ Hence we conclude that the observedQ!bursts which coincide with the occurrence of red sprites are due to the long impulse currents of positive return strokes[This slow _eld variation is rarely observed in connection with negative return strokes[ Even when it is present\ in theevent of a negative return stroke\ the amplitude and the duration of the tail are much less than those of its counterpartin positive return strokes[ This explains why ionospheric lightning is predominantly associated with positive returnstrokes but not with negative return strokes[ Þ 0887 Elsevier Science Ltd[ All rights reserved[

0[ Introduction

In general\ negative return stroke radiation _elds riseto their peak values in about a few microseconds[ Afterreaching the peak\ these _elds decrease and cross thezero line within about 49 ms[ The total duration of theseradiation _elds is about 099 ms[ On the other hand Coorayand Lundquist "0871# and Cooray and Perez "0873#\reported that many of the positive return stroke radiation_elds observed in Sweden do not follow this typicalbehaviour[ After 49Ð099 ms following the initial peak\ the_elds of the positive return strokes start to increase again[This secondary increase lasts for about 199Ð499 ms atwhich time the _eld reaches a maximum[ Subsequent tothis secondary peak\ the _eld decays and crosses the zeroline in about 0Ð4 ms[ Henceforth\ we refer to this _eldcomponent as Long Impulse Fields "LIF# and the return

� Corresponding author[ Tel[ ] 9935 07 422525 ^ fax ] 9935 07491508 ^ e!mail ] vernon[coorayÝhvi[uu[se

stroke current of the positive ground ~ash which gen!erates this _eld as Long Impulse Current "LIC#[ Such a_eld generated by a positive return stroke observed inSweden is given in Fig[ 0[

Fig[ 0[ Flash no[ P959685[16[ Parameters Ein\ Eim\ T0 and T1 aredescribed in the text[

C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588583

In recent years\ after the discovery of red sprites\ astriated glow phenomenon occurring in the mid!latitudeover mature and dissipating thunderstorms\ a signi_cantinterest has developed in studies of the positive returnstroke currents\ as they are associated with such pheno!mena "Boccippio et al[\ 0884 ^ Burke and Jones\ 0885#[ Inthis paper we present a quantitative analysis of LIFsand estimate the signatures of LICs pertinent to positivelightning ~ashes of a thunderstorm observed in Sweden[

1[ Experimental

The measurements were conducted in Uppsala"48[7>N\ and 06[5>E#\ Sweden on 5 July 0885[ The dataset is pertinent to a frontal thunderstorm which occurredin the daytime[ Some 72 cloud!to!ground ~ashes wererecorded\ of which 30 were positive ~ashes[ Twenty!sixof these positive ~ashes contained well detectable LIFs[The antenna system used to capture the _elds is identicalto that described previously by Cooray and Lundquist"0871#[ The vertical _eld was sensed by a ~at plate ante!nna[ After passing through a bu}er ampli_er\ the signalwas directly fed through a properly terminated coaxialcable to a transient recorder[ The zero!to!peak rise timeof the output of the antenna system for a step inputvoltage was a few hundred nanoseconds ^ the decay timeconstant of the system was about 14 ms[ The recordingsystem is the same as that described previously by Coorayand Perez "0883#[ This system consists of a LeCroy tran!sient recorder with 0 megabyte of memory[ The samplingtime was 9[4 ms with a pre!trigger delay time of 099 ms[Some 49 Hz noise is superimposed on the observed waveforms but\ compared with the amplitudes of the _eldtraces concerned in this study\ the e}ect of this back!ground noise is negligible[

2[ Theory and analysis

Wait "0859# provided a mathematical treatment of thepropagation of ELF components within the EarthÐiono!sphere waveguide[ The results of this mathematical treat!ment could be used to understand how the signatureof the LIFs of positive return strokes change as theypropagate di}erent distances over the surface of theEarth[ In the mathematical derivation given by Wait"0859#\ the Earth was assumed to be a perfect conductorand the ionosphere was considered to be a homogeneousconductor for ELF frequencies[ The e}ective conduc!tivity of the ionosphere is taken as o9vr\ where o9 is thepermittivity of free space and vr is a parameter whichhas a daytime value of 0[1×094 s−0[ The daytime heightof the lower edge of the ionosphere is taken as 69 km[According to Wait "0859#\ when the current moment ofthe source that gives rise to the ELF component is a

Dirac delta function\ the vertical electric _eld\ E"t#\ of thezero!order waveguide mode\ at the ground at a distancer from the source\ is given by

E"t# �m

1p1h 0c1r1

0:1 p9

b2:1 $Pa 0t?b1−

07

ct?r

Pb 0t?r1

¦8

017 0ct?r 1

1

Pc 0t?b1¦ = = =% u"t?# "0#

where P9 is unity

b � 0r

1h11 0vr

Pa"t# � 00

1T−01

0

T2:1e0−

03T1

Pb"T# �1

T2:1e0−

03T1

Pc"T# � −3

T2:1e0

03T1− 1p0:1

T1e rfc0

0

1T0:11t? � t−r:c

where c is the speed of light in free space and u"t?# is theHeaviside unit step function[ Once the response for thedelta function is known\ the response corresponding toan arbitrary source current moment can be derived fromthe convolution theorem[

For the _eld calculations\ we employed the positivereturn stroke model of Cooray "0884#[ The basic conceptsof this model are as follows[ The total charge brought toground by the return stroke is initially stored on thecorona sheath of the leader channel[ As the return strokefront surges upwards\ the corona sheath collapses drai!ning its charge into the highly conducting return strokecore[ Consequently\ each point of the leader channel wastreated as a current source that injects a current into thereturn stroke[ Subsequently\ this corona current travelsalong the return stroke core to ground at the speed oflight[ Since neither the temporal variation nor the spatialdependence of the corona current in positive return stro!kes is known\ their nature was inferred by appealing tothe available experimental observations on positivereturn strokes and long sparks[ Measured current wav!eforms due to positive return strokes "Berger et al[\ 0864#have an initial fast rising portion that takes a few micro!seconds\ a relatively slow decaying part that takes somefew tens of microseconds\ and a very slow varying sec!ondary peak that lasts for several hundred microseconds"return strokes with long continuing currents are notconsidered#[ Cooray "0884# considered this as evidencefor the existence of three distinct regions in the coronasheath*a hot region "innermost region of the corona

C[ Gomes\ V[ Cooray:Journal of Atmospheric and Solar!Terrestrial Physics 59 "0887# 582Ð588 584

sheath# which is neutralised almost immediately by a{return stroke| like neutralisation process\ an inter!mediate region which is neutralised slowly by radial nega!tive streamers originating from the central core\ and athird region "outermost region of the corona sheath#which is neutralised very slowly by corona dischargesand ion transport[ He represented the corona currentgenerated by these three regions by three exponentialfunctions with di}erent decay time constants[ The mag!nitudes of these time constants were evaluated by appeal!ing to experimental data on long sparks and comparingthe model simulations with the observed properties ofpositive return strokes[ Since it is the charge and the timeconstants of the current component from the outermostsheath which are responsible for the amplitude and theduration of the slow tail "i[e[ the ELF component of theradiation _eld#\ we changed these parameters to get anexact _t to the slow tails of the measured positive returnstrokes[ For a given set of model parameters\ the vari!ation of the model simulated current moment as a func!tion of time was evaluated and that was combined witheqn "0# through the convolution theorem to calculate thedistant ELF _eld "or LIFs#[ This procedure was repeatedby changing the model parameters until a match wasobtained between the model simulated and the measuredLIFs[ In estimating this best _t it was necessary for us topinpoint the location of the peak of LIF which\ some!times\ was oblique due to the various _ne structuressuperimposed on the _eld[ Thus\ there is some sub!jectivity involved in its estimation[

3[ Results and discussion

The 15 ~ashes with LIFs used in this study were locatedbetween 399 km and 499 km from the measuring station\with most of them clustering around 349 km[ Hence\ inthe calculations we considered r � 349\999 m for all ofthese ~ashes[ This choice does not in~uence the calculatedpeak LICs and the corresponding charge transport bymore than 4)[

Several examples of the measured and the model simu!lated LIFs together with the corresponding positivereturn stroke current waveforms are depicted in Figs 1Ð3[ In the calculations\ we did not attempt to simulate theVLF component of the _eld "i[e[ the initial peak# becauseeqn "0# is valid only in the ELF region[ Therefore\ themodel parameters that in~uence the VLF componentincluding the initial peak were not changed from oneexample to another[ This is the reason why the initialpeak of the calculated current waveform does not changefrom one example to another[ By integrating these cur!rent waveforms\ we estimated the total charge componentthat was brought down to ground during the _rst 2 msof these return strokes[ In this estimation\ however\ weexcluded the _rst 099 ms\ which includes the initial peak[

Our analysis shows that the charge transported duringthis time to ground does not exceed about 4 C[ We havealso calculated the electric _elds generated by these returnstrokes at 0999\ 2999 and 4999 km[ Several examples ofsuch _eld signatures are shown in Figs 1Ð3[ As describedlater\ these calculations made it possible for us to compareour results with some of those available in the literature[

In Table 0\ we have tabulated the values of variousmeasured and calculated parameters such as the initialpeak of the measured _eld "Ein#\ the peak of the LIF "Eim#\the time from the initial peak to the peak of LIF peak"T0#\ the time from the initial peak to the zero!crossingof the LIF "T1# and the charge transported to ground bythe LIC for the 15 return strokes "these parameters areshown in Fig[ 0#[ In addition\ the peak values of the LIFsat 0999\ 2999 and 4999 km "Exxxx#\ together with the peakvalue of the magnetic _eld of the LIFs at 4999 km "M4999#\are also given in this table[ The last row of the table givesthe mean value of these various parameters[ The meancharge lowered during the _rst 2 ms after the initial peakis 49 C\ whereas the mean of the peak LIC "Iim# is 27[1kA[ The mean duration of the LIF "T1# is 0[13 ms andthe mean rise time "T0# of that is 9[21 ms[ In seven ~ashesthe Eim ] Ein ratio was equal to or more than 49)\ whilethe mean of this value is 30)[

Note that\ in the case of the initial peak of the measured_eld "Ein#\ propagation e}ects have not been taken intoaccount\ in the given values[ For the initial peak of nega!tive return strokes\ the propagation of 349 km\ over landof conductivity 9[990Ð9[994 S:m\ will result in a reductionin amplitude of 19Ð29) "Cooray\ 0876#[

The estimated electric _eld at 4999 km "E4999# has amean amplitude of 05 mV:m while the horizontal mag!netic _eld\ calculated by assuming the _elds to be radi!ation _elds\ at the same distance "M4999# has a mean peakvalue of 41 pT[ The full!width of the LIF at this distanceis 4Ð09 ms[ We have made this calculation in order tocompare our results with those of Boccippio et al[ "0884#which are pertinent to red sprites[ They have observedthat most of the red sprites occur subsequent to positivereturn strokes\ which are associated with Q!burst eventsin the ELF Schumann resonance band[ The amplitudesof the Q!bursts which they measured at about 4999 kmfrom the mesoscale convective systems which initiatedred sprites are in the same range as of our estimation[With these results\ we may conclude that all or some ofthe 15 positive return strokes we have considered in thisstudy\ are associated with subsequent red sprites[ Figure4 shows the estimated magnetic _elds of the 15 ~ashes at4999 km as a function of the charge brought to groundby the corresponding LICs[ The values of these magnetic_elds are comparable to the peak values of Q!burstsassociated with positive return strokes that gave rise tored sprites at similar distances "Boccippio et al[\ 0884#[The authors of the last reference found that most of thepositive return strokes with initial peak currents larger


Fig[ 1[ Flash no[ P959685[00[ "a# Measured electric _eld "0# and calculated _eld "1# ^ "b# channel base current that was employed tocalculate the _eld ^ "c# calculated _eld at 0999 km "0# and calculated _eld at 2999 km "1# ^ "d# calculated _eld at 4999 km[




than a certain threshold gave rise to red sprites[ Sincetheir peak current estimation was based on the initialpeak of radiation _elds\ their results indicate that positivereturn strokes generating radiation _eld peaks larger thana certain threshold are capable of generating red sprites[However\ Fig[ 5 shows the relationship between the initialpeak of the radiation _eld and the amplitude of the LIFof the measured electric _elds[ The two parameters areapproximately linearly correlated[ Thus\ one can expectthe peak amplitude of the LIC to increase linearly withthe initial return stroke peak current of positive returnstrokes[ Since the peak of LIC increases almost linearlywith the charge brought to ground by the LIC "Fig[ 6#\it is reasonable to expect a linear correlation betweenthe initial peak current and the total charge brought toground by the LIC[ If this is true\ the results of Boccippioet al[ "0884# suggest that red sprites are generated bypositive return strokes with LICs that transport chargemagnitudes larger than a certain threshold[ This sugges!tion is further strengthened by the fact that the estimatedduration of the LICs is about a few milliseconds and thered sprites are generated within 1Ð2 ms after the initiationof positive return strokes[

The results of this study further support the conceptoriginally set forth by Wilson "0845# for the mechanismof the triggering of sprites\ in which the rapid removal ofa large positive charge from a vertically extensive chargelayer stresses the mesosphere to dielectric breakdown[

The long impulse _eld is rarely observed in connectionwith negative return strokes at the same range ofdistances[ In the 31 negative cloud!to!ground ~asheswhich we recorded on the same day\ there were merelythree _eld traces in which the LIF is detectable[ In thesecases too\ the amplitude and the duration of the LIFs aremuch less than those of its counterpart in positive returnstrokes[ This fact further con_rms that the presence of adominant long impulse current of a cloud!to!ground ~ashis an essential ingredient for the onset of a subsequentred sprite[ It is also obvious why ionospheric lightning ispredominantly associated with positive return strokes butnot with negative return strokes[

4[ Conclusions

A large fraction of the positive cloud!to!ground ~ashesobserved in Sweden lowers a considerable amount ofcharge to ground through a long impulse current "LIC#which lasts for about 9[4Ð2[9 ms[ the mean of the longimpulse _eld "LIF# peak is more than 39) of the initial_eld peak of the return stroke[ the peak magnetic _eldsobserved at distances of about 4999 km from positivelightning ~ashes\ which were associated with red sprites\are comparable with the peak magnetic _elds due to theseLICs that we have calculated for the above 15 ~ashes[


Table 0Statistics of the _elds and currents due to the 15 positive return strokes

Charge Iim Ein Eim Eim:Ein T0 T1 E0999 E2999 E4999 M4999

Flash ID "C# "kA# "V:m# "V:m# ")# "ms# "ms# "mV:m# "mV:m# "mV:m# "pT#

P959685[00 013 097[7 ×6[5 3[7 ³52 9[20 9[87 832 041 31 039P959685[06 89 59[7 5[3 1[5 30 9[24 0[23 419 89 17 82P959685[10 13 10[1 1[5 0[9 28 9[20 9[76 081 17 8 29P959685[13 23 04[9 0[3 9[5 32 9[31 0[14 013 14 7 16P959685[16 43 25[7 2[3 0[2 27 9[24 0[19 181 38 04 49P959685[17 23 29[1 2[5 0[5 33 9[10 9[72 174 27 09 22P959685[18 35 45[5 4[1 2[1 51 9[10 9[71 412 53 06 46P959685[20 49 49[1 6[1 1[1 20 9[17 9[74 336 54 07 59P959685[21 33 11[3 1[3 0[9 31 9[23 0[20 089 24 01 39P959685[22 23 06[1 2[5 9[5 06 9[21 0[11 035 15 8 29P959685[24 37 18[9 1[5 0[1 35 9[28 0[35 134 33 03 36P959685[25 35 18[9 1[9 0[1 59 9[27 0[34 134 33 03 36P959685[28 15 02[7 0[3 9[5 32 9[33 0[24 006 11 6 12P959685[31 83 39[5 2[7 0[1 21 9[59 1[64 181 58 15 76P959685[35 53 33[5 3[7 0[7 27 9[22 0[33 279 53 08 52P959685[36 41 55[9 5[1 2[5 47 9[08 9[62 480 62 08 52P959685[45 29 33[5 1[3 9[7 22 9[29 0[29 070 18 8 29P959685[50 55 53[7 4[5 2[9 43 9[18 9[85 455 74 13 79P959685[52 69 36[7 3[9 1[9 49 9[22 0[30 398 69 11 62P959685[54 13 10[1 2[9 0[9 22 9[19 9[81 081 17 8 29P959685[55 37 28[9 4[9 0[7 25 9[18 0[09 231 43 05 42P959685[57 11 00[1 1[5 9[3 04 9[36 0[59 82 07 5 19P959685[61 41 34[9 3[5 1[9 33 9[15 0[91 284 50 06 46P959685[62 49 13[9 2[1 9[7 14 9[30 0[42 086 28 02 32P959685[63 29 12[1 2[9 0[9 22 9[19 0[11 101 29 8 29P959685[72 31 18[5 1[3 0[1 49 9[17 0[29 143 31 02 32Mean 49 27[1 3[9 0[5 30 9[21 0[13 211 41 05 41

Iin ] Amplitude of the calculated long impulse current[ Ein ] amplitude of the initial peak ^ Eim ] amplitude of the impulse _eld ^ T0 ]time duration from the initial peak to the peak of the impulse _eld ^ T1 ] time duration from the initial peak to the zero!crossing timeof the impulse _eld ^ E0999\ E2999\ E4999 ] calculated _elds due to the long impulse currents at 0999 km\ 2999 km and 4999 km respectively ^M4999 ] calculated magnetic _eld at 4999 km[

Fig[ 4[ Correlation between the amplitude of the estimated mag!netic _elds at 4999 km and charge lowered by the LIC[

Fig[ 5[ Correlation between the amplitude of the LIF and initialpeak of the measured _elds[ "Note that the propagation e}ectshave not been taken into account in the case of the values of theinitial peaks of the measured _elds[#


Fig[ 6[ Correlation between the peak LIC and the charge loweredby LIC[

Hence\ we conclude that the observed Q!bursts\ whichcoincide with the occurrence of red sprites\ are due to thelong impulse currents of positive return strokes[ The LICis very rarely observed in the _elds generated by negativecloud!to!ground lightning observed in Sweden[ This maybe the reason it is that ionospheric lightning is pre!dominantly associated with positive return strokes butnot with negative return strokes[

Acknowledgements

The research work reported here was conducted withinthe framework of the lightning research program at the

Institute of High voltage Research[ The authors thankProf[ Viktor Scuka for placing excellent research facilitiesat their disposal and Dr R[ Thottappillil for fruitful dis!cussions[ The comments made by Prof[ Alexander P[Nickolaenko "one of the referees# helped us to improvethe _nal version of the manuscript[ Financial assistancegiven by the IPPS of the International Science Programs\Uppsala University\ and the Swedish Natural ScienceFoundation is gratefully acknowledged[

References

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Boccippio\ D[J[\ Williams\ E[R[\ Heckman\ S[T[\ Lyons\ W[A[\Baker\ I[T[\ Boldi\ R[\ 0884[ Sprites\ Q!bursts and positiveground ~ashes[ Science 158\ 0977Ð0980[

Burke\ C[P[\ Jones\ D[L[L[\ 0885[ On the polarity and continuingcurrent in unusually large lightning ~ashes deduced from ELFevents[ J[ Atmos[ Terr[ Phys[ 47\ 420Ð439[

Cooray\ V[\ 0876[ E}ects of propagation on the return strokeradiation _elds[ Radio Sci[ 11\ 646Ð657[

Cooray\ V[\ Lundquist\ S[\ 0871[ On the characteristics of someradiation _elds from lightning and their possible origin inpositive ground ~ashes[ J[ Geophys[ Res[ 76 00\192Ð00\103[

Cooray\ V[\ Perez\ H[\ 0883[ Some features of lightning ~ashesobserved in Sweden[ J[ Geophys[ Res[ 88\ 09\530Ð09\541[

Cooray\ V[\ 0884[ A model for positive return strokes[ Inst[Phys[ Conf[ Ser[ No[ 032[

Wait\ J[ R[\ 0859[ On the theory of the slowtail portion ofatmospheric wage forms[ J[ Geophys[ Res[ 54\ 0825Ð0835[

Wilson\ C[T[R[\ 0845[ A theory of thundercloud electricity[ Proc[Roy[ Soc[ "A#\ 186Ð206[

Long impulse currents associated with positive return strokes

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