1-10 (1967) ATMOSPHERIC ELECTRICITY, J. Alain Chalmers 2nd Edition PDF

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ATMOSPHERIC ELECTRICITY 2nd Edldoll J. ALA CHALM ERS, MA. Ph.D.. F.Insl.P. hoItsKJr 0/ Pl<ysks. DttrltiMt !I'.,,",,'" PERGAMON PRESS C)XIOkl>' tONOON' I1DINIIURGII . NIW YUIt .. TOr-ON III . :;"I)NfV . !'AllIS • IIKAL"'S< 11'" Ill. lJcrg...

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ATMOSPHERIC ELECTRICITY 2nd Edldoll

J. ALA

CHALM ERS, MA. Ph.D.. F.Insl.P.

hoItsKJr 0/ PlURE appca ... to have been the firsl lO discover an annual variation in lhe magnItude of the ecr.·ct • which arc grcaler ;n fine weather in winter than in _"ummer.

\I.,

1.7. Early Theories

1n the timc of DE SA SURE it was con idered thaltbe phenomenll of atmospberic cl ctricity could be explained by supposing that the :Jir in fine \.. 'emher carries a positive charge, increasing WiUl the: hc' 'hI above the ground. Tllis would account for the positive 'e acquired by a point or a strelched wire and al for DE SM So, R", induclion effecls. At that time it was not pos ible to CSlilllUtc the vl1ri;Jlinn or charge WJlh Ill'ight ~md so il \\as not le.lIl/ell th.,t lhe mail1 rart of Ihe posilive charge lie well abo,e the polll "I' lh,' "lmo'phcr close to lhe ground.

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It W.I' .. d.\n m:l".'(.". ~.II

0

1o ~ug!!C~t Ihe orj!;in or the positive charge

in Ih'" rCf'"'' .Iu,l 11 Iheo. \\,,,, rut fomard by VOLTA (1782) lbat th e(fcch \\ere l.IU ul hy a '.eparation of dU:lric charge ccompanying the eh.ll1fe "I 1.llc I'",m waler 10 "'rour. VOLTA believed thaI, a well ..... '''llI11 helll, """e ;IIUo""t of po.itive electricily would be n eded f. r lhe eomcr ,"" Ill' \\lIler to vapour; tb.i \\ould 6

give a negative charge 10 the earth (apparently Ihe first recognition f thi charge) and a positivc charge in the ir. Tbi allraetivc and simple Ihoory mighl, cv n now, account for a number ofpbenomena in atmospheric electricilY, but il bas found no upport from direcl e perimelll In pite of numerous searches. .laning "ith those of VOLTA himself. for electrical effe I accompanying the change of Slate from wal'-r 10 vapour ( ee § 3.21.). 1.8. The Flame Technique OLTA (1782) w Ihe fir>! 1(1 ",a~e u..c of .1 new technique of mea uremenl. He found that if he pl.lccd " calldle or ligbted fuse in c ntacl with an exposed olldlle'or, the 1"lIer acquir d a charge of the some ign as that blainnl by the a point. bul of increased magnilude. He proved Ihal Ihis ould ''''I be due 10 any lectrical effeel of thc combustion bcc.,u>c he found IlU "'''''sing in a conlrol experiment carried oul in a c1o"'d room. AI-n••• Iler Ihc conductor i earthed, when there is a name the charge ""prea" almost immedialely, instead of taking some time, as IS the C:I\e In the absence of thc name. In modern lerms, Ihe flame :Iel, :" a p"tential cqualizer, providing charged panicl s and ion' \\h'ch quickly bring the condu I r to Ihe potential of it surroundi"g', \ hile without th flame this takes a lime of the order of an hou,. The usc of a flame first made po sible Ihe mcasuremcnt of changes in potcntial gradient over period as hon minule~.

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1.9. Theory of the Charge on the Earth The idea tb. t the phenomena of atmospheric electricity could be accounted for by the earth being cbarged, "ithout any cbarge being necessary in the lower air, wa first brought fonsard by RMAN (1804), who showcd that similar clTects 10 tbo e f on SAUSRI! could be obtained by moving a conductor horizontally from an exposed 10 a sheltered position. But ERMAN did not devel I' hi ideas v ry far. nor does he seem to have reali7.ed that tJ,ere must be, somewhere in the air. a positive chllrge equlll and opposite to lhat n the earth. It was left to PI:LTlER (1842) 10 confirm the ideas of ERMAN. lie put forward again the hypothesis or an original pennanent negalive eleetrificali n of Ihe eartb, witbout at fir t discu in its onl',n Cl! reali?ing lhe necc ity of discussing its replenishment 1'" r" R ,ho\\ed how lhe re ulLS of OL SA SSURE and or L'R\lA "",d be accoullted ~ r by the indueti n from' llC!!all\'d lhMp'd earth, 7

Hinorical Survey

Atmospheric. El ctricity

and he poinled oUlthe Importance of reaJizlOg Ihal an el:Clrometer mea ures only Ihe difference belween Ibe ebarges (wc would now say pOlenlial,) nil the cage alld on Ihe moving system (gold-leaf or pitb b.IUs). thus C\plaining why on earthed electrometer does nOI how UII ,n"et uue 10 the negative charge on the earth. PI I lUll allemptcd 10 account for Ihe phenomena by lhe idea th.1I wnkr vUflllur leaving Ihe earth might carry wilh il some of the cllrlh', negulive charge, thus giving nn explanation of unnual .IIIU ,Iiuraal variations, the electri uJ effects of clouds, etc. But this Ihe"ry never found any experimenlal upport and there are many "Iels not covered by it. 1.10. Kelvin's Contributions Important contributions to Ihe ubjeet "ere made by W. TIIOMSON, later LORD Ka.Y!. . (For convenience, he will be referred to a K[L\'I, even in eonneelion wilh work carried out before his elevation 10 tbe peerage.) KELVIN had mode considerable lIdvances in the theory ofelectroslalic and applied the ame idea in atmospheric electricity. He (KavIN, 18600) introduced lbe idea of"potemial" and showcd that Ihe name. as used by VOLTA (see § I.K. and the water-dropper (see § 5.6.) wbich he him If invenled (KELVIN, 1859b) serve 10 equalize Ihe polential of a conductor with that of the ir in il neighbourhood. He also explained tbe connection between the Iwo melhods of m a uremenl in atmospheric electricity at the time, Ihat of the potential equalizer and Ihal of the movable conductor (see 1.6.). J,rn (1900) realized thal such a m Ihod could nOI give an • bsoIule \'alu of lhe polenliuJ gradient or. from Ihis: "I the charge per unil area of the earth' urface, and he tin" ·,1 methods "I' obtaining Ihe .. rednction factor" or .. expo'ur' l':1elll' " tn con..'crl obser\'cd values to corresponding abSi\hllC \,11111,.'0, U\el Ic\ I 'r,,"nd (,~e ~ 5.18.).

/

Atmospheric Electricity

Historical Survey

•.

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f)o. 2. 111C reduction r:lttor.

More modern ,,~rk b.a .hown Ihat a reduction factor i 001 very s"uSfacl ry. speCially If space charges are present, and it i preferable 10 measure ullder condilions when il is not required. 1.12. Relation with Humidity Following 1)11 p, Crtl R' theory III I walersapour carrie negotlise cbar~e from Ihe .",Ih. Ihere \\ould be a relalion betw en polential gradlenl and hUlludlly. and Ihi EXNER believed he had establi bed. BUI such U Iheul) w uld involve 0 galive charges on Ihe waler vapour III Ihc 111\\0< atlllosph re ,nd so \\ould predicI an increa e IIf pOlellll3lllrudlell1 \\ ilh heighl, a a re ult of line of force wilh Ihell 11l\\« ellds on Ihcse charges. Kit V,N (I H81) proposed lhe u~ of IWO watcr-droppers onc 10 fl "hu\c Ihe III her, ,lunched la a balloon. TIle earliest mea uremcnls hy 1 I 11111 ,mu 1llMA appeared to give an increase of polenlial gra. IlIrlll wllh heighl, hUllnler rcsults by Ls CADET (1898) and TU"A (ISII'I) l',,\e ,Iclillile evidence Ihal above. al most. a few hundred ,. I, Ihc r~llCIIlial !'radient decrea with heighl alld Ihepacc

.• h",rbed hefore reaching the lower layers, and lbus is of no imJl"'t..nce "' atmo. pherie electricity. The origin and nature of lbe 1'1 "n,1l\' e","'ie ray, and tile proces e by which secondary ra)'S .11' 1'""1,, 'd \1/11 nol be deall wilh here; fr m the point of view of al",,"ph ". ,. "icity. all If,,,t matters is ti,e fael that there is Il>IU/"IHtrl \\ III 'h lIu.:rca,c\ (lO rising abo\; the c3rlh. nnd that for the pari (11 Ihe.: all1lo phttc of C(Ulcern to us the i nizution is indepcndent uf (liar ftr .,,,,krl;al liml:'. 11 i ho\\c\- r. of interest that the disco\cry .,nd eMly h"lory of m,m, my. derived from lbe ubjccl of atmosJlhen' eketlle,I). ('In' I" th~ earth, ionization due to f:ldioacli"ity in the 1.':lrlh :md III lIu..· :Ihnosphcrc is import:lIll. I~

Historical Survey

1.16. Stormy Weather Phenomena In slormy Md disturbed \leather Ihe poteotial gradient has been f,,"nd to be larger than in fine \lea I her. to vary rolpidly and often to h"w negative wlucs. In addilion to the conduction Cllrrenl. therc lire other currents in Lhe lower atmo!-pherc. for example. urttnh brOllght dO\vn by rain. and lI.c e"ndllcti\it) may be different from Ihe normal valu . by reason of illn, Jln'duced in prace se conne tedwith the"eatherdi.turbanee.ltc lilt, hlmed that there mu t he charge. in tbe c1oud~. ilIH.I "lIltHI 11l\(\t1~.llinn~ have been IIndertaken to determine the ,i~n,. ",a,'II11l1d'·, ,"'d location r I hese harge. The carlicsl DleasureDlelllS of Ihc ch,"~c h'""rht ,I"wn hy min showed an ",ce, of negulivc ~harge. hut the Illnjllrlly III Ihe (,Iter measurements have '\ho\\ n un c~ce" or po\iliH~ (,:har le (,,~c hartcr 10 .

1.17. The Atmosphere as a Condenser Ilhough KllslI' (l86Ob) (see . § 1.10. and 2.21.) had 'U~~C"ClI Ihc exiSlence of a conducting lay r in the upJlCr atmo phere an" Ihe analogy of Ihe \lhole (\lmo phere 10 a condenser, Ihis id a "a' n t brought into use in atmospheric el lricity unlil very much I"tcr. Even in the treatise fCHA u(1922, 1924. (925), the nly Illention of a region or high conduClivity in the uJlper utma'phere loes nol relale ilIa phenomena of atmospheric electricity near the pround. The first menlion of the" Heavisidc la,er" "' conneclion with fltmo phcrie electricity in this cenlury apl'Cars 10 have been due to WII~, (1920). but its importance w.s nOl recognized by all, even III 1929,' hen 'MPSON in discu i n on a paper by WHIPPLL(l929a) ;IIgued that lhe potcntial gradieOl was n t due 10 charge in the Ileaviside layer. Howe\'er, in CHONLANO'S (1932) book. the conducti nil layer is accepted a a facl 10 account for the constancy or air-earth current ,vilh height. and SCIlO LAND distingui hed beh,een Ihis conduetjn~ layer. whose condueti,ily i deriC, lh ". I.U. sy lem. the .. U. system and the system "I' 11I.lcli '.i1 units based on lhe .M.U. system with factors of rH\\' ." III 10. Ilu,' ..uhJct.:t ur ollllH'\llhcricclcclricity j" OnC in which the question 01 UIII" " fMlli ~ulal'ly ~m kward bccau~c

here,

than perhaps be.. twccn phCIHlIl1'Il-1 01 \1.1111: :Ind urrcnl electricity; if the different syslems of unil, .If' lI'led \\' h 're Ihcy ,eel1l 10 be mo t appropriate. there very often OIn\c!'l the need ur dUll Ill' rrom ODe sy tcrn to the other, and therefore of I'cmclUocrill ur Inuking up, the approprime conversion factof, mOrC

in uny uther IU.HH:h 'll clcelrieity, there is 3n interconnection

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18

1.3. The Rationalized M.K.S. System Ir we are to u e the prnclic31 units or pOl nll:ll ,tnd \:U!r\'nl the \olt and the ..mpere, Ih n lhe unit of po\\'cr i Ihc \"," (nr \nh.unpere). If wc retain lhe econd a thc unit f time. \\'e rcl.lln thc c ulomb a the unit of charge and the unit of energy i the J,,"lc. ince the joule is 10· erg. where the Ng i Ihe unll 0 enerl.') hosed On the centim Ire. gram and cond, it follow thal wc "",11 have 10 choose new unit of length and mass. Therc ore varoou, ra sible choi e • but by far lhe most convenicnl is Ihal of the metre IInd the kilogmm, which, it i imple 10 sce. agrees wilh the joule and 0 ' ilh the volt and the ampere. It is a fort una le accident lhat makes it ra ible 10 choose Ihe two uni those of which tbe material tundards are preserved. and il might well have happened that the original definitions of the practical cl ctrical uaits would n t have filled with bolh Ihe melre and the kilogram. For a sy tem of unit which is 10 include electrical phenomena, four fundamental units must be defined, and in the M.K.S. sy tern these are the metrc. kilogram, second nnd ampere. It i s mewhal more conveaient. in cleclrostatic theory. to consider the coulomb as the fourth unit, and, if it wCre a question fa matcria I tandard. it migbt be beller to ehoo e lhe ohm. From ome points f vie" Ihcre arc advantages in selecting the VOll, a well as lhc ampere. '" a fundamental unit and leaving the kilogram as a derived IInil tthe same time a the h nge is made from E. . . tn 1\I ... S.. iL i con\cnient to make :loother change which i'i :) Wall tllll'''' independelll of thc hange of unilS and either eh,,",'e '0111- hlle le peralure. Ihe mohililY and " Ihe eharge.

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be "rinen a i.IX.

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wh~re }.t

i the: o;;pecific conductl\ll)'

n 11tH: ins. liltlll,ul . for nCfwtlYC ion, the currcnl i\'

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J. . \ 29

Gene.ral Principles and Results

Atmo5pheric Electricity

th.: ,uOi'\ 2 u:fclrin' 10 lhe ncgati\'c ion. I he tutul ('tllrenl dcn~ily i

, = ;, + ;, = ()., + I.,) X. If Iho r "flen been .llOkcn" a. the "lIeavi idc la)er". With the dis· cowry Ih.1t Ihere is not just one such conducting Jayer, it has becn c n"dercd preferable to adopt some oth r name for the whole region which refl. I radio wave and the tcrm "iono phcre" inow generally used. hum Ihe point of view of atmo pherie electricity, thc interesl in n conduel",g region in Ihe upper atmosphere i not concerned with the refleclion of radio "ave , bUI with the conduetivily being IIISh ,n relahon 10 the currents flowing, lhal the wholc region is t effectivcly the samC pOlential. While the conductivity of the iono· sphere is certainly high cnough to achieve thi , it lurns OUI that the height at which the equipotential condil; n is reached i around 50 km (cc . 11.I8.) and it is therefore desirable I dislingui h thi, region from Ihe ionosphere, as defined by reflection of radio wave. . ome worker have used the term "equnlizing layer", but a belter lerm is "eleetro phere"; in much of the literature of atmo pheric electricit (in luding the earlier edition of thi ok), the t rm "ion ph rc" i used for what "e now call the "c1ectrosphere". Onc advantage of distinguishing the eleelrosphere from the iono~phere i that it is now possible 10 define atmo pherie cl ctrieity a, ele trical phenomena bel\veen the eleclro phere and Ihe earth, thu. eXcluding the properties of Ihe ionosphere itself. The eleelrosphere is all at a definile pot nlial. different from Ihal of the earth (sec § 11.2.). It is beli ved that the pOlenlial differ. ence between lhe electrosph re and the earth fluetunte, with Ih time of day and probably" ith the eason. Wc hall also sec ( 11.6.) thal the total charge on Ihe inner side oflhe eleetr phere. regarded .1' :l conductor, i 1cro. Since lhe electro phere is a good conductor, il acts n a perfeel e1ccl""talic hield. TIlU thunderstorms or other electrical ph nom· "'Ill .Ill'" 10 the earlh can ha,e no elfecl out ide Ihe eleetrosphere. Ill' UII" hnc' of rorce rrom them must tcrminutc :llthe 10\" rid!: ul" Ihe ·k"·Clm.. nhcfC. In the :..~Hnc W3)', ~In}l charge arriving 3t thl.: ",oll'l'hrr' '" e1ecl" ,phere from out ide can have nO elfect in ide IInle. Ihe I 'n ·tr.,le 11 hi Ihrough Ihe ciectro,phen:. Thi c praelieally al the snme potential. ince there is ul\v.,y' ,,,,, "."t of the arth experiencing fine "eather, il follows that ,I· I.ctrosphcrc is Iways at a positive potenlial witb respect to 11, .lIlh. Ihough tlte aetu.1 value of this potenti I may vary wilh "10 lit,,· of day "nd tinle or yenr. Measuremenls hnve shown that , .,,·tu,1I value of lho average potcntl31 of the eleetrosphere is I '"1 1·9 )( 10' V (sce § 11.2,), I

11. Quo.i.stotic State

hill ugh a eurrerl i, flowing in Ihe atmo pherc, and SO Ihe lll"l charges do not remain \Iatie. yel in steady conditions "11I nf the phenomena of atmospheric cleetricity ho" a "quasi. I 11\" "nle, charges which have becn moved from :IIIY region being , 1'1" 'ell hy othcr charges which h""e arrived in this region. 0 IhaL '" IlI'hllle u· picture of the disLributi n of charge laken at differ'It 1I",e' "ould be lhe samc. In tbese quasi· lalie condition. (some111111' referred I a condition of "dynamic equilibrium "'. it i, d I~ lI\Sumed Ihal the laws f eleelrostal;es c:ln still he appheu. "" Iltere is nO l'Ca.s n for doubling thi a umplion.

\ hell a qU:.L.,i. tutic talc cxi '\, \\c .111 cOIl,idc.:r 'Ht! 0111)- Ih.1l

., ill Irihution nrcharp.c rcm:lin\ Ih' "mill' 1111 ,h"lll,l1 III '(e

j,

General Prindple..s and Results

Atmospheric Electricity

at an leveh. I he fundamental fael is the chunge in onduelivil, :lI1d the ch.lI1ge 111 potential gradient is a eonscqucn e of this. The "bove di,cus ion in term of current den ity gives all thc i"format' " that might be required in rcgard to the value of lhe pOlential grndienls nl different height. wilhout needing to take ,Ill a eounl of space charges. Ho\\ever, to obtain a eomplele p,clure of the location of charges we can consid r lines of force, the ,kns,ty of which gives the potential gradient. If a po iti.e potential gradi nl de reases on rising, Ihere must be fe\\er line of force higher up than lower down, and the missing line of force must have posilive charges at their upper cnd, giving a posilive ,pace ehargc and hence an excess of positive over negative ion. It is interesting and instructive to con ider how a change of conductivily with beight could actually bring aboul the change of potential gradienl with height and the po iti.. space charge, starting with an original condition of uniform potcntial gradienl all the way from the carth to the clcctro pherc. Then line of force would be continuous and there would be no sp ee charge. '01", because the conductivity increases wilh hcighl, there will be a larger vertical current higher up than lower down, and so. if ions of both signs carry the current. there will be more positive ion mOI·ing down al a high levclthan at a lower level and so the number of positive ions in any volume \\ill increase; in Lhe same way. since negative ions move upward, the number of negalive ion in a volume will decrense. Any volume in the air lhu acquires a positive space charge which produces a difference in potential gradient as between the lOP lInd bOllom of the I olume. Thi process will conlinue until Ihe numbc:rs of posilive and ncgnlivc ions enLering nnd leaving Ih ,,,Iume arc equal, the difference in conductivily al thc top and h"1I01l1 be,ng balanced by differences in potcntial gradient. 2.16. Rota ion bctwc n Space Conductivity

Charge

I rum ~ 2,H.. lhc pill.:C dmrrc t! I' ph "

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It

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Change

of

dFltlh = ; tlrldh. ~ -

-col drl"h.

11 lie con ider a boundary bel\\ccn t\\O region of specific resisr, and then, by inlcgralion :tcm. s the boundary, the IlIhll harge per unit area on the boundary IS·

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Q

I1

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conductiviLic mther than "lCcilic "0

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I h , .....uh ,11111 I nl \\uy.

\lcre obtained by Rurm (19 Sh) in " '"r"ll .

I 11 R loxotion Time 11 iI I>ort,on of a conductor. of arcll S, "olrrie n cllarge (! nnd i, I"' ecl '" the atmosphere. the chargc Q i gradually dissipated I /'tIU' condu tion 3nd the raLe 31 \\hich this occurs gi\'cs n ·'time ,'111 IlllH" or "relaxation time" for clcctricul phenomena in the 11110

I1hcrc.

I he "' r"cc den ity of charg is QIS if the chargc is uniformly 11 Illhllt cl and so the potential gradient close to th unace i, t;1 "' .. , lhe currcnl, of ncg:ltivc ion if Q is po -hive, is tltu

i.,QI

Co

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per unit arca for the whole ore...

I 11 11 dQ

i.,Q

Ji= ---;;

by:

where ri. Ihe polent"d r"I\I"'nl, I'""ided Ih'llthc equipotentials arc horizoDlal. If j is the current dl.'n'lly lint! rill" 'Jl'.'cdic rcsi tance, I ri.

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11 Ihere arc qua i-SIalic condition. I is the sa11le at all level...