Effect of electric field inhomogeneity on kinetic Alfven wave in an inhomogeneous magnetosphere

Transcription

1 Inan Journal of Rao & Spac Physcs ol 46, Jun 07, pp ffct of lctrc fl nhoognty on ntc Alfvn wav n an nhoognous agntosphr A K Dwv a *& M S Twar b a Dpartnt of Physcs, Harsh Chanra P G Collg, aranas 00, Ina b Dpartnt of Physcs, Dr H S Gour Unvrsty, Sagar , Ina Rcv 7 Octobr 06; rvs 3 Fbruary 07; accpt 5 March 07 Th ffct of lctrc fl n-hoognty prpncular to th abnt agntc fl on Kntc Alfvn wavs n th prsnc of on an lctron ba vlocts ar nvstgat. In th prsnt stuy w hav aopt th partcl aspct approach to nvstgat th trajctors of charg partcls n th lctroagntc fl of a ntc Alfvn wav. xprssons ar rv for th fl-algn currnt, th prpncular currnt an th sprson rlaton. nrgy consrvaton tho was us to obtan th growth/apng rat of th wav. Th ffct of nhoognty of lctrc fl an lctron an on ba vlocts ar scuss. In prsnt stuy, w assu that th plasa s an ansotropc an wth low-. Th rsults ar scuss for th spac plasa paratr approprat to th auroral acclraton rgon of th arth s agntosphr. Kywors: Kntc Alfvn wav, lctrc fl n-hoognty, Ion an lctron ba, Auroral currnts Introucton Obsrvatons fro spaccraft crossng th auroral acclraton rgon hav rval n grat tal th crophyscs of partcl acclraton an th varty of plasa ffcts that occur wthn ths rgon of spac. Onshchno t al. hav stat that, th spaccraft obsrvatons 3-6 prov th vnc that sall-an larg-apltu prturbatons of th rft wav an ntc Alfvn wav (KAW) ar pranntly prsnt n th nar arth s plasa nvronnt. KAW play an portant rol n nrgy transport n rvng fl-algn currnts, partcl acclraton an hatng, nvrt- structurs n auroral acclraton rgon, solar flars an th solar wn 7-. Atonal support for KAWs rol n auroral phnona cos fro global strbuton aps at both low (FAST satllt) an hgh (Polar satllt) alttus showng that ntc Alfvn wavs occur on auroral fl lns along th ntr auroral oval -6. Th Clustr obsrvatons on 8 March 00 n th vcnty of a rconncton X-ln of th arth s agntopaus 4 rval sall apltu lctroagntc wav prturbatons that hav bn ntf as ntc Alfvn an rft-alfvn wavs wth prpncular wavlngths of th orr of th on Laror raus 7. *Corrsponng author (-al: awv@yahoo.co.n) Fl-algn currnts ar of grat portanc n agntosphr-onosphr couplng 8,9. Fl algn currnts play a funantal rol n th transfr of ontu along th fl. Thy ar prhaps of ost portanc n agntosphrc physcs n th stuy of couplng btwn rgons, whr ffrnt ynacal contons prval but whch ar thra by th sa fl 0. Obsrvatons of lctrc fls n th onosphr an th agntosphr usng varous tchnqus hav l to portant avancs n th unrstanng of agntosphr-onosphr couplng. lctrc fls of th orr of hunrs of ll volts pr tr hav bn prct n th hgh lattu onosphr, th auroral zon, agntotal an th plasa sht -6. In a varty of stuatons n a partcular at th t of substor onst th ntrplantary agntc fl rvrss ts rcton, an two oppostly rct nhoognous lctrc fls ar rport n th plasa sht an n th auroral zon,. Ovr th last ca t has bn stablsh that auroral lunosty s u to th pact of an acclrat lctron ba cong towars th onosphr an at th sa vnt th upcong on ba has also bn obsrv towars th agntotal 7,8. Svral paprs 9-3 consr th paralll lctrc fl of th ntc Alfvén wavs wth th agntc rror ffcts ar tan nto account.

2 DWIDI & TIWARI : FFCT OF LCTRIC FILD INHOMOGNITY ON KINTIC ALFN WA 47 Chn t al. 3 prsnt a thory of th ntc Alfvén wav nstablty n prsnc of th fl-algn currnts. Klushn an Magr 33 consr th paralll lctrc fl of th Alfvén wavs whn th couplng wth th coprssonal o s tan nto account. In th rcnt past partcl aspct analyss was us to xplan th auroral partcl acclraton n th trs of Alfvn wavs an ntc Alfvn wavs propagatng paralll to or oblquly wth rspct to th abnt agntc fl 6, Th an a of ths stuy s to nvstgat th ffct of on an lctron bas on th ntc Alfvn wav n th prsnc of an nhoognous lctrc fl n th auroral rgon by usng partcl aspct analyss. Th thory s bas on Dawson s thory of Lanau apng whch was furthr xtn by any rsarchrs 6,35-4 for th analyss of lctrostatc an lctroagntc wavs. Th avantag of ths approach s ts sutablty for alng wth auroral lctroynacs an nrgy xchang by wavpartcl rsonant ntracton. Basc Assuptons In ths ol, th plasa s v nto two groups of partcls: rsonant an non-rsonant. It s suppos that rsonant lctrons partcpat n th nrgy xchang wth wavs, whras non-rsonant partcls support th oscllatory natur of th wavs. A wav propagatng oblquly to th agntc fl n a plan noral to th nsty grant an appl lctrc fl s consr, n an ansotropc plasa. Th abnt agntc fl s rct along th z- axs, an th nsty grant an prpncular lctrc fl ar n th y-rcton. Th wav s propagatng n th (x, z) plan. W hav tan nsty grant an rlat rft vlocty n our analyss. Th ffct of prssur grant an rlat currnt s gnor as th approxaton sutabl to th auroral acclraton rgon. Th ntc Alfvn wav s assu to orgnat at t = 0 whn th rsonant partcls ar unsturb. W consr low β (rato of plasa prssur to th agntc prssur) collson lss plasa satsfyng th contons. ;, ; T T...() Whr T an T ar th thral vlocts of ons an lctrons along th agntc fl, Ω, ar gyraton frquncs an ρ, th an gyrora of th rspctv spcs. W consr a ntc Alfvn wav of th for 6, () Whr, an cos( x z, cos( x z (3a) (3b) Whr ϕ an ψ ar assu to b a slowly varyng functon of t t, an ω s th wav frquncy. an fn th coponnts of wav vctor prpncular an paralll to th agntc fl B 0. lctrons strang wth thr thral vlocty along th fl lns ar assu to ntract wth th lctrc fl of th ntc Alfvn wav. lctrons whos vlocty s slghtly lss than th paralll phas vlocty ω/ of th wav caus Lanau apng of th wav. Th nhoognous appl lctrc fl (y) has th for of a stabl o, an s gvn as 6 : y ( ) 0 a y Whr a s tan to b coparabl to th an on gyroraus but uch largr than th Dby lngth. Th ol rlat to th lctrc fl rprsntaton ay b prtanng to th two oppostly rct lctrc fls n th auroral acclraton rgon. y =0 rprsnts axu lctrc fl at th -plan of th acclraton rgon whch crass both th ss of th cntral part by ncrasng th valu of y an attans zro valu at y = a of th orr of th on gyroraus. Th varatons as th squar of y coornat prcts two oppostly rct lctrc fls slar n natur. Whn y /a <<, (y) bcos a constant unfor fl. In th cas y > a, th lctrc fl changs sgn an s oppostly rct. 3 Dstrbuton Functon W aopt th prturb nsty for non-rsonant partcls n th prsnc of th ntc Alfvn wav

3 48 INDIAN J RADIO & SPAC PHYS, JUN 07 for th nhoognous plasa 6. To trn th sprson rlaton an th assocat currnts, w us th strbuton functon of th for ' y, Whr f ( ) xp{ T / f ( ) xp T T }...(5) Dj / T...(6) Whr s a sall-scal paratr of th orr of nvrs of th nsty grant scal lngth. Dj fns th ba vlocty of th partcls. Hr s th ass an, T & T ar th tpraturs of charg partcls prpncular an paralll to th agntc fl B 0 whch s rct along th z-axs. Th wav s propagatng n x-z propagatng n x-z plan noral to nsty grant whch s along th y-axs. 4 Dsprson Rlaton Th ntgrat prturb nsty for non-rsonant partcls n, s gvn as n, n( r, 0 (7) W us th xprsson of n for non-rsonant partcls whch has bn valuat by Barona an Twar 6 as n( r, N( ) Jn ( ) q an nant n Jl cosnl (8) s th aagntc rft vlocty whch s fn by T N N y (9) an 0, rprsnts th hoognous plasa, q s th charg whch s qual to for ons an for lctrons. n whr ( y ) a n nl n n y q ( y ), '' y y 4 y z t..... n l t...( 0 ) θ s th ntal phas of th chargs partcls, n an l ar runnng sybols an ntgr. In vw of th approxatons (q. 3), th onant contrbuton cos fro th tr n = l = 0 as th contrbutons u to hghr n ar nglgbl 39. Th rsonant crtron s gvn by 0, whch ans that th lctrons s th wav npnnt of t n th partcls fra. Hr rprsnts B rft vlocty of th partcls of by th nhoognty of th lctrc fl. In fnton of th rsonant crtra w hav gnor th ffct of nhoognty of lctrc fl u to larg scal lngth of th nhoognty, othrws woul la rft nstablty by fbac chans 4. Th partcls satsfyng th abov conton ar call rsonant. J s ar Bssl s functons whch ars fro th ffrnt procal varaton of charg partcls trajctors. Th tr rprsnt by Bssl s functons show th ructon of th fl ntnsts u to fnt gyroraus ffct. Wth th hlp of qs (4) an (8) w fn th avrag nsts for nhoognous plasa p n 4 T p n 4 T p, 4N 0 /,...()...()

4 DWIDI & TIWARI : FFCT OF LCTRIC FILD INHOMOGNITY ON KINTIC ALFN WA 49 Whr T s th squar of thral vlocty paralll to th abnt agntc fl. s th aagntc rft vlocty of ons. Usng th quas-nutralty conton 7,6,36,37 n n,. W gt th rlaton btwn ϕ an ψ as (3) p D...( 4 ) p T Usng prturb on an lctron nsts n an n an Aprs law n paralll rcton 7,36,37, w obtan th rlaton 4 ( ) J, z t Z (5) c whr J Z [( N( ) u z ( r, n ( r, ) ( N ( ) u z ( r, n ( r, ) ] 0 (6) u z (r, s th prturb vlocty of charg partcls n th prsnc of a ntc Alfvn wav. J Z s th currnt nsty whch nvolvs frst-orr prturbatons of nsty an vlocty. Th xprsson for u z (r, s calculat by Barona an Twar 6, whch s gvn as uz( r, q ( ) n Jn J l [cosnl cos( nl n], n...(7) Whr η = 0 for th non-rsonant partcls an η = for th rsonant on. In th analyss w hav assu th plasa consstng of non-rsonant an rsonant partcls. Th non-rsonant partcls support th oscllatory oton of th wav, whras th rsonant partcls partcpat n nrgy xchang wth th wav. To stngush th non-rsonant an rsonant partcls w hav aopt th sybol η = 0 for nonrsonant partcls an η = for th rsonant partcls 37. Th thoology of ths papr s bas upon th partcl aspct analyss 37 whch s focus to valuat th partcl trajctors n th prsnc of wav lctroagntc fls. Wth th hlp of qs (4) an (5) w obtan th sprson rlaton for th ntc Alfvn wav n nhoognous plasa as: ca s A D v A D p A p T p T p A A c T 3 c Whr s th squar of on-acoustc sp an c v A p D A D v A (8) s th squar of Alfvn sp. Th sprson rlaton of th ntc Alfvn wav rucs to that rv by Hasgawa an Chn 4, Barona an Twar 6 unr th approxaton, =0, D =0, D =0 an I 0 ( )xp(- )-, for = ½ < as w hav appl. I 0 ( ) s th of Bssl functon. 5 Currnt Dnsty Snc th avrag valu of currnt vanshs whch s contrbut by frst-orr prturbatons of nsty an vlocty u to thr procal varatons, w valuat th avrag currnt pr unt wavlngth whch s th scon-orr prturbaton. To valuat th prturb currnt nsty pr unt wavlngth w us th followng st of quatons N n u J, s N (9) 0 0, An J = J - J (0)

5 50 INDIAN J RADIO & SPAC PHYS, JUN 07 Wth th hlp of qs (4), (8) an (7) w obtan followng rlatons: p J X 8 T T p J Z 8 p 4 T Whr D () p 8 4 T T 4 T () In th valuaton of th currnt nsts t was assu that th fl-algn an prpncular currnts ar u to an lctroagntc ntc Alfvn wav an th contrbuton u to aagntc rft was nglct. 6 Growth/Dapng Rat valuatng th wav nrgy nsty pr unt wavlngth an changs n nrgy of non-rsonant an rsonant partcls, Trasha 38, ara an Twar 40 an Dwv t al., 36,37 hav rv th growth/apng rat by prforng a consrabl aount of algbrac calculatons, whch s of th for (/ )( / ( / ) ( / ' ) ( / )3...(3) ( A T f f T / ) Twar 6,34. Th ntc Alfvn wavs ar gnrat by nsty nhoognty f th lctrc fl nhoognty s absnt. Howvr, u to th lctrc fl nhoognty th conton s altr. Th lctrc fl nhoognty rqur for wav xctaton can b stat by th argnally stabl conton (γ = 0), unr th approxaton ω/ T <, w obtan B 0 T 0 D T...(5) Whch s of th orr of 0.89 for = 0.5, ω = s -, D = 0 7 c/s, D = c/s, 0 = 50 -, an th paratrs us n rsult an scusson 7 Rsult an Dscusson In th nurcal valuaton of th growth-rat, currnt an sprson, w hav us th followng paratrs for th auroral acclraton rgon 6,7,34-37 B 0 =4300 nt, Ω =4 s, KT =, KT =0, 00 c/s, ω p /Ω =0 an K s th Boltzann constant. 7. Dsprson rlaton Th sprson rlaton q. (8) has bn solv nurcally usng th Nwton-Raphson tho an th valu of ar plott vrss n Fg.. It s clar that th wav frquncy ncrass wth Substtutng q. (6) w fnally obtan th growth/apng-rat as T / xp...(4) T T T Whr T, ( T, / ); rprsnts lctron aagntc rft vlocty an th valu of ω for th rft ntc Alfvn wav has to b subtt. In cas of D = 0 w rcovr th growth rat as rv by Dwv t al. 36,37, Barona an Fg. Frquncy (ω) vrsus prpncular wav nubr ( ) for ffrnt 0 ; D = c/s; D = 0 7 c/s; δ = 0.4

6 DWIDI & TIWARI : FFCT OF LCTRIC FILD INHOMOGNITY ON KINTIC ALFN WA 5 ncras of th appl lctrc fl. Th cras of wth ncrasng s u to th fnt Laror-raus ffct. Th ffct of lctrc fl nhoognty on wav frquncy s pct n Fg.. Th wav frquncy crass wth ncrasng gr of nhoognty. Wav frquncy crass wth ncras of. Fgur 3 shows th varaton of wav frquncy wth for ffrnt valu of on ba vlocts. It s obsrv that wav frquncy crass wth ncras of on ba vlocts. Fg. Frquncy (ω) vrsus prpncular wav nubr ( ) for ffrnt δ; D = c/s; D = 0 7 c/s; 0 = 50 - Fg. 5 Growth/apng rat (γ/ω) vrsus prpncular wav nubr ( ) for ffrnt δ; D = c/s; D = 0 7 c/s; 0 = 50 - Fg. 3 Frquncy (ω) vrsus prpncular wav nubr ( ) for ffrnt on ba vlocty D ; D = 0 7 c/s; 0 = 50 - ; δ = 0.4 Fg. 6 Growth/apng rat (γ/ω) vrsus prpncular wav nubr ( ) for ffrnt on ba vlocty D ; D = 0 7 c/s; 0 = 50 - ; δ = 0.4 Fg. 4 Growth/apng rat (γ/ω) vrsus prpncular wav nubr ( ) for ffrnt 0 ; D = c/s; D = 0 7 c/s; δ = 0.4 Fg. 7 Growth/apng rat (γ/ω) vrsus prpncular wav nubr ( ) for ffrnt lctron ba vlocty D ; D = c/s; 0 = 50 - ; δ = 0.4

7 5 INDIAN J RADIO & SPAC PHYS, JUN Growth/apng rat Fgurs 4 an 5 show th varaton of growth/apng rat wth for ffrnt valu of lctrc fl an lctrc fl nhoognty, rspctvly. It s obsrv that lctrc fl crass th growth/apng rat, whras lctrc fl nhoognty ncrass th growth/apng rat. It s also foun that wav s ap at lowr whl xct at hghr. lctrc fl an lctrc fl nhoognty ar or ffctv at hghr. Fgurs 6 an 7 show th varaton of growth/apng rat wth for ffrnt valu of on an lctron ba vlocts. Th on ba vlocty nhancs th Fg. 8 Paralll currnt (J Z ) vrsus prpncular wav nubr ( ) for ffrnt 0 ; D = c/s; D = 0 7 c/s; δ = 0.4 Fg. Paralll currnt (J Z ) vrsus prpncular wav nubr ( ) for ffrnt lctron ba vlocty D ; D = c/s; 0 = 50 - ; δ = 0.4 Fg. 9 Paralll currnt (J Z ) vrsus prpncular wav nubr ( ) for ffrnt δ; D = c/s; D = 0 7 c/s; 0 = 50 - Fg. Prpncular currnt (J X ) vrsus prpncular wav nubr ( ) for ffrnt 0 ; D = c/s; D = 0 7 c/s; δ = 0.4 Fg. 0 Paralll currnt (J Z ) vrsus prpncular wav nubr ( ) for ffrnt on ba vlocty D ; D = 0 7 c/s; 0 = 50 - ; δ = 0.4 Fg. 3 Prpncular currnt (J X ) vrsus prpncular wav nubr ( ) for ffrnt δ; D = c/s; D = 0 7 c/s; 0 = 50 -

8 DWIDI & TIWARI : FFCT OF LCTRIC FILD INHOMOGNITY ON KINTIC ALFN WA 53 growth/apng rat whras lctron ba rucs th growth/apng rat. No apng rat s obsrv n th cas of lctron ba vlocty. 7.3 lctrc currnt Th ffct of lctrc fl an lctrc fl nhoognty on paralll currnt s shown n Fgs 8 an 9. Th lctrc fl crass th paralll currnt whras lctrc fl nhoognty ncrass th paralll currnt. Fgurs 0 an show th varaton of paralll currnt wth for ffrnt valu of on an lctron ba vlocty. It s sn that on ba vlocty ncrass th paralll currnt, whl lctron ba vlocty crass th paralll currnt. Th crasng valu of J z s sn for hghr valu of. Thus th agntu of th fl-algn currnt ay pn upon th prpncular wav nubr an th on gyroraus. Fgurs an 3 show th varaton of th prpncular currnt wth for ffrnt valu of lctrc fl an lctrc fl nhoognty. It s obsrv that lctrc fl nhanc th prpncular currnt whras lctrc fl nhoognty rucs th prpncular currnt. Th ffct of on an lctron ba vlocty on prpncular currnt s shown n Fgs 4 an 5, th on ba vlocty crass th prpncular currnt whras lctron ba vlocty ncrass th prpncular currnt, th prpncular currnt also crass wth. It s also sn that on an lctron ba vlocts ar or ffctv towars hghr. 8 Conclusons Th ntc Alfvn wav ay b gnrat n th stant agntosphr thr by on an lctron ba vlocty or lctrc fl nhoognty or nsty nhoognty 0 at substor ts an propagats towars th onosphr lang to acclraton an currnt pattrn as rport by Frja an FAST satllt ata. Th prsnt nvstgaton of ntc Alfvn wav ncorporats th ffctvnss of lctrc fl nhoognty n th prsnc of on an lctron ba. It s notc that on an lctron bas ar uch ffctv towars hghr n th prsnc of lctrc fl nhoognty as copar to arlr wor 37. It s also notc that lctrc fl nhoognty s or ffctv on paralll currnt n th prsnc of on an lctron ba as copar to arlr wor 6. Th lctrc fl nhoognts support th ntc Alfvn wav gnraton. Th partcl aspct analyss aopt hr also to prct Fg. 4 Prpncular currnt (J X ) vrsus prpncular wav nubr ( ) for ffrnt on ba vlocty D ; D = 0 7 c/s; 0 = 50 - ; δ = 0.4 Fg. 5 Prpncular currnt (J X ) vrsus prpncular wav nubr ( ) for ffrnt lctron ba vlocty D ; D = c/s; 0 = 50 - ; δ = 0.4 th currnts assocat wth th wav. Th on an lctron bas ar capabl of gnratng ntc Alfvn wav an th rcton of currnt s controll by th lctron an on ba vlocts. In th past varty of thors ar prouc for th vlopnt of paralll lctrc fls on auroral fl lns. Ths paralll lctrc fl ay la upflowng on ba an owncong lctron ba whch ay gnrat th ntc Alfvn wavs an ajust th currnt pattrn on auroral fl lns. Th wav frquncy, currnt pattrn an wav nubrs ar also nflunc by th lctrc fl nhoognty, an lctron an on ba. Th rcton an agntu of th currnt pn strongly upon th fnt-gyroraus ffct, whch also controls th wav spctru. Th prsnt nvstgaton ay b usful to xplan obsrv Poyntng flux 43,44 along auroral fl ln towars th arth by th larg scal Alfvnc wavs. Th wavs gnrat abov th

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