Recent Progress on VLF Wave and Its Interactions with Energetic Particles in the Magnetosphere

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1 IOSR Journal of Applid Physics (IOSR-JAP) -ISSN: Volum 9, Issu 3 Vr. III (May - Jun 017), PP Rcnt Progrss on VLF Wav and Its Intractions with Enrgtic Particls in th Magntosphr Anil Kumar * Dpartmnt of Applid Scinc (Physics), Bharati Vidyapth s Collg of Engg. Paschim Vihar, Nw Dlhi (India). Abstract: Vry Low Frquncy (VLF) wav is th plasma wav in th magntosphr with frquncy rang of 3 khz to 30 khz. Th univrsal distribution proprtis of Vry Low Frquncy wav (VLF) in th magntosphr and its intractions with nrgtic particls, such as th wav-particl rsonanc, modulation, and particl acclration, ar activ topics in spac physics rsarch. Ths problms ar fundamntally important issus to undrstand th nrgy transport from th solar wind into th magntosphr. In this papr w brifly rviwd th rcnt rsarch progrss on VLF wav and its intractions with nrgtic particls in th innr magntosphr; furthrmor, w suggstd som opn qustions for futur study. Kywords: Pitch angl diffusion, Fokkr-Planck quation, Chorus, Hiss. I. Introduction Exprimntal and thortical studis hav shown that radiation blts dynamics display a substantial variability during diffrnt lvls of gomagntic disturbancs, which is associatd with a numbr of diffrnt procsss. During th main phas of storms (usually lasting for a fw hours), th flux of nrgtic lctrons can dcras by two or thr ordrs of magnitud in th outr radiation blt 3<L<7. During th rcovry phas of a storm, fluxs can incras by a factor of ovr a priod of hours to days, with a pak building up nar location L=4. Such substantial variations in flux ar considrd as th comptition btwn two procsss: th pitch angl scattring procss primarily by th Elctromagntic ion cyclotron and ELF hiss wavs; and th stochastic acclration procss mainly by th VLF chorus wav, togthr with inward radial diffusion through drift rsonanc with nhancd ULF wavs. During gomagntic storms, ~MV lctron fluxs can also b nhancd with paks at pitch angl 90 by th magntosonic impuls launchd by an intrplantary shock comprssion of th magntopaus. During gomagntically quit conditions, rsonant intraction with ELF hiss provids th primary scattring procss at location L>.5, lading to losss ovr tns of days at nrgis ~1MV. At lowr L-valus, rsonant intractions with lightning-gnratd whistlrs and man-mad VLF transmissions dominat th pitch angl scattring procss. II. Wav-particl Scattring Whistlr-mod chorus missions ar obsrvd outsid th plasmasphr ovr a broad rang of local tims ( MLT) with typical frquncis in th rang , whr is th lctron gyrofrquncy [Tsurutani and Smith, 1974, 1977; Koons and Rodr, 1990; Mrdith t al., 001; Santolik t al., 003, 004]. VLF chorus occurs in two frquncy bands, a lowr band ( ) and an uppr band ( jwj) [Burtis and Hlliwll, 1976; Mrdith t al., 001]. Equatorial chorus (jlj < 15 dg) can b xcitd by cyclotron rsonanc with anisotropic kv lctrons injctd nar midnight from th plasmasht [Knnl and Ptschk, 1966]. High-latitud chorus (jlj > 15 dg) may b gnratd in th horns of th magntosphr [Mrdith t al., 001]. Santolik t al. [005] find that quatorial chorus in th uppr band xtnds to about L = 8, and in th lowr band (blow 0.4 jwj) to L = Typical chorus amplituds ar pt [Burtis and Hlliwll, 1975; Mrdith t al., 003a], though amplituds up to 1 nt hav bn rportd during intns gomagntic activity [Parrot and Gay, 1994]. Chorus missions ar prdominantly substorm dpndnt, and all chorus missions intnsify whn substorm activity is nhancd [Mrdith t al., 001]. Wavparticl intractions occur whn multipls of gyrofrquncy qual th wav frquncy in th lctron rfrnc fram, and this can b xprssd in th lab fram by ω v k = n Ω /γ, n=±1, ±,... (1) Hr v = vcosα with v bing th vlocity and α bing th pitch angl, γ is th rsonant rlativistic Lorntz factor. Figur 1 prsnts a schmatic graph of th possibl wav-particl intractions associatd with nrgtic lctrons in th Earth s innr magntosphr. Th dottd black lins rprsnt th powr flux dnsity in ach wav s frquncy rang (lft Y-axis). Th thr long narrow rgions rprsnt th gyrating, bouncing, and drifting frquncy in diffrnt L-shlls for lctrons with diffrnt rsonant nrgy (right Y-axis). DOI: / Pag

2 Rcnt progrss on VLF wav and its intractions with nrgtic particls in th magntosphr Figur 1. Schmatic distributions of chorus, plasmasphric hiss, and EMIC wavs in th cass of high gomagntic activity and rlativly comprssd plasmasphr (cas A) and following high gomagntic activity during th volution of a plasmasphric plum (cas B) during th main phas (A) and rcovry phas (B) of a storm. Wav-particl intractions lad to th violation of th first and scond adiabatic invariants and diffusion of lctrons in pitch-angl and nrgy. Pitch-angl diffusion scattrs lctrons into th loss con and producs prcipitation of lctrons, whras nrgy diffusion can gnrat acclration of lctrons and hardn th nrgy spctrum. To valuat ths procsss, a solution of -D bounc-avragd Fokkr-Planck quation dscribing th local acclration and loss procsss, togthr with incorporation of dtaild information of th amplituds and spctral proprtis of th wavs is rquird. Such diffusion quation associatd with th phas spac dnsity can b writtn by 1 1 G D D p t Gp p p 1 1 G Dp Dpp G p p p Hr p is th particl s momntum, G=p T( α)sinαcosα with α bing th quatorial pitch angl, T( α ) sinα givs th normalizd bounc tim; Dαα, Dpp, and Dαp = Dpα rprsnt bounc-avragd diffusion cofficints in pitch angl, momntum and cross pitch angl-momntum. III. Mthod of Calculation of Pitch angl diffusion W assum infinit, homognous, collisionlss plasma immrsd in a uniform, static magntic fild B 0 B0z, in th prsnc of suprposd lctromagntic wavs [Inan, 1977]. W us quasi-linar diffusion thory to dscrib th ffcts of th wavs on th particls in trms of a kintic quation for th gyrophas-avragd phas-spac dnsity. Ensmbl avraging of th wav filds is carrid out. Th gnral, rlativistic quasi-linar diffusion quation for, in th limit of gyrorsonant diffusion, can b writtn in th form [.g., Mlros, 1980], Summrs t al (007) sin sin (1) sin D sin D p p p p D p p p D pp t p p p whr D, D p = D p and D pp ar th diffusion or Fokkr-Planck cofficints which dpnd on th proprtis of th wavs; p m v is th momntum of th particl of spcis, rst mass m and spd v; v 1 / (1 ) is th Lorntz factor (c is th spd of light); is th pitch angl of th particl, and t c dnots tim. In th prsnt study w trat only th spcial cas of lctromagntic wavs propagating paralll or antiparalll to th background magntic fild B 0. W assum that th R-mod (s=1) and L-mod (s=-1) wavs ach hav th Gaussian spctral dnsity, DOI: / Pag

3 Rcnt progrss on VLF wav and its intractions with nrgtic particls in th magntosphr with Ws ( ) Bs ( ) m, () m 1 m rf rf, (3) whr 1 is th lowr frquncy limit, is th uppr frquncy limit, m is th frquncy of maximum wav powr, is a masur of th bandwidth, and rf is th rror function. Th wav spctral dnsity () has bn normalizd, so that (Summrs t al, 007). Bs 8 Ws ( ) d (4) whr Bs is th man wav amplitud. Following th study of Summrs t al (005, 007), w can now xprss th diffusion cofficints for th particl spcis as follows: xjcos R1 dxj / dyj xj xm 1 1 yj x D (5) ( E 1) s j x cos dxj / dyj x x cos R 1 dx / dy D p p ( E 1) x dx dy j j j j xj xm 1 1 sin y j yj x s j cos j / j 1 (6) whr w hav introducd th dimnsionlss variabls, x, y ck (7) and E is th dimnsionlss particl kintic nrgy givn by 1 / v E Ek / ( mc ) 1; [ E( E )] / ( E 1); B0 /( mc) c is th nonrlativistic lctron gyrofrquncy, whr is th unit charg; q B0 /( m c) is th nonrlativistic particl gyrofrquncy, whr q is th particl charg; R Bs / B0 is th ratio of th nrgy dnsity of th turbulnt magntic fild to that of th background fild, i.., th rlativ wav powr; m x m, x disprsion rlation. ; and th drivativ dxj / dyj dx( yj) / dy is dtrmind from th appropriat IV. Rsults and Discussion Variation with Frquncy: Figur (1) shows variation of pitch angl diffusion cofficint [Dαα (J**/S)] with intracting frquncis at diffrnt L-valus. Thr paralll lins in this figur ar corrsponding to L=1.3, 1.5 & 1.7 at VLF frquncis 3 khz.,4 khz & 5kHz. rspctivly. Thr is also an xponntial variation btwn [Dαα (J**/S)] & VLF frquncis.w s that as intracting frquncis incrass pitch angl diffusion cofficint of particls also incrass. Morovr this variation is not only intracting frquncis dpndnt but also L-valus dpndnt; w s that pitch angl diffusion cofficint is low for all intracting frquncy rangs for L=1.3 and DOI: / Pag

4 Pitch angl Diffusion (J**/S) or Enrgy (MV.) Rcnt progrss on VLF wav and its intractions with nrgtic particls in th magntosphr it is high for L=1.7. It is in agrmnt with works don by various author in India (Singh DP) as wll as Stanford Univrsity. Thr ar pculiar situations that pitch angl diffusion cofficint incrass with intracting frquncy linarly, i.. Dαα and frquncy graph is almost a straight lin. Such things appar for all L-valus. W can conclud that larg frquncy and larg L-valus taks ffctiv rol in th diffusion of lctrons into loss con. As w hav said this is an agrmnt with works of larg numbr of whistlr mod wav workr. In this cas th wav-width valu takn to b 50 Hz. and wav magntic fild Bw= 0.001nT and th pitch angl has takn to b 50⁰. It is clar that at low L-shlls, diffusion is wak and at high latitud it incrass from modrat to strong diffusion (Singh 1991). 7E-13 6E-13 5E-13 4E-13 Pitch angl diffusion at L=1.3 Pitch angl diffusion at L=1.5 Pitch angl diffusion at L=1.7 3E-13 E-13 1E-13 9E-14 8E-14 7E Frquncy ( Hz.) Fig. 1: Variation of pitch angl diffusion cofficint Dαα (J /s) with intracting frquncis at diffrnt L- Valus, Kping ΔF=50 Hz., Bw = 0.001(nT) and pitch angl 50⁰. Variation With L Valus: Figur () shows variation of nrgy diffusion cofficint [Dpp (J**/S)] with L-valus at diffrnt wav magntic fild. Thr paralll lins in this figur ar corrsponding to Bw = 0.001, 0.01&0.1 (nt) rspctivly. Thr is also an xponntial variation btwn Dpp & L-valus.W s that as L-valus incrass nrgy diffusion cofficint of particls also incrass. Morovr this variation is not only L-valus dpndnt but also wav magntic fild (Bw) dpndnt; w s that nrgy diffusion cofficint is low for all L-valu rangs for Bw=0.001 (nt) and it is high for Bw=0.1 (nt). It is in agrmnt with works don by various author in India (Singh DP) as wll as Stanford Univrsity. Thr is a pculiar situation that nrgy diffusion cofficint incrass with L-valu linarly, i.. Dpp and L-valus graph is almost a straight lin. Such things appar for all wav magntic fild (Bw). W can conclud that larg wav magntic fild (Bw) and larg L-valus taks ffctiv rol in th diffusion of lctrons into loss con. As w hav said this is an agrmnt with works of larg numbr of whistlr mod wav workr. In this cas th wav-width valu takn to b 50 Hz. and intracting frquncy = 3 khz, th pitch angl has takn to b 50⁰.Thr xist various magtohydrodynamic wavs with diffrnt frquncis and othr proprtis, such as ULF wav, Vry Low Frquncy wav (VLF), Elctromagntic Ion Cyclotron wav (EMIC), tc. If th corrsponding rsonanc conditions ar satisfid, thr can b wav-particl intraction btwn ths wavs and nrgtic particls in innr magntosphr, causing th damping (amplifying) of th wav and acclration (dclration) of th particls. DOI: / Pag

5 Pitch Angl Diffusion (J**/S) or Enrgy (MV) Rcnt progrss on VLF wav and its intractions with nrgtic particls in th magntosphr 1E-9 1E-10 Pitch angl Diffusion at Bw (nt) = 0.1 Pitch angl Diffusion at Bw (nt) = 0.01 Pitch angl Diffusion at Bw (nt) = E-11 1E-1 1E L - Valus Fig. : Variation of nrgy diffusion cofficint Dpp(J /s) with L-valus at diffrnt Bw (nt), Kping intracting frquncy = 3kHz., ΔF=50 Hz. and pitch angl 50⁰. V. Conclusions Th currnt numrical simulations in this papr dmonstrat that rsonant intractions with VLF/ELF wavs play crucial rols in th dynamics of th innr magntosphr. Pitch angl scattring of radiation blt lctrons will produc lctron losss, whil nrgy diffusion can produc acclration comparabl to or strongr than losss. Diffusion with rspct to any of th variabls (pitch angl, nrgy, or L) will chang th gradints with rspct to two othr variabls. For xampl, pitch angl scattring at lowr L shlls may incras radial gradints and incras inward radial diffusiv transport. If wavs that produc pitch angl scattring ar in rsonanc with lctrons only for a limitd rang of nrgis, pitch angl diffusion will also chang nrgy gradints and will affct nrgy diffusion. Radial diffusion will chang th nrgy spctrum by acclrating or dclrating lctrons and will also chang th pitch angl distribution. Whil this papr provids an initial assssmnt of th dominant acclration and loss procsss. Acknowldgmnts Author is vry thankful to BVCOE, Nw Dlhi principal for providing his support during xprimntal work don in th collg physics lab. Rfrncs [1]. Burtis W J, Hlliwll R A. Magntosphric chorus: Occurrnc pattrns and normalizd frquncy. Plant Spac Sci, 1976, 4: 1007 []. Grn J C, Kivlson M G. Rlativistic lctrons in th outr radiation blt: Diffrntiating btwn acclration mchanisms. J GophysRs, 004, 109: A0313. [3]. Fok, M.-C., R. B. Horn, N. P. Mrdith, and S. A. Glaurt (008), Radiation Blt Environmnt modl: Application to spac wathr nowcasting, J. Gophys. Rs., 113, A03S08, doi:10.109/007ja [4]. Horn, R. B., and R. M. Thorn (1998), Potntial wav mods for lctron scattring and stochastic acclration to rlativistic nrgis during magntic storms, Gophys. Rs. Ltt., 5, , doi:10.109/ 98GL0100. [5]. Horn, R. B., t al. (005a), Wav acclration of lctrons in th Van Alln radiation blts, Natur, 437, 7 30, doi: /natur [6]. Hudson, M. K., S. R. Elkington, J. G. Lyon, C. C. Goodrich, and T. J. Rosnbrg (1999), Simulation of radiation blt dynamics drivn by solar wind variations, in Sun-Earth Plasma Connctions, Gophys. Monogr. Sr., vol. 109, ditd by J. L. Burch, R. L. Carovillano, and S. K. Antiochos, pp , AGU, Washington, D. C. [7]. Inan US, Non-linar Gyro-rsonant intractions of nrgtic particls and cohrnt VLF wavs in th magntosphr, Tch. Rpt. No Stanford Univ., Stanford, CA [8]. Jordanova, V. K., L. M. Kistlr, J. U. Kozyra, G. V. Khazanov, and A. F. Nagy (1996), Collisional losss of ring currnt ions, J. Gophys. Rs., 101, , doi:10.109/95ja0000. [9]. Knnl, C. F., and F. Englmann (1966), Vlocity spac diffusion from wak plasma turbulnc in a magntic fild, Phys. Fluids, 9, 377, doi: / [10]. Parrot M, Gay C A. A statistical survy of ELF wavs in a gostationary orbit. Gophys Rs Ltt, 1994, 1: [11]. Santolik O, Macusova E, Yarby K H, t al. Radial variation of whistlr-mod chorus: First rsults from th STAFF/DWP instrumnt on board th Doubl Star TC-1 spaccraft. AnnGophys, 005, 3:937. [1]. Shprits, Y. Y., and R. M. Thorn (004), Tim-dpndnt radial diffusion modling of rlativistic lctrons with ralistic loss rats, Gophys. Rs. Ltt., 31, L08805, doi:10.109/004gl [13]. Shprits, Y. Y., R. M. Thorn, R. Fridl, G. D. Rvs, J. Fnnll, D. N. Bakr, and S. G. Kankal (006b), Outward radial diffusion drivn by losss at magntopaus, J. Gophys. Rs., 111, A1114, doi:10.109/006ja DOI: / Pag

6 Rcnt progrss on VLF wav and its intractions with nrgtic particls in th magntosphr [14]. Summrs, D., R. M. Thorn, and F. Xiao (1998), Rlativistic thory of wav-particl rsonant diffusion with application to lctron acclration in th magntosphr, J. Gophys. Rs., 103, 0,487 0,500, doi:10.109/98ja [15]. Summrs, D., B. Ni, and N. P. Mrdith (007), Timscals for radiation blt lctron acclration and loss du to rsonant wavparticl intractions:. Evaluation for VLF chorus, ELF hiss, and lctromagntic ion cyclotron wavs, J. Gophys. Rs., 11, A0407, doi: / 006JA [16]. Singh DP, strong diffusion of rsonant lctrons by VLF wavs, Indian J Radio and Spac Phys, 0 (1991) 44. DOI: / Pag