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1 ORIGINAL ARTICLE Thrtical tudy f bliquly prpagatig whitlr md wav fr rig ditributi i th magtphr Grg Varugh, Jyti Kumari, Pady RS, Sigh KM Varugh G, Kumari J, Pady RS, t al. Thrtical tudy f bliquly prpagatig whitlr md wav fr rig ditributi i th magtphr. J Md Appl Phy. 08;():-7. ABSTRACT Chag i plama dity ad magtic fild hav a trg ifluc th prpagati f vry lw frqucy wav i th Whitlr md. It i uggtd that th arth magtic fild b calld th magtphr rgi. Va All ad thr brvati hw that thi ara rach 5 t 0 Earth radii dpdig th dgr f magtic itrfrc. I th prt papr, whitlr md wav i th magtphr f Earth hav b ivtigatd. Fr whitlr md wav, liar prprti f rig ditributi fucti ar ud t driv th dipri rlati. Mthd f charactriti by th kitic apprach ha b ud t ivtigat whitlr wav. Th prt aalyi hw that th grwth rat f lctrmagtic circularly plarizd whitlr md wav ha b fud t b icraig with icraig tmpratur aitrpy ad umbr dity. It ha b fud that th grwth rat dcra with a icra i th agl f prpagati. A th lctr rgy hw igificat ffct grwth rat. Th grwth rat icra alg with a igificat hift i wav umbr with icraig tmpratur aitrpy, umbr dity ad rgy dity. Th aalytical mdl dvlpd ca al b applid t th thr platary magtphr fr udrtadig variu typ f itabiliti. Ky Wrd: Magtphr f Earth; Whitlr md wav; Rig ditributi fucti INTRODUCTION I all plat with magtic fild, th mai rgy drivig urc fr th magtic layr prc ar platary rtati ad lar wid. O Earth, th mai urc f rgy i lar wid. A magtphr i that ara f pac arud a plat which i ctrlld by th plat magtic fild. It hap i a dirct rult f big blatd by lar wid. Th ffct f lar wid i th cmpri f it uward id up t 6 t 0 tim th radiu f th arth (RE6400 Km). Du t thi a upric hck wav i cratd kw a Bw hck at which mt f th lar wid particl ar hatd ad lwd ad dtur i th magthath arud th Earth. Th Earth magtphr i th trgt f all th rcky plat amg th lar ytm. Cvctiv mti f chargd mlt ir far blw th urfac f Earth utr cr i f th ra fr th grati f it magtphr. Th aurral magtphr f Earth i a activ rgi fr umru activiti f plama wav. Th plama i aurral rgi i charactrizd by Γ < whr ( ) 4π m i th plama frqucy ad Γ B m i th gyrfrqucy. Larg umbr f grud bad brvati ad paccraft hav hw that wav particl itracti ar vry imprtat prc i th aurral rgi. Th baic ccpt f wav particl itracti hav b rprtd by () i th cllii-l plama. Radi wav mii i th grud lvl f aurral rgi hav b brvd by () i th frqucy rag f khz. Thrtical tudy d by () idicat that th whitlr md wav prpagatig paralll i th frqucy rag f khz ar xcitd by th rgtic lctr trappd i th aurral rgi with highr rgi f kv du t th tmpratur aitrpy. Diffrt urc f fr rgy xitig i th arth magtphr giv ri t itabiliti, lik uv ditributi f tmpratur, ambit magtic fild, rgy dity tc. Earth magtic fild ca b viwd a a dipl with rth ad Suth Pl which ar actig a a bar magt. It i w pibl t tudy th ara abv th iphr, whr th Earth magtic fild ha dmiat ctrl vr th mvmt f ga ad rapidly chargd particl. It i kw that th ara xtd t a ditac f 0 Earth radii ad i calld th magtic layr. Althugh ly th mt baic ifrmati abut th bhavir f th ara i availabl at th mmt, it mak t ivtigat th law that dictat th mvmt f matrial thr. O f th glbal wav md brvd i th pac plama i Whitlr md wav. Thir brvati i th magtphr, i th lar wid, i uptram f platary bw hck, i cmtary frhck ad i uptram f itrplatary hck hav b rprtd by (4-8). Vry lw frqucy whitl md wav ar miprt i th Earth magtphr, pcially th plama layr. It i wll kw that whitl ca b cfid t a hacd r dpltd fild-aligd plama dity irrgularity r duct rgi, i a prc calld a ductig. Th brvati mad by paccraft hav prv th prc f duct i th plama phr ar quatr (9,0), which ar crrlatd with a cidrabl whitlr activity, maily ar th plamapau (9). Th wav ar righthad plarizd lctrmagtic wav. Whitlr md wav ca prpagat alg th magtic fild, prpdicular t th magtic fild ad bliquly t th magtic fild a a quai lctrtatic md ar th rac c (). Th wav prvid a varity f mii i th magtplama () Ergtic lctr triggrd by xtral mii ca cau chrt whitlr mii (). It i aumd that whitlr md wav ar driv utabl by tmpratur aitrpi f lctr i th magtphr (4). Bcau f th trg itracti f whitlr md wav with rgtic particl (4,5), it ha b accptd that th wav play a imprtat rl i glbal radiati blt dyami. Thu, whitlr md wav hav b a tpic f attti fr vr 40 yar i magtphric phyi. I 966, cattrig f lctr it th l c by ichrt whitlr radiati wa tratd by Kl, t al. (4). Ua (6) cidrd pitch agl cattrig by mii f chrt whitlr. Th ffct f tmpratur aitrpy ad pitch agl aitrpy grwth rat ad mii frqucy i ca f ht rgtic lctr ha b tudid. HuagL t al. (7) calculatd th charactriti f ichrt whitlr md wav which ar gratd i th magtphr alg L5 gmagtic fild li. Maurmt f plama wav ar maily citd f tim-avragd pctral itity data fr th pat 0 yar. Fr lctric fild, tim avragd pctral zr-t-pak amplitud fr whitlr md wav ar 0.5 mv/m (8) ad fr magtic Dpartmt f Phyi, Vr Kumar Sigh Uivrity, Bihar, Idia; Dpartmt f Phyi, Amity Ititut f Applid Scic, Amity Uivrity, Uttar Pradh, Idia Crrpdc: Dr. Rama Shakar Pady, Dpartmt f Phyi, Amity Ititut f Applid Scic, Amity Uivrity, Sctr 5 Nida, Uttar Pradh, Idia, mail: rpady@amity.du Rcivd: April 9, 08, Accptd: May 04, 08, Publihd: May, 08 Thi p-acc articl i ditributd udr th trm f th Crativ Cmm Attributi N-Cmmrcial Lic (CC BY-NC) ( crativcmm.rg/lic/by-c/4.0/), which prmit ru, ditributi ad rprducti f th articl, prvidd that th rigial wrk i prprly citd ad th ru i rtrictd t cmmrcial purp. Fr cmmrcial ru, ctact rprit@pulu.cm J Md Appl Phy Vl N March 08

2 Varugh t al. fild, it i T (9,0). Larg amplitud whitlr md wav wr dicvrd i th radiati blt havig amplitud >00mV/m uig th STEREO paccraft (), ad aftrward it wa brvd by paccraft Wid () ad THEMIS (). Elctr ca gai rgy by mr tha a MV i l tha a cd by th wav () ad citcy btw thi ad tt particl timulati ha b fud by (4,5). Th utabl rig ditributi fucti prvid a imprtat urc f fr rgy, it ca xcit plama wav (8,6,7). I wakly clliial plama, fr diffrt typ f itabiliti, th rig ditributi fucti act a a urc f fr rgy (8,9). Effctiv tmpratur aitrpi ad diffrtial cattrig ar fud t b th ra f thi (0-). Elctrmagtic whitlr wav, blw th lctr cycltr frqucy, ar xcitd by tmpratur aitrpy i ht rig ditributi (). W hav tudid whitlr md wav uig rig ditributi fucti. Thrfr, i th prt wrk, w ivtigat liar grwth f whitlr md wav i th Earth magtphr. Sic Earth magtphric plama cit f a hug umbr f particl ad wav itractig with ach thr (4), it i uitabl t prt a macrcpic dcripti f plama phma by uig a tatitical apprach. (5) wr firt t dvlp Kitic apprach. Thu i prt wrk aalytical apprach ha b applid t driv th dipri rlati fr rig ditributi. Uig dimil itgral, dpdc f wav grwth rat ha b dtrmid. W hav btaid aalytical luti i trm f Bl fucti i th fllwig cti. Dipri Rlati Spatially hmgu aitrpic, clliil plama ubjctd t xtral magtic fild ha b cidrd t gt dipri rlati. Liarizd Vlav-Maxwll quati ar btaid aftr glctig highr rdr trm ad paratig th quilibrium ad -quilibrium part. Fllwig th tchiqu f (6,7), Vlav quati ar giv a blw: f f v ( v B ) r m v f f f v t r v dv Whr frc i giv a F m dt ( ) 0 ( F m ) S ( rv,,t) F v B () Th particl trajctri ar btaid by lvig a quati f mti dfid i quati () ad S(r, v, t) i dfid a: f S ( rv,,t) ( m) E ( v B ) (4) v Whr S dt pci ad E, B ad f ar prturbd quatiti ad ar aumd t hav harmic dpdc i E, B ad fxp i(k.r t). Th mthd f charactritic luti i ud t dtrmi th prturbd ditributi fucti, f, which i btaid frm Eq. () by f ( r, v,t) { r ( r, v,t ), v ( r, v,t ),t t } dt (5) 0 Th pha pac crdiat ytm ha b trafrmd frm ( r, v,t) t ( r,v,t t ). Th particl trajctri which ar btaid by lvig q. () fr th giv xtral fild ad wav prpagati, k k ˆ,0, ˆ x k z ar: vy x it t x vx v (6a) y v x y t it y vx v y (6b) z z v t (6c) z Ad th vlciti ar v v t v i t (7a) x x y y x y v v i t v t (7b) v v (7c) z z Whr v B z m z v cycltr frqucy f pci Aftr m algbraic implificati ad itgrati, th prturbd () () ditributi fucti i giv a: ( ) i( k.r t) Jm λ ( r, v ) x y { } x m m,,p,q kv λ f,t E J U ie J C J E J W { } iλ( iθ) ikθ Whr Jk ( λ) i th Bl idtity. It ha b ud a a k argumt f th fllwig fucti: kv λ C δf δf ( kv) k v δv δv U C (8a) (8b) v (8c) v δf δf W v δv δv ( λ ) (8d) dj J (8) dλ Th cductivity tr i writt a: S ij σ d m v (9) m, kv vj A ivjb vj W λ λ S v JJA v JB iv JJW J A J B J W v v v (0) A U B JC () λ Frm J σ.e ad tw Maxwll curl quati fr th prturbd quatiti, th wav quati ca b writt a: ( c ) (, ) k k.k k E 0 () Whr ( k, ) ( 4π i ) σ ( k, ) dilctric tr () π d vsij 4 ij (k, ) m kv (4) Expri fr Grwth Rat Fr whitlr md prpagati ad itability with k 0(6), th brach f gral dipri rlati (4) rduc t: N ε ±ε θ (5) N kc / i rfractiv idx. Thrfr dipri rlati fr may b writt a: 4π v f f d v N. ( kv ) k m v v v kv (6) Whr ( ) Th ditributi fucti fr trappd lctr i tak a Maxwllia Rig vlcity ditributi (8,9): / f ( v,v ) xp / {( v v ) / } ( v / ) π B (7) v B xp( v / ) π rfc( v / ) (8) á I quati (7), / i th rati f trappd rgtic lctr t ttal lctr dity ( / ). Equati (8) giv th xpri fr cmplimtary rrr fucti. Th v ad v ar paralll ad prpdicular vlciti with rpct t magtic fild. v i th drift pd. 4 J Md Appl Phy Vl N March 08

3 Thrtical tudy f bliquly prpagatig whitlr md wav fr rig ditributi i th magtphr Fllwig ar th xpri fr aciatd paralll ad prpdicular lctr thrmal vlciti: / / kt kt m m Uig quati (7) ad ubtitutig d v v dv dv π 0 i quati (6) w lv th itgral t gt dipri rlati a: kc 4π / X Z( ξ ) X( ξz( ξ) ) (9) m B k Whr, v v X π v v v v v X Z π rf π π á t ξ dt π ±c i th plama dipri fucti with ξ t ξ ( ) Applyig cditi 4 π / p Bm iγ kc r Th quati (9) rduc t >> fr whitlr wav k aitrpy i uppd t vary frm.5 t.75 ad l c agl θ i t vary frm 0 t 0. Elctr rgy, KBT i tak t b KV, 5KV ad 7KV. Accrdig t thi chic f plama paramtr, th xplaati ad dtail f th rult ar giv a fllw. DISCUSSION I Figur dimil grwth rat ( γ / c ) ha b plttd fr variu valu f T /T with rpct t wav umbr. It baically hw th variati f tmpratur aitrpy ( A T ) a AT T /T. A rati f T /T icra frm.5 t.75, grwth rat icra frm t with light hift i wav umbr frm 0.4 t 0.8. It hw that whitlr md wav hav grw du t l f prpdicular kitic rgy f rig lctr. It impli that tmpratur aitrpy act a a urc f fr rgy fr th amplificati ad prpagati f wav. It ha b hw that with icra i th tmpratur aitrpy, grwth rat hw a igificat icra (40). Thrfr, th miimum lctric fild trgth i ufficit t triggr th whitl mii ad icra th grwth rat. Figur hw th variati i grwth rat f whitlr md wav with rpct t wav umbr fr diffrt valu f prpagati agl ( θ ). Th tudy cidr prpagati f th wav at a agl f 0, 0 ad 0 with rpct t ambit magtic fild f Earth. Thi figur hw that th grwth rat dcra with icraig valu f l c agl ad hiftig th badwidth fr highr rdr f l c agl. Th maximum grwth rat dcra frm t a th agl f prpagati chag frm 0 t 0 with k hiftig frm 0.8 t 0.4. It ma that th l c agl d t prvid ufficit rgy t prduc th itabiliti ad prpagati f wav. Thi rult i i agrmt with th rult hw by (4), thy ccludd that thr will b dcra i th grwth rat a th wav bcm mr bliqu ithr du t ladau dampig r cycltr rat frqucy ad th brad f frqucy rag icra. D k, X X i xp p k ξ ξ ξ k kc X X ( ) ξ { π ( ξ )} (0) k Itrducig th dimil paramtr a k Th grwth rat i trm f th dimil paramtr ad X i btaid a k, β,k,x π X X -X X ( X) xp- k X -X k γ c k k X X -X -X X - X Th ral part f q. (0) i: ( ) ( ) r c X () k X β X K. () β Figur ) Variati f Grwth Rat with rpct t fr variu valu f at 5 06 m-, KBT5KV, θ00 ad thr fixd plama paramtr. KT B µ Whr β, K, B.B X k k θ ad X X π V V0 π V0 X rf V V π 0 0 Plama Paramtr Fllwig plama paramtr hav b adptd fr th calculati f grwth rat fr th whitlr itability i th magtphr. Ambit magtic fild B 0-7 T, lctr dity m - ad magitud f A.C lctric fild E 0 - V/m ha b cidrd. Tmpratur Figur ) Variati f Grwth Rat with rpct t fr variu valu f θ at.5, m-, KBT5KV ad thr fixd plama paramtr J Md Appl Phy Vl N March 08 5

4 Varugh t al. Figur hw th graph with grwth rat f whitlr md wav vru wav umbr fr diffrt valu f umbr dity. I Figur, th grwth rat chag frm t fr icraig valu f umbr dity frm x 0 6 m - t 7 x 0 6 m - with wav umbr chagig frm 0.8 t Thrfr, a th umbr dity f lctr i plama rgim icra grwth rat f whitlr md wav icra. Figur 4 hw th chag i dimil grwth rat ( γ) / c fr diffrt valu f rgy dity ( KT) B f lctr. Th lctr tmpratur vari frm abut KV t 7KV. Thrfr, th grwth rat f whitlr wav ha b calculatd i th am rag f rgy dity i th prt papr. I Figur 4, th maximum grwth rat calculatd a , ad with a pak valu at wav umbr 0.8, 0.4 ad 0.4 rpctivly. It i brvd that grwth rat icra by icraig th thrmal rgy ad th badwidth icra fr th highr rdr f k. Thi impli mii i pibl fr xtdd valu f k. S it ca b that th rgy dity f lctr i f th imprtat paramtr affctig th grwth rat f whitlr md wav. 6 CONCLUSION Thi papr prt th paramtric aalyi f grwth rat f whitlr md wav i th magtphr f Earth uig rig ditributi fucti. Numrical calculati wr prfrmd by cidrig th kitic apprach ad applyig th charactritic luti mthd. Th drivati xpri f th dipri rlati ad th grwth rat f th whitlr wav prpagatd bliquly alg th ambit magtic fild ar aalyzd. Dtaild tudi hw that th grwth rat f lctrmagtic whitl md wav icra with th icra f tmpratur aitrpy. Thi ca al b ud t tudy variu itabiliti i th platary magtphr. Th graph hw that tmpratur aitrpy act a a urc f fr rgy i th magtphr f Earth. Al icra i umbr dity ad rgy dity f th lctr icra grwth rat f whitlr wav. It ca b aid that l f prpdicular kitic rgy i th cau f whitlr md wav. Figur ) Variati f Grwth Rat with rpct t fr variu valu f 0 at.5, KBT5KV, θ00 ad thr fixd plama paramtr Figur 4) Variati f Grwth Rat with rpct t fr variu valu f KBT at.5, m-, θ00ad thr fixd plama paramtr ACKNOWLEDGEMENT Th authr ar gratful t th Fudr pridt Dr. Ahk K. Chauha Amity Uivrity, Dr. Atul Chauha (Pridt, Amity Uivrity) ad Dr. Balvidr Shukla (Vic Chacllr, Amity Uivrity) fr thir imm curagmt. W al xpr ur gratitud t th rviwr fr thir xprt cmmt fr th maucript. REFERENCES. Turutai BT, Lakhia GS. Rv Gphy. 997;5:49.. B RF, Dch MD, Huuckr RD, t al. J Gphy R. 988;9:77.. Wu CS, Y PH, Frud HP. 989;6: Burti WJ, Hlliwll RA. Badd chru: A w typ f VLF radiati brvd i th magtphr by OGO ad OGO. J Gphy R. 969;74(): Nubaur FM, Muma G, Dhml G. Fat magtic fluctuati i th lar wid: Hli. J Gphy R. 977;8: Wil LB III, Cattll CA, Kllgg PJ, t al. Lw-frqucy whitlr wav ad hcklt brvd at quai-prpdicular itrplatary hck. J Gphy R. 009;4:A Hpp MM, Rull CT, Frak LA, t al. Uptram hydrmagtic wav ad thir aciati with backtramig i ppulati: ISEE ad brvati. J Gphy R. 98;86: Turutai BT, Thr RM, Smith EJ, t al. Stpd magtic wav at cmt Giacbii-Zir. J Gphy R. 987;9: Mullard O, Ma A, Laak H, t al. Dity mdulatd whitlr md mii brvd ar th plamapau. Gphy R Ltt. 00;9(0). 0. Haqu N, Ia US, Bll TF, t al. Clutr brvati f whitlr md duct ad badd chru. Gphy R Ltt. 0;8:(L807).. Bll TF, Ng HD. Elctrtatic lwr hybrid wav xcitd by lctrmagtic whitlr md wav cattrig frm plaar magtic fild aligd plama dity irrgulariti. J Gphy R. 990;95(A): Pady RP, Sigh KK, Sigh KM, t al. A thrtical tudy f whitlr md itability at uraia bw Shck. Earth M ad Plat (Th Nthrlad). 00;87: Hlliwll RA. A Thry f Dicrt VLF Emii frm th Magtphr. J Gphy R. 967;7: Kl CF, Ptchk HE. Limit tably trappd particl flux, J. Gphy. R. 966;7: Ly LR, Thr RM, Kl CF. Pitch-agl diffui f radiati blt lctr withi th plamaphr. J Gphy R. 97;77: Ia US, Bll TF, Hlliwll RA. Nliar pitch agl cattrig f rgtic lctr by chrt VLF wav i magtphr. J Gphy R. 978;8:5. 7. Huag JG, Hawki, L LC. O th Grati f th Pulatig Aurra by th L C Driv Whitlr Itability i th Equatrial Rgi. J Gphy R. 990;95: Mrdith NP, Hr RB, Adr RR. Subtrm dpdc f chru amplitud: Implicati fr th acclrati f lctr t rlativitic rgi. J Gphy R. 00;06: Hr RB, Thr RM, Glaurt SA t al. Timcal fr radiati blt lctr acclrati by whitlr md chru wav. J Gphy R. 005;0:A Hr RB, Glaurt SA, Thr RM. Rat diffui f radiati blt lctr by whitl-md chru. Gphy R Ltt. 00;0(9):49.. Cattll C. Dicvry f vry larg amplitud whitlr-md wav i Earth radiati blt. Gphy R Ltt. 008;4:L005.. Kllgg PJ, Cattll CA, Gtz K, t al. Elctr trappig ad charg traprt by larg amplitud whitlr. Gphy R Ltt. 00;7:L006. J Md Appl Phy Vl N March 08

5 Thrtical tudy f bliquly prpagatig whitlr md wav fr rig ditributi i th magtphr. Cully CM, Bll JW, Ergu RE. THEMIS brvati f lg livd rgi f larg-amplitud whitlr wav i th ir magtphr. Gphy R Ltt. 008;5:L7S6. 4. Omura Y, Furuya N, Summr D. Rlativitic turig acclrati f rat lctr by chrt whitlr md wav i a dipl magtic fild. J Gphy R. 007;: A Brtik J, Thr RM, Ia US. Nliar itracti f rgtic lctr with larg amplitud chru. Gphy R Ltt. 008;5:L0. 6. Sharma OP, Patl VL. Lw-frqucy lctrmagtic wav driv by gyrtrpic gyratig bam. J Gphy R. 986;9: Gldti ML, Wg NK. A thry fr Lw-frqucy wav brvd at cmt Ciiacbii-Zir. J Gphy R. 987;9: Wu CS, Krau-Varba D, Hu TS. A mirrr itability aciatd with wly cratd i i a mvig plama. J Gphy R. 988;9: Gary SP, Madlad CD. Elctrmagtic i itabiliti i a cmtary virmt. J Gphy R. 988;9:5. 0. Kill K, Omidi N, Krau-Varba D, t al. Liar ad liar prprti f ULF wav driv by rig-bam ditributi fucti. J Gphy R. 995;00:585.. Gray PC, Smith CW, Matthau WH, t al. Hatig f th lar wid by pickup i Alfvé i cycltr itability. Gphy R Ltt. 996;:.. Vada M, Hlligr P. Lir dipri prprti f rig vlcity ditributi fucti. Phyi f Plama. 05;: Umda T, Ahur-Abdalla M, Schrivr D, t al. Particl-i-cll imulati f Maxwllia rig vlcity ditributi. J Gphy R. 007;:A Frak LA, Burk BG, Ackr KL t al. Plama i Satur magtphr. J Gphy R. 980;85(A): L YC, Kaw PK. Paramtric itabiliti f i cycltr wav i a plama. Phy Fluid. 97;5:9. 6. Kumari J, Kaur R, Pady RS. Effct f ht ijcti lctrmagtic i cycltr wav i ir magtphr f Satur. Atrphy Spac Sci. 08;6:. 7. Kaur R, Pady RS. Study f whitlr md wav fr rig ditributi fucti i Satur magtphr. Advac i Spac Rarch. 07;59: Wu CS, Y PH, Frud HP. A thry f lctr cycltr wav gratd alg aurral fild li brvd by grud faciliti. Gphy R Ltt. 989;6(): Kumar S, Sigh SK, Gwal AK. Effct f upflwig fild-aligd lctr bam th lctr cycltr wav i th aurral magtphr. Pramaa J Phy. 007;68(4): Pady RS, Kaur R, Bhadria S, t al. Study f Whitlr Md Wav fr L C Ditributi Fucti with Prpdicular AC Elctric Fild i Magtphr. Atr Spac Sci. 06;: Zhu Q, Xia F, Shi J, t al. Itability ad prpagati f EMIC wav i th magtphr by a kappa ditributi. J Gphy R. 0;7:A060. J Md Appl Phy Vl N March 08 7

Bohr type models of the atom give a totally incorrect picture of the atom and are of only historical significance.

Bohr type models of the atom give a totally incorrect picture of the atom and are of only historical significance. VISUAL PHYSICS ONLIN BOHR MODL OF TH ATOM Bhr typ mdls f th atm giv a ttally icrrct pictur f th atm ad ar f ly histrical sigificac. Fig.. Bhr s platary mdl f th atm. Hwvr, th Bhr mdls wr a imprtat stp