Theoretical Analysis of Incoherent Scatter Radar Spectra Behavior for Different Maxwellian Ionospheric Plasma Conditions

Transcription

1 Intrnatonal Journal of Engnrng & chnology IJE-IJENS Vol:13 No:04 4 hortcal Analyss of Incohrnt Scattr Radar Spctra Bhavor for Dffrnt Maxwllan Ionosphrc Plasma Condtons Bashkm Dalp 1, Nam Syla 1 1 Unvrsty of Prshtna, St. Mothr rsa, 10000, Prshtna, Kosovo Abstract h powr spctral dnsty of an ncohrnt scattr radar sgnal contans nformaton on svral onosphrc plasma paramtrs. hr s a clos rlatonshp btwn th plasma condtons n onosphr and th shap of powr spctral dnsty. h snstvty of th shap, n th on part of th spctra, roughly dpnds on th plasma paramtr fluctuatons. Hr w wll study and analyz th rlatonshp btwn lctron tmpratur to on tmpratur rato ( / ) and th corrspondng shap of th spctra consdrng Maxwllan plasma condtons. In addton, th rlatonshp of on mass (m ) and th rspctv shap of on ln for hydrogn (H + ), hlum (H + ), oxygn (O + ), datomc oxygn (O + ), ntrogn (N + ), datomc ntrogn (N + ) and ntrogn monoxd (NO + ) s dscussd. Indx rm Incohrnt radar tchnqu, onosphr, plasma dagnostcs, powr spctral dnsty. I. INRODUCION h nflunc of th on mass and othr plasma paramtrs such as lctron tmpratur and on tmpratur n th shap of ncohrnt scattr radar spctra s xpctd from th thory of ncohrnt scattr tchnqu. In fact, th spctral dnsty of plasma fluctuatons dtrmns th scattrd spctra. Such fluctuatons ar studd assumng plasma n thrmodynamc qulbrum, statonary, unform, unmagntzd and collsonlss [1]-[3]. h ncohrnt radar tchnqu s a ground-basd and rmot snsng tchnqu whch s snstv to th nrgy scattrd by th onosphrc plasma [4]. h thory of plasma of ncohrnt scattrng for Maxwllan plasma condtons ylds a fnal quaton that dscrbs th powr spctral dnsty of th scattrd radaton by th fr lctrons. Insd of such spctra th onosphrc plasma proprts ar sgnd. h total shap of powr spctral dnsty s composd by two partal spctra s,.. th lctron part and th on part [5]-[7]:,,, S k S k S k (1) PlasmaLn IonLn k, S k, N 1 d f ( ) ( ) PlasmaLn v v k v k, S IonLn,, k k N d f ( ) ( ), v v k v k () (3) p k, k L k f ( v) v dv kv, 1, k k (5) 0 1/ n p m Whr: k - wav numbr, k - wav vctor, - wav angular frquncy, - lctron plasma frquncy,, N - lctron p numbr dnsty, k, - lctrc N - on numbr dnsty, suscptblty for spcs, ( v ) - vlocty dstrbuton functon for spcs,, f (4) (6) k - dlctrc functon, v - lctron vlocty, n - lctron dnsty n plasma, - lctron charg, m - lctron mass, - lctrc prmttvty n vacuum 0 and s dlta functon. h rspctv autocorrlaton functon of dlta functon, du to Landau dampng, s dampd wth a tm constant. hs stuaton affcts th spctral lns n such a way that th lns broadn and partly ovrlap ach othr. h total vlocty dstrbuton functon assumng Maxwllan dstrbuton for on populaton n plasma, n thr dmnsons, s [8], [9]: 3 m vx vy vz m k B f v f vx, v y, v z 4 v (7) k B Whr: m - on mass, k B - Boltzmann constant, tmpratur, v - on vlocty. - on In thory of wavs n plasma a functon of complx argumnt calld th plasma dsprson functon s consdrd whnvr th vlocty dstrbuton s takn to b Maxwllan [10], [11]: Z 1/ t dt (8) t Physcally, x y s th rato of wav phas vlocty to thrmal vlocty and s qual to k 1 / v 1, whr k IJE-IJENS August 013 IJENS

2 Intrnatonal Journal of Engnrng & chnology IJE-IJENS Vol:13 No:04 43 s phas vlocty and v Z s closly rlatd to th rror functon. s thrmal vlocty. h functon Equatons () and (3) rprsnt th lctron part and th on part, rspctvly, for th powr spctral dnsty (1). h lctron part of th spctra s a rspons of hgh frquncy wavs or lctron-acoustc wavs, whl th on part s a rspons of low frquncy wavs or on-acoustc wavs. h on part of th spctra has a charactrstc shap, consstng of two shouldrs, (doubl-pakd shap), partly suprmposd, and xtnds around th radar transmttr frquncy, whl th plasma part ls on both sds of th radar transmttr frquncy, but at a dstanc of ( ) fw MHz away from radar mttng frquncy. h rght-pak/shouldr corrsponds to on-acoustc wav (IAW) propagatng towards th rcvng antnna, whl th lft-pakd/shouldr corrsponds to IAW propagatng away from th rcvng antnna [1]. h on part of th spctra (Eq. ) racts vry snstvly to th changs of physcal paramtrs n th onosphr. From ts shap (Fg. 1) on can drv, drctly, data on svral mportant physcal paramtrs of th onosphr, such as: lctron dnsty n, lctron tmpratur to on tmpratur rato, lctron tmpratur to on mass rato m, on tmpratur, lctron tmpratur, mass of ons n plasma m, tc [13]. In our obsrvaton, w focus nto thr onosphrc plasma paramtrs: lctron tmpratur, on tmpratur and on mass. II. MEHODOLOGY Usng (1) to (8), w wrot a cod n Mathmatca, capabl to gnrat th graphc shap of th functon for powr spctral dnsty for th on part of spctra, only. Whl manpulatng wth th cod nputs for plasma paramtrs, w wr abl to study analytcally th dpndnc btwn th plasma paramtrs and th shap of th on ln spctra. From th on ln shap bhavor, w can conclud a rang of plasma paramtrs [13]. In our study w wll consdr two cass: 1. h on mass s constant (th mass of on s gvn) and th lctron to on tmpratur rato fluctuats.. h lctron to on tmpratur rato s constant and th on mass changs. h lctron to on tmpratur rato s dtrmnd from th rato of paks-to-vally of th spctra. h sharpnss of th on lns dpnds on rato [13]. III. RESULS AND DISCUSSION Frstly, usng th cod, w wll smulat dffrnt on ln shaps for dffrnt ratos. h valus for ar chosn arbtrarly. h followng cass ar consdrd: 1,, 3, 4, 5 and 6. ABLE I RELAIONSHIP BEWEEN ELECRON O ION EMPERAURE RAIO ( ), AND RAIO OF PEEK-O-VALLEY OF HE SPECRA ( h) FOR OXYGEN ION. Elctron to on tmpratur Rato of pk-to-vally of th rato spctra h Fg. 1 shows 16 th typcal shaps of 1.70 ncohrnt powr spctral dnsty gnratd by th cod, for dffrnt ratos, corrspondng to oxygn atom wth th rlatv atomc mass As w s n Fg. 1, th rato of paks-to-vally of spctra ( h) ncrass sgnfcantly as th rato ncrass. abl I shows th rlatonshp btwn valus of and th rato of paks-to-vally of th spctra ( h). As w s on abl I (also shown graphcally n Fg. ), th rato of paks-to-vally of th spctra ncrass untl th lctron to on tmpratur rato rachs th valu 1 and, aftrwards, th rato of pk-to-vally of th spctra ( h) dcrass. hr s vdnt an qual oppost frquncy shft of th paks, symmtrcally n both sds of th spctra, as th tmpratur rato ncrass. h comparson btwn two on ln sts for two dffrnt on spcs,. oxygn vs. datomc oxygn, s shown n Fg. 3. W can not that for th sam valu of rato, both spcs show on ln paks at th sam frquncy shft, qually on th lft and on th rght, whl th powr rcvd vars gratly for datomc oxygn compard to oxygn. Scondly, w wll analyz th rlatonshp btwn th on mass of onosphrc plasma spcs and th shap of th spctra. Our focus wll b to hydrogn ( H ), hlum ( H ), oxygn ( O ), datomc oxygn ( O ), ntrogn ( N ) and datomc ntrogn ( N ). Assumng that th rato s constant, w wll calculat and graph th shap of th spctra for ons wth corrspondng rlatv masss: Ar ( H ) , Ar ( H ) 4.006, Ar ( O ) , Mr ( O ) , Ar ( N ) and Mr ( N ) hs mass IJE-IJENS August 013 IJENS

3 Intrnatonal Journal of Engnrng & chnology IJE-IJENS Vol:13 No:04 44 valus wll srv as an nput for th cod. In Fg. 4 and Fg. 5 ar shown th spctral shaps for chosn ons. In th frst cas th lctron to on tmpratur rato s chosn to b constant for all ons and ts valu s 1 and, n th scond cas ts valu s 3. Analytcally, w can conclud a progrssv ncras of th rato of paks-to-vally of th spctra. h rato s much lss for lghtwght ons than for havy ons. Howvr, th paks n th frquncy doman rman unchangd. What changs sgnfcantly s th spctral hght and ara undr th on lns spctra. hs ara s rlatd proportonally to th lctron dnsty wthn th scattrd volum [14]. hs rlatonshp ndcats that undr an quvalnt plasma condtons, n trms of, havy ons scattr mor powr than lghtwght ons from th sam amount of plasma volum. If w compar th coordnats of th paks n rlaton wth th frquncy, durng two constant valus of, (n our cas 1 and 3 ), t s clarly notd that th poston of th paks ar cntrd at th sam frquncy, for lghtwght ons and also for havy ons. In th followng w wll comparatvly analyz th on ln shaps for two on spcs: ntrogn monoxd ( NO ) and datomc oxygn ( O ) wth thr rspctv on masss. M ( NO ) A ( N) A ( O) r r r M ( O ) A ( O) r r hs two ons populat manly th E-rgon and th F- rgon of onosphr as rsult of chmcal procsss nfluncd by sun radaton [15]. Usng th cod and applyng dffrnt nputs for lctron tmpratur ( ), whl consdrng th on tmpratur as a constant valu ( 1000 K), w hav found on ln shaps for ntrogn monoxd as shown n Fg. 6. h blu ln rprsnts th lctron to on tmpratur rato qual to 1 and th rd ln rprsnts th lctron to on tmpratur rato qual to. h paks of on ln shouldrs ar cntrd at 0,0034 MHz for 1, and for th paks ar cntrd at MHz. h rato btwn th sparatons of spctral paks, n frquncy doman, for ths two cass s about 0.66,.. th sparaton of th paks for 000K s about 66% gratr than for 1000K. From Fg. 6 and abl II, on can s that th snstvty of on ln shaps s wll-markd. For dffrnt valus of, th paks show dffrnt sparatons ( f ). In Fg. 7 and n abl III, ar shown th on ln shaps dffrncs btwn ntrogn monoxd ( NO ) and datomc oxygn ( O ), consdrng th sam tmpratur condtons. Undr such tmpratur condton, th man dffrnc btwn ths two on ln shaps s th spctral hght and th total spctral ara. Evn thought th spctral hghts ar dffrnt, th pk-to-vally of th spctra ( h) s mantand unchangd for both ons. Also, thr s no dffrnc n th postons of paks n frquncy doman (s abl III, last column). Both ons ar cntrd at th sam frquncy for a gvn lctron to on tmpratur rato. ABLE II RAIO OF PEEK-O-VALLEY OF HE ION LINE ( h), AND SEPARAION OF ION LINE PEAKS ( f ) FOR NIROGEN MONOXIDE ( NO ). Ion tmpratur (K) Elctron tmpratur (K) Rato of pkto-vally of on ln h (arbtrary unts) Sparaton of paks f (MHz) COMPARISON OF Ion Ion tmp. (K) ABLE III h AND f BEWEEN NIROGEN MONOXIDE ( NO ) AND DIAOMIC OXYGEN Elctro n tmp. (K) ( O ). Rato of pkto-vally of on ln h (arbtrary unts) Sparaton of paks f (MHz) NO O From th on ln hght, on can conclud that th powr rturn rgstrd by th radar for datomc oxygn s largr than for ntrogn monoxd. So, thr xst proportonalty btwn th on mass valu of a partcular onosphrc spcs and th powr rturnd rgstrd by ncohrnt scattrng radar. It would b of ntrst to analyz th on ln dpndncs n rlaton wth radar frquncy changs and n rlaton wth ln-of-st on vlocty changs. IV. CONCLUSIONS It s shown that th on ln shap of powr spctral dnsty s vry snstv and, n a clos rlatonshp wth lctron to on tmpratur rato. For a gvn on, th rato of paks-to-vally of spctra ncrass sgnfcantly as th rato ncrass. For oxygn atom, th maxmum of th rato of paks-to-vally of th spctra s achvd whn th lctron to on tmpratur rato s around 1. Undr quvalnt plasma condtons, n trms of lctron to on tmpratur rato, havy ons scattr IJE-IJENS August 013 IJENS

4 Intrnatonal Journal of Engnrng & chnology IJE-IJENS Vol:13 No:04 45 mor powr than lghtwght ons from th sam amount of plasma volum. Also, undr such condtons, th on ln paks ar cntrd at th sam frquncy, for lghtwght ons and as wll for havy ons. What changs sgnfcantly, undr such condton, s th spctral hght and ara undr th on lns spctra. For futur work t would b of ntrst to analyz th on ln shap snstvty n rlaton wth radar frquncy changs and n rlaton wth ln-of-st on vlocty changs. REFERENCES [1] W. E. Gordon, Incohrnt scattrng of rado wavs by fr lctrons wth applcatons to spac xploratons by radar, Proc. IRE, 46, 184, [] J. P. Doughrty, and D.. Farly, A thory of ncohrnt scattrng of rado wavs by a plasma, Proc. Roy. Soc., A59, 79-99, [3] J. A. Fjr, Scattrng of rado wavs by an onzd gas n thrmal qulbrum, Can. J. Phys., 38, 1114-, [4] J. K. Hargravs, h Solar-rrstral Envronmnt. Cambrdg Unvrsty Prss, Nw York-London, 199. [5]. Grydland, A. Strømm,. van Eykn, and C. La Hoz, 00. h capablts of th EISCA Svalbard Radar for ntr-hmsphrc coordnatd studs, Chns J. Pol. Sc., 13(1), [6] M. N. Rosnbluth, N. Rostokr, Scattrng of lctromagntc wavs by a nonqulbrum plasma. Physcs of Fluds. 196; 5(7), [7] N. Rostokr, st partcl mthod n kntc thory of a plasma. Phys. Fluds. 1964; 7(4), [8] P. A. plr, A. R. Llwllyn, Modrn Physcs. hrd Edton. ISBN W.H. Frman and Company, [9] J. A. Bttncourt, Fundamntals of plasma physcs. Scond dton. ISBN rt [10] R. N. Frankln, h computaton of th plasma dsprson functon Plasma Phys [11] S. D. Baalrud, h ncomplt plasma dsprson functon: Proprts and applcaton to wavs n boundd plasmas. Physcs of Plasmas. 0, [1] J. Lund, B. Gustavsson, U. P. Løvhaug, D. A. Lorntzn, Y. Ogawa, Partcl prcptaton durng NEIAL vnts: smultanous ground basd obsrvatons at Svalbard. Ann. Gophys. 007, 5, [13] W. J. G. Bynon, P. J. S. Wllams. Incohrnt scattr of rado wavs from th onosphr. Rp. Prog. Phys., Vol. 41, [14] M. Hdn, Advancd applcatons of th EISCA ncohrnt scattr radar for mult-bam and lctron ln studs. ISSN Swdn, 00. [15] A. Brkk, Physcs of th Uppr Polar Atmosphr. Jon Wly and Sons Ltd, ISBN Fg. 1. Shaps of th on ln for oxygn atom for 1,, 3, 4, 5 and IJE-IJENS August 013 IJENS

5 Intrnatonal Journal of Engnrng & chnology IJE-IJENS Vol:13 No:04 46 Fg.. Shap of th on ln for oxygn atom ( O ), for 1,,3,...,16. Fg. 3. Ion ln shaps for oxygn (rd) compard to datomc oxygn (blu) for: 1,, 3, 4, 5 and IJE-IJENS August 013 IJENS

6 Intrnatonal Journal of Engnrng & chnology IJE-IJENS Vol:13 No:04 47 Fg. 4. Shaps of th on ln for hydrogn, hlum, ntrogn, oxygn, datomc ntrogn and datomc oxygn assumng th lctron to on tmpratur rato s qual to 1. Fg. 5. Shaps of th on ln for hydrogn, hlum, ntrogn, oxygn, datomc ntrogn and datomc oxygn assumng th lctron to on tmpratur rato s qual to IJE-IJENS August 013 IJENS

7 Intrnatonal Journal of Engnrng & chnology IJE-IJENS Vol:13 No:04 48 Fg. 6. Ion ln shaps for ntrogn monoxd ( NO ) consdrng a constant on tmpratur ( 1000 K), whl applyng dffrnt lctron tmpraturs ( 1000 K, 000 K, 3000 K, 4000 K, 5000 K, and 6000K ). Fg. 7. Comparson btwn th on ln shaps for ntrogn monoxd ( NO ) and for datomc oxygn ( O ) for two dffrnt lctron tmpraturs: 1000K and 000K IJE-IJENS August 013 IJENS