CHARACTERISTICS OF ELECTROMAGNETIC WAVE PROPAGATION THROUGH A MAGNETISED PLASMA SLAB WITH LINEARLY VARYING ELECTRON DEN- SITY

Transcription

1 Progrss In Elctromagntics Rsarch B, Vol. 21, , 2010 CHARACTERISTICS OF ELECTROMAGNETIC WAVE PROPAGATION THROUGH A MAGNETISED PLASMA SLAB WITH LINEARLY VARYING ELECTRON DEN- SITY Ç. S. Gürl Dpartmnt of Elctrical & Elctronics Enginring Hacttp Univrsity Bytp 06800, Ankara, Turky E. Öncü TUBITAK Turkish Scintific and Tchnological Rsarch Council ODTU 06531, Ankara, Turky Abstract Charactristics of lctromagntic wav propagation through a magntizd plasma slab with linar lctron dnsity profil is analysd. In th numrical analysis, cold, wakly ionizd, collisional and stady stat plasma layr is dividd into sufficintly thin, adjacnt subslabs, in ach of which plasma paramtrs ar constant. Rflction and transmission cofficints ar calculatd for discrtisd plasma by considring lctron dnsity profil with positiv and ngativ slops. Widband absorbtion charactristic is obtaind with high collision frquncy and high lctron dnsity combination in linarly dcrasing profil as wll as widband transmission charactristic is obtaind for low collision frquncy and low lctron dnsity combination in linarly incrasing profil of finit lngth. Th gnral rsults show that in stady stat, plasma layr bhavs as a frquncy slctiv mdium satisfying th major rquirmnts of currnt shilding applications as th function of plasma paramtrs and th strngth of xtrnal magntic fild xcitation. Proposd plasma layr can b usd in currnt shilding and stalth applications as a matching layr btwn th surfac and th incidnt lctromagntic wav. Corrsponding author: Ç. S. Gürl (cigdm@hacttp.du.tr).

2 386 Gürl and Öncü 1. INTRODUCTION Th subjct of intraction of lctromagntic wavs and magntizd plasmas has takn considrabl intrst in litratur [1 18]. It has found that inhomognous plasma bhavs as frquncy slctiv mdium and can b usd as a broadband radar absorbing layr in gnral shilding and military stalth applications, radio communications and radio astronomy [3]. Elctron dnsity profil considrably affcts frquncy slctiv charactristics of th plasma in such applications. In litratur, diffrnt lctron numbr dnsity functions ar considrd such as xponntial, parabolic, stppnd, hyprbolic, tangnt, sinusoidal and xponntial with tim variation [8, 14 16, 18]. In th analysis of plasma-wav intraction in litratur, scattring matrix mthod [6], dirct formulation [8] hav bn usd. In ordr to simplify th solution, total plasma layr is firstly dividd into vry thin homognous subslabs in ach of which plasma proprtis ar constant. Thn rflction, absorbtion and transmission cofficints of th plasma in multilayrd form ar rcursivly obtaind [6] without taking multipl rflction ffct into account. Rung Kutta Mthod has also bn usd by Haifng t al. [9] to analys intraction of microwav with nonuniform and unmagntizd plasma. Thy concludd that th rsults of numrical solution coincid with th analytical solution. Spcial plasma rsponss undr crtain circumstancs ar invstigatd in litratur by Gradov and Stnflo [19, 20]. Nonlinar transparncy of a dns magntisd plasma is discussd and it is shown that according to th paramtric xcitation of th surfac wavs, significant part of th radiation can pntrat through th plasma. In a following study, a mchanism to amplify th transmittd and rflctd lctromagntic wav powr from an immobil plasma is discussd and it is shown that total radiation nrgy can b largr than th incidnt nrgy during short priods du to rlas of th stord wav nrgy in th plasma [19]. In rcnt studis various nw plasma applications and analysis mthods hav bn discussd in litratur [21 30]. In th prsnt study, normally incidnt lctromagntic wav propagation through a magntisd plasma with linarly varying lctron dnsity profil having positiv or ngativ slop is firstly studid as a nw frquncy slctiv mdium. Various multilayrd structurs hav bn analysd in litratur but plasma layr having linarly varying lctron dnsity distribution with positiv and ngativ slops has not bn considrd yt. Such a layr bhavs as a tunabl matching layr which is vry important for maximum absorbtion of incidnt lctromagntic wav and intrfac mdium in som critical

3 Progrss In Elctromagntics Rsarch B, Vol. 21, shilding and stalth applications whr othr matrials dsignd in multilayrd form can not provid its advantags such as tunability with xtrnal magntic fild, ffctiv collison frquncy, plasma frquncy and lctron-cyclotron frquncy. In th analysis, plasma layr is takn as cold, wakly ionizd, stady stat and collisional. Background magntic fild is assumd to b uniform and paralll to th propagation dirction. In th study, linarly varying lctron dnsity with diffrnt slop valus ar considrd rsulting with diffrnt rflction, absorbtion and transmission charactristics. In th analysis, inhomognous plasma is dividd into sufficintly thin, adjacnt subslabs, in ach of which plasma paramtrs ar constant. Thn starting with Maxwll s quations, rflctd, absorbd and transmittd powr xprssions ar drivd. In th rlatd studis in litratur, multipl rflctions ffct whil calculating th rflction and transmission cofficints is not considrd. In this study, th ffct of multipl rflctions on th plasma rspons is calculatd and rsulting contribution is compard with th rsults of no multipl rflctions cas. Th ffcts of collision frquncy, maximum valu and variation of th lctron numbr dnsity function and xtrnal magntic fild strngth on th plasma rspons ar prsntd by dtrmining appropriat conditions for good rflction and absorbtion prformancs for th purpos of dsigning a widband, frquncy slctiv mdium tunabl via xtrnal magntic fild xcitation. It is shown that du to amount of matching providd btwn th propagating wav and plasma mdium dtrmind by positiv and ngativ slops of th linar lctron dnsity, plasma layr can b usd as good absorbr or good rflctor in practical shilding and stalth applications as an altrnativ to th prvious multilayrd dsigns. 2. FORMULATION For a magntizd, sourc fr plasma mdium, plasma prmittivity is in tnsor form. This tnsor form prmittivity can b approximatd by a scalr prmittivity. In th cas of normally incidnt lctromagntic wav scalr plasma prmittivity is givn by th Applton s formula [1] ε r = 1 (w p /ω) 2 1 ± j v n ω w c ω whr ω is th angular frquncy of th incidnt lctromagntic wav, ν n is th ffctiv collison frquncy, w p is th plasma frquncy, w c is th lctron-cyclotron frquncy. Th prsnc of th ± sign in (1) is du to two sparat solutions for th rfractiv indx. In th cas (1)

4 388 Gürl and Öncü of propagation paralll to th magntic fild, th + sign rprsnts a lft-hand circularly polarizd mod, and th sign rprsnts a right-hand circularly polarizd mod. In this study, magntic fild is takn paralll to th propagation dirction and thus sign is usd in th prmittivity xprssion in (1). In (1), plasma frquncy w p and lctron-cyclotron frquncy w c ar givn as [1] w 2 p = 2 N mε 0 (2) w c = B (3) m whr is th charg of an lctron, N is th lctron numbr dnsity, m is th mass of an lctron, ε 0 is th prmittivity of fr spac and B is th xtrnal magntic fild strngth. In this study, normally incidnt lctromagntic wav with progagation constant γ is takn in th form E i = â x E 0 xp(jωt γz). In th formulation of th rflction cofficint, plasma layr is dividd into qual width, sufficintly thin, adjacnt subslabs through which lctromagntic wav propagation will b modlld, as shown in Fig. 1. In ach sublayr, plasma paramtrs ar takn as constant. Elctron dnsity N along th plasma layr for a linarly varying profil with positiv or ngativ slops is takn along th plasma as { Nm z/l N = (4) N m (L z)/l whr N m is th maximum lctron numbr dnsity valu and L is th thicknss of th plasma. x B P i P a E i M P t P r k Figur 1. Elctromagntic wav propagation through a plasma layr with qui-width subslabs. L z

5 Progrss In Elctromagntics Rsarch B, Vol. 21, d 1 B T A jγd 21 5 T T jγd D T j2γd C 23 T 21 jγd 6 23T21T 32 jγd T T j2γd F E T T 2 4 jγd T 2 jγd H J T 2 4 jγd T 3 jγd T G 2 3 jγd I 7 T T 2 3 jγd T jγd z=-d z=0 Figur 2. Rprsntation of multipl rflction in a subslab of th plasma layr. By taking multipl rflctions into considration as shown in Fig. 2, rflction cofficint (j, z) at th j th intrfac and total rflction cofficint at z = d intrfac (j = 1, z = d) for normal incidnc cas can b obtaind as [31] in (j = 1, z = d) = 12 + T 12T γd γd (5) From Fig. 2, th rlation btwn th rflction and transmission cofficints can b givn as 21 = 12 (6) T 12 = = 1 12 (7) T 21 = (8) Whn multipl rflctions ar ignord du to highly lossy plasma, by taking 12 1 and 23 1, rflction cofficint on th (j + 1)th

6 390 Gürl and Öncü intrfac is obtaind as [31] in (j + 1) = εr (j) ε r (j + 1) εr (j) + ε r (j + 1) (9) Th rflctd powr is thn calculatd by using attnuation constants α(i) of ach subslabs and rflction cofficints (j) valuatd at thir intrfacs as M ( )} P r =P i { in (2) 2 + in (j) 2 j 1 Π (xp[ 4α(j)d](1 in (j) 2 )) (10) j=2 i=1 whr d is th thicknss of th subslabs, M is th total numbr of subslabs and α is th attnuation constant of th mdium which is th ral part of th propagation constant γ = α + jβ. Thn, total transmittd powr and absorbd powr in th plasma slab can b calculatd from M { } P t = P i xp [ 2α(j)d] (1 in (j) 2 ) (11) and i=1 3. RESULTS AND DISCUSSION P a = P i P r P t (12) In this sction, firstly th plasma slab is assumd to hav linarly incrasing lctron dnsity profil ndd with th maximum lctron numbr dnsity valu, N m. Total plasma lngth is takn as L = 24 cm. In ordr to invstigat th ffct of multipl rflctions in plasma-em wav intraction problm, normalizd rflctd powr variation with and without multipl rflctions ar shown in Fig. 3. It is sn that vry small diffrnc occurs btwn two cass. This is th rsult of high valu of imaginary part of th complx plasma prmittivity of highly lossy plasma and thus high rat of EM wav absorbtion during propagation. For this rason, in th following parts rsults ar prsntd by ignoring th multipl rflctions. Anothr important point in Fig. 3 is that plasma layr bhavs narly as a nonrflcting mdium along a wid frquncy rang which is du to providd good matching btwn th EM wav and th plasma by mans of th slowly incrasing lctron dnsity valu along th dirction of propagation. In Fig. 4, th normalizd absorbd powr variation for diffrnt collision frquncy valus is shown whn N m = m 3 and B = 0.25 T. As th collision frquncy incrass, absorbtion band gts

7 Progrss In Elctromagntics Rsarch B, Vol. 21, widr. For th lowr valus of collision frquncy, absorbtion band gts narrow and normalizd absorbd powr dcrass sharply. Th plasma slab having both high lctron dnsity and high collision frquncy valus can absorb all of th wav powr along wid frquncy rang vn though such a cas is not so asy to achiv [8] No Multipl Rflctions Multipl Rflctions 0.1 Pr/P i f (GHz) Figur 3. Normalizd rflctd powr for N m = m 3, ν n = 1 GHz, B = 0.25 T v n =1GHz v n =5GHz v n =60GHz Pa/Pi f (GHz) Figur 4. Normalizd absorbd powr. N m = m 3, B = 0.25 T.

8 392 Gürl and Öncü As shown in Fig. 5, for th lowr valus of N m, narly all of th wav powr is transmittd spcially in highr frquncis and th ovrall transmission charactristic is th dual of absorbtion charactristic du to vry small rflction as shown in Fig. 3. This mans that narly all of th incidnt powr is absorbd or transmittd according to th frquncy of th lctromagntic wav with ignorabl amount of rflction. In Fig. 5 indicats that in ordr to dcras transmittd powr and thus improv th absorbtion, it is rquird to incras lctron numbr dnsity along th plasma layr whil collision frquncy has low valu. In this cas vry narrow absorbtion band is xpctd as th dual of th transmission chractristic again with vry small rflction. In th scond part of th rsults, plasma slab is assumd to hav linarly dcrasing lctron dnsity profil with maximum valu N m at th bginning of th plasma layr. Th normalizd rflctd powr variation is shown in Fig. 6 for N m = m 3 and B = 0.25 T cas. It is clar that rflctd approachs to zro as th collision frquncy incrass spcially at high oprational frquncis. Th plasma slab is mor likly to b a rflctor as th collision frquncy dcrass. It can b gnrally concludd that rflctd powr amount is highr with rspct to th prvious cas, i.., linarly incrasing lctron dnsity profil cas as shown in Fig. 3 du to th high input impdanc xrtd on th lctromagntic wav by th plasma as th rsult of high lctron dnsity valu N m. For high collision frquncy valus, plasma bhavs as a good absorbr according to th valu of N m and ν n as shown in Fig. 7. Doubl Nm=1* Nm=5* Nm=1* Pt/P i f (GHz) Figur 5. Normalizd transmittd powr. ν n = 1 GHz, B = 0.25 T.

9 Progrss In Elctromagntics Rsarch B, Vol. 21, v n =1GHz v n =5 GHz v n =60GHz Pr/Pi f (GHz) Figur 6. Normalizd rflctd powr. N m = m 3, B = 0.25 T v n =1GHz v n =5GHz v n =60GHz Pa/Pi f (GHz) Figur 7. Normalizd absorbd powr. N m = m 3, B = 0.25 T. absorbtion bands ar obsrvd for υ n = 1 GHz and ν n = 5 GHz and plasma slab bhavs as a bandrjct filtr. Th rflction charactristic of th plasma slab bcoms strongr whn th collison frquncy is lowr around 10 GHz. Normalizd absorbd powr incrass as th collison frquncy incrass accompanid with singl and widr absorbtion band. Normalizd transmittd powr can b dtrmind from (11) which is not th dual of th absorbd powr as shown in th prvious part du to incrasd amount of rflctd powr.

10 394 Gürl and Öncü In th last part of th study, linarly incrasing and dcrasing profils ar compard in trms of rflction and absorbtion charactristics in Fig. 8 and Fig. 9 for ν n = 1 GHz, N m = m 3 and B = 0.1 T. Figur 8. Normalizd rflctd powr comparison for linarly incrasing (cas 1) and dcrasing profils (cas 2). ν n = 1 GHz, N m = m 3, B = 0.1 T. Figur 9. Normalizd absorbd powr comparison for linarly incrasing (cas 1) and dcrasing profils (cas 2). ν n = 1 GHz, N m = m 3, B = 0.1 T.

11 Progrss In Elctromagntics Rsarch B, Vol. 21, It is shown that linarly dcrasing profil shows bttr rflctor charactristics whil linarly incrasing profil xhibiting bttr absorbtion prformanc du to amount of powr matching providd at th input of th plasma layr. It must b notd that according to slctd valus for magntic fild, maximum lctron dnsity and collision frquncy cntr frquncy (i.., th rsonant frquncy) and th bandwidth of rflction and absorbtion charactristics considrably chang. Undr such conditions proposd plasma layr provids widband frquncy slctivity which is dsirabl in critical shilding applications. 4. CONCLUSION In this study, intraction of lctromagntic wav and finit lngth plasma slab having linarly varying lctron dnsity profil undr dc magntic fild xcitation is firstly analysd. Th ffcts of linar profil with positiv and ngativ slops on rflction, absorbtion and transmission charactristics ar dtrmind. It is shown that plasma rspons considrably changs du to adjustmnt of th slop of th lctron dnsity. According to th amount of matching providd at th intrfac, widband absorbtion or transmission charactristics can b obtaind. In th analysis, ffct of multipl rflctions ar includd and shown to b ignorabl du to high loss providd by th plasma itslf. It is shown that by tuning th plasma paramtrs such as collision frquncy, maximum valu and slop of th lctron numbr dnsity and xtrnal magntic fild strngth, proposd plasma mdium can b usd as broadband absorbr in shilding and stalth applications. ACKNOWLEDGMENT This study is supportd by TUBITAK-Turkish Scintific and Tchnological Rsarch Council undr contract EEEAG-104E046. REFERENCES 1. Ginzburg, V. L., Th Propagation of Elctromagntic Wavs in Plasmas, Prgamon Prss, Nw York, Hald, M. A. and C. B. Wharton, Plasma Diagnostics with Microwavs, Krigr, Nw York, Vidmar, R. J., On th us of atmosphric plasmas as lctromagntic rflctors as lctromagntic rflctors and absorbrs, IEEE Trans. Plasma Sci., Vol. 18, , 1990.

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