Sharma, Subhas Chandra

Verma, J S

English

IACS Institutional Repository

In d ia n  J. P h ya, 5lA, 343-349 (IDTl)Excitation of the cylindrical plasma columns with the ring of magnetic currentsSuBHAS Chandra S harma and J .  S. V srm aD ejiaH m ent o f  Physios,B i r la  hisUt'utv. o f  T ochnoloyy  am i Scio.ncc, J^ ilav i-X V M rM  [Received  18 M a r c h  197(), revised 1) A u g u s t  ll)7 ti)A cyliudi'ical geomolry haviiij^ a. c‘(mdiicl,or (radius ring sourco (radius a), air coluuui (j'adius b), gas(‘(Uis f)lnsma (radius r). solid stiilo somiconductor plasma (radius d) and gaH(M>ijs plasma eoluniu (radiirs e) is studied. This mullilavorcMl syslcm gi\a\s riidiatioji peaks lor particular values o1’ b, r. d and e l^iilc^  llic source of (excitation Ixuug the ring of magnetic' (‘uriMuits. Tlu^  am]>litu(lc of tJics(e radiation peaks gets alTecdod with 1.h(e (Change in tliese ])arametcrs. Almost in aU th(i cases l adiation j>atteru lui})pons to 1)0 of the same nature in the directions from 71‘" t(> 00'^’.1. IntroductionExcitation of k^aky wavi-s on plasma columns was studied by Tamir ei al (1902, 1963). They (considered the (^xcutation of kaiky waves on jdasma surfact^s. Criipta el a l (1967) discussed tlu^  radiation jiatturn diu^  to ring soiii ee while plasma column was assumed to l)^  ^ (iylindrical shaped and extending upto infinity in axial direction. Thc y^ also int-eiprettod this type (»f pattern diu^  to leaky Avaves. Welonhancod peaks l>eJoro and ii(?ar critical angle wore obtained by DJiani Bam ct a l (1972) when they included a central conductor along the i3-axis of tlu  ^ cylin­drical coordinates. They assumed the source to be iniinorsed in plasma which unfortunately for exiierirnents posivs a serious problem. To Ix^  safe on tlu^  experimental side Sharma et a l (1975) discussed t-lui problem assuming the ring source situated outside the plasma column. In cuuitinuancc  ^ of the above cited work hero we have studied the plasma columns wit-h the holj; of ring of magnetic cut‘rents. Plasma columns are assumed to be homogeneous, losf l^ess, isotropic and in-compressiblc in nature while the semiconductor plasma column being lossy in nature. The columns are assumed lo be extending uplo infinity along ::-axis and the source is placed in — 0 plane.2. ANALYSiSStating from the Maxwelfs equations (Dhani Ram et a l 1972, and Sharma et a l 1975) one can expand the inhomogeneous eqn. in cylindrical coordina^s3431144 Subhash Chandra Sharma, J .  S. Vennafor tir* first asymmet rical mode and can come across witli the solution in the form of bcssei's and hankoJ’s lunctions which can bo given as,A, --- A iJ t (V a p )  \-B iY ^{v„p) <  f) <  a (la)Aj Ji^Yj^Vgp) a  <  f) <  b (lb)A3 -  A^J^{V fP)-\ B :iY i(V ip ) h <  p  <  c (Ic)A4 -  A iJ i { v . j P  -\~BnYy{>up) V <  p  <  d (Id)h,, -- A ,J i ( r - iP )  \ B ; ,Y i{ v ^ i> ) d <  p  r (le)r p (11)whore k  IS i‘ transform (jT I I given l)yh{fj. kz) = J dkz^  JOand llu  ^ inverse* traiisioj’in is givmi byz) ■= i  h{p,—ooJit. Y n ,  and aic rosptrctivoly bassel liinc.tjon of first, kind, 2nd kind andhanders fnnetioji of fir.si kind of' y/-th orderwliere  ^ n\ //„, Cj, and are*. rebspecti\xdy tlie se)urce frce|uency free spacei jununeability, jaainitt ivily, redalive peainit-t ivity of gaseous plasma, somiconduc- |,e»r ])liisnia anel [Me>pagatie>n ve^ cle>r.Aj)])Iying tliev propeu' boundary eemditions (Dluini Kain et <d 1972) and subst ituting k^ -  /r„ SiiW^ the^  magnitude of the radiatiem field can be made kne)wn with the^  help e>r steepens! descent, method e>f saddle point integi*ation (Slianim cl at 1975). N n w  | A o ( A ; z I  inagnitude of theradiat ion uie>eie^  of the structure^ analys(Ml here  ^ The expression for consists e»f bessefs fiinet iems, liaukors liinetions, r,, etc. and happens to be lengthy. 'JMie e'xpressieui l'e)r readsI I I  I ■^•^*711l ' ‘ ‘ l " l A „ l-^ 7^4U‘ 7H •^ ‘*7g) /, _ -^ 7^2^ 3^3It-jm —AN, p A 31A 72A .Aairi _  a^aANa7^U-^74 — •^72 ^  ■^ 70 “  -^06 ==■ ^aa ~—=Ar.7 ^^^ :>5- -*^63-^60■ 7^0- 0^2 “F-^ G4-^ 0B * 2^0-^ 2^2 28 '^25*^50E xcita tion  o f  p la sm a  colum ns 345■^ 01-^22*^ rj8-^ V»i■^^ 5-^ 51 ’^ 52-^57y *54/1 rjr)/*?4By^i 5"  ^ j 1y?j7/l^ o(V7^ 5] — y7^ r,yi?2o -^ 2^1-^11/»?4 y^ 47 —-^45 ~^^ 4^3y^4i —y^ Mi, -/? I -**'4.'>-'*'4G ‘^ ‘*42 *1“ ~ r»7 4^87^r7^ 30 -^40-^7y^ a-^ aft*^78y»?7iy^ fiai?rt4y^ Vi2y^ «oy?r.By^ riGy^ o^iyv.2 ^y*^ r.n -  y*^■^ 7^1^ 0^2 ~1“ -y^ G^Oy^ OS yi?27y^ 22 ■yyasy^ as y^ 23-y^ 28 y^2ftyy22— y^ 59-y^ 24;7yri0 y^ gjjTy^ i;.^ 51- y^osy a^?l-'*^ 144^0J^w> yy.j^y?],y^^ oj 7i*n,7ii*j5]y*^ 2o ■““7 1^87 1^44^84r»"'^ 47yy.y?.4flR ^ R \ \  y^ ioy*^ j,yy^yyii yy5 2-yy8^^ 447 4^27 4^0yy««-  7^ 41^ *%-  7 5^7 4^0—^ 7?3g7?4 7ygfl72g7-  yy^ y^ g 7 4^7 7^ ^^y?37 —  i t i ^ R R ^ — R 9R 21 ’ 7^30R .y R ^y y ; "7^36 — '^ 1 ^o('*'’l^)> 7^34 ~  "^l*7o('*^ 1^ '’)? 7^33 “  ^l^o7yo(^0®)/?32 —  y7l('i^o^)i 7^31 “  Y ^(v^c), 7*^ 30 7i(?^^e)7^20 —  <^ 1^ 2 • 7^28 t’x?^ 2«7l(^ 2^^ y)- 7^27 ~  ^2^1^o(^l^)7^20 ™ 2^" 1^*7o('^1^)? 7^25 - - 7^24 “-  7i(vjeZ)7^23 ^ 7^22 *71(^ 2^ ) ’ 7?2j =  0(^1^^ )7^20 ^2^i '7o(^ v 0 , R%1\ -— Cj ^ 2 ^ o (  *^ 2^ ) ’ 7^18 ”  ^l'^2*7o(^^2^)y^i? =  Y^iv^c)^ ^16 ”  *71(^ 2^ ) ’ 7^16 “  ^ l(^ l^ )^  — v^Y^)(vjb), Ry2, ~E E q ^  J iiih P )^  -"— Yi('oJ}), /I'r, — J^(vyb),340 Subhash Chandra Sharma, J .  S. VermaK  ^  ^i(^o«)Ay — Jx (vJ ))^  v ^ a Y ^ { v ^ ) -Y x (v ^ a )7^ 3 — Vf^aJ y^{o^ a^) -'/j(vy;.). A  ^ -— i„(7;o«j), — */o(^ o%)'1 -<4(, I haw been eoiuimit^d wit-b tli('. help of IBM-llJiO computer for the different \ralue.s of the various parameters e.g. a.y, a, b, r, d  and f.3. R esults  a n d  ConolustonTheoretical cojuputed values ni' 1^1,J h>i‘ the maj.^mtude of the radiation field hav(’ beiai ^iv(5ii fo?- numerical values of flu  ^ various parameters ^iven as io -  2 t7 X 10 ‘^^  rad s(H' -h A:j, — 27t/H c;tu“ .^ (jraseems plasma electron frequency -- 2 x 10 “^ rad see’ ’ , iVp,, —  1-57x10^^ rad s(^ c~’ (for (j|a-As type semiconductoj) and Vy ((Jollision frequeiu* '^ of tlu  ^ scuniconductor plasma column) =: iO X 10^ '^  m>c A various features of tlu  ^ radiation pattern are following ;.*>, I o f  r ( id a  o f  conductor a n d  r in g  -sourceThe elianjj e^ in and a does no1 cause any importani- variation in fhe field pattern. Tlu^  pattern contains the {‘o,\v peaks and almost the same in te is ity  of the radiation liekl beyond 72". One plot for l\ /i ^  4-188 has boon given in^the figure with dot ted line. This plot, gives the gmieral bidiaviour of the field ampli- t.ude with k^/l i.e. a. The same kind of variation was computed in the radiation field wlum th(^  change in occurs. Iliis is not reported herf^11.2 Rffcct o f  the radiums o f the a ir  co lu m nOne plot is given for /cJ j — (vl78 with dot. aaid cross in the figure. This shows the general nature of the field pattern with change in b.'fable 1 . Kffect of change in h on radiation pattern Values of the various parameters= 0-209. k^a ---- 3-874, k j > ^  5-235k „ f  =  7-330, J c^d  —  9-424 and V- 11-519Dirocl ion of rad ia iio n  poak (in dogrooH)M agnitude of tho rad iation  fiold (in rel. units)/.-(,?»= 5.5r. kji -  0.178 hob = 0.8001 0.270743 0.310089 1.30650002 0.39780f> 0.312701 1.10023904 0.140932 1.637920 4.33099871 2.406507 0.068649 0.003632Excitation of plasma colutTins 347The peak occuih at 04 . Also in (1“ to 74" tlK're occui'k no rndiatiou. Beyond 74 the maf^nitiulo of tlie field almost attains llio eonstant value upto {)0“. Few more data are also givcui iji l.ahle I for change in h. These data show that peaks appear and diminish with change in h. The maximum intense peak appears in the direction ol 71" for Ic^h —  fi'riO0^R‘i.3 Effect o f chamje vn ra d iu s  of gaseous p la sm a  colum n {u u ie r)Tho change in k^f affects tlic ladiation pattern appreciably as <ixlhbitcd in tnblc 2. Ill diroclions 01", and 74" to 78' tlu^ rc ocenrs the contimionsTable 2. Effect of change in e on radiation patternDiroctioii u( radiation pcaK {in tlegroes)Magniiiulo on ho radiation fluid (in rol, uihIh)V  =  8.377 *(,c =  !t.424 V  lh47Jfil 0.947127 0. i62i:ir» 0.07613662 5.27164ri 0.1398:i9 0.06201071 0,187475 0.360986 0.19851972 o ..j:«76:; 1.000000 J.00000074 to 78 l.OOUOOO Ko radiation No radiationdecrease in the amplitude of Ihe radiation field when increase iu c is caused. In the region viewed through 74^ ' to 78^ ' the decrease in the amplitude occurs348 Subhash Chandra Sharma, J .  S. Vermaso drastically that for k^c --  9*424 and k^c —  10*471 the directions (74° to 78°) have no radiation field at all. The stroug(vst peak happens U  be in the direction of 62" for V  8*377.3.4 I^ffaci o f  change  i n  ra d iu s  o f  the sem icond u cto r p la s m a  (d)This is shown ir table 3. No rtigulai* foaturt! can be pointed out by viewing this tables. For some directions, flie inei‘eas(^  in Vr causes the decrease in ampli-Tal)le 3. Effect of cliaiigc in d  on j adiation patterjiDinxition of radiatioTi pjxik (ia dogrocH)Maguitudo of tho radiation (in rol, unitH)holdJc^ d =  0.7:i8 ^  10.053 Jc^ ,d -  10.995(il 1 . 20o;n7 0.0952770 0.28805702 :i.058.S28 0.0179770 0.04260157 0.107812 0.0530900 18.441030f)8 0.159423 10.8036100 0.21874070 0.482713 2.3968930 0.52002371 1.751459 0.0939700 0.02799.3tude of th(^  hold whik^ for some otluu' Olios, increase in that.. Th(? maximumintense radiation pc^ ak occurs at 57° for■ V  ^  10*905.3.5 Effect o f  change  in ra d iu s  o f  the outer gaseous p lasm a, c o lu m n  CFor k^ c^ — 11*833 tlu  ^ plot is given with solid line I h r  peak o('cnr at 62°for this value of In 61°, 62°. 71° and 72° direcLions the increase in e gives tlio (continuous increase in tlu  ^ magnitude of the ladiaticui fi(^ ld while no change  ^ill magnitude is found a i  72°. Another important feature of the pattern is the oteurreuce of vanishing amplitude of the field in the region viewed through 74° to 79° directions.Table 4. Effect of change in e on radiation pattern‘Direction of meUation poak (in degroeH)Magnitude of tho ra,diaiion field (in rol. units)K e  =  11.833 hoe =  12.147 V  -  12.46161 0.562196 0.679040 0.77557662 1.653001 2.231304 2.88764571 0.172674 0.175839 0.18050372 1.000000 1.000000 l.OOOOOO74 to 79 radiation No radiation No radiationExcitation of plama columns 349Having a glance at the abov e^ results one (‘an eoiiclude that tlio theoretically calculated radiation pattern is appreciably ailbclcd A\ ith thc^  change ixi fe, o, d  and c. For particular values of these paraineiiu's ther(' ot*cin‘s certain peaks of radiation which may happen to be useful while seiuliug the signal in some jm -  ferred directions. The geometry analysed heri  ^ comes into cxrsteiuu  ^ AAhile a radiating antenna having a central conductor, scinix‘ouductt>i cohiinn ajul ring source (jxlaced in between them) encounters lh(' ionospheric ]dasnia Mhi( h consti­tutes the inner and out^r layer of the gas(H)us plasma l(\aving thi* ring in the air The physical explanation can be borrowed Iroxn Tamil rt a l (11Hi2 I9();i) and Dhani Ham et a l  (1972) to excite such giuiinctries Aviih sourcesAokmow l^edcj me n 'rThe author (SA .^S.) (expresses his sim‘cr«^ - thanks lo (\S1H (Kcav Delhi) lor aAvarding him research fclloNcship. The timi'ly litdp from tin I Id - staff oJ' the Institute is also aeknmvledgod with tlmnks. Tha-idcs ai(^ - also dm^  to the referet^  tor ])ointing out few errors in the original manuseri])!.R efeuisncesDhani Ram  & Vorma J .  S. 1972 fn.dia.7i J .  J^7jre d' AppL Pliya. 10. 7H).Gupta K . C. &. iSingh A. 1907 I n t .  J .  TJlccfrov. 23,Sharm a Subhash Chandra. R am  Ohuiirlra k A^onna 9. S. l ‘)7r» huhan  -f P v re  tl‘ Appl. Phija. 13, 820.Sharm a Subhash Chandra & A^^rma .1. S. 1975 fnditni J .  Had, d' Pptt cr  /Vo/.v. 4 282.T am ir T. & Olinor A. A. 1902 IHE Trails. Antenna Pro'pag. AP-10, 55 Tam il' T. & Olirujr A. A. 1903 Proc. I.E.E. llO, 325

Excitation of the Cylindrical Plasma Columns with the Ring of Magnetic Currents

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Excitation of the Cylindrical Plasma Columns with the Ring of Magnetic Currents

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