Banerjee, S K

Khastgir, S R

English

IACS Institutional Repository

ON THE PO LARIZATIO N OF RAD IQ -W AV E  T R A V ELLIN G  T H RO U GH  THE IONOSPHEREjS. K. BANEBJEE and S. KHASTGTBU n i v k h s i t v  C o l l e o k  o f  S i ' i E N i 'E ,  U j s j v e h s i t y  o f  C a l c u t t a  (Received, June, S, 196H)S3ABSTRACT. TJio Innitjng jjo lanzatioi) uh doduccrj by Haket unci (jlieen without taking the uhuuI Appleton-Hart rep formulue ban been Hbown io be identical will) the  lim iting polarization deduced directly from the Appleton-H artroe lorinula From  Bn ile j' h formulae for the am plitude-ratio of the normal to the abnuiraal eomponei)t.s o f the inagriotic vector 0  ^ the radio-wave, tho phaso-differonce between them  nt any level of the ioiioephero luiH boon deduced foi r Pc where p^  i« the critioal oolliuional freci[Ueney. I t  haa alao been ehown th a t fur r vc, tlit* amplitude ratio ir neiuly unaffocted at any level by electroncolliKional frequoney1. Identity of the earpression for the limiting polarization as given hy Baker and Green with that deduced directly fro?n the Appleton-Harlree formulaeWithout taking tlie usual A])pleton-Hartreo formulae (1927, 1929) it was shown hy Baker and Green (1933) tliat tlie limiting polarization Ra given by the roots of the following eejuation .R a ^ y lg 'R a - l^ OnwherejEtsin ^6 eos 6 jj—p  ' me' - r(1)(2)0 — angle between the direction of propagation of the radio-wave and the positive direction of earth's magnetic field.Ey — component of the electric vector along 0 7  (Fig. 1 ).Et =  component of the electric vector along OT (Pig 1).H  — intensity of earth’s magnetic field. e,m  — clcctronie charge and mass.V =  electronic collisionaJ frequency, c — velocity of light in vacuum. -473474 S ,  K. Banerjee and S .  B. Khastgir3^’jp 1. C()-ordinn.U'.syBimi UHPil b y  Bakor ami Fig 2 Higlil-bnndrid ro-nrdinati(Ji'Hpn. OS— AvnvBunimal O T— w avefront K  - earth 's magrietu' holdRyniom iiflerl by Ap])lelon O X  —Ava\o normal H — oartli’M magnel le fieldG^)Wlicn the riglii -lmiidod co-ordinalt* system of 2  is used, where the direc­tion of propagation of the radio-t  ^av(‘ lias been lakeii along OJS^ -axis, it (;an he shown ill at-n)Ewhorehz --  oomjjoiient of the niagiietK; vector along OZ (Fig. 2). hy — component of the magnetic vector along OT (Fig. 2 ).From Eq. (I^ )AV (hz \)  \ hy }hzhySolving Eq (1 ), we have'In " ’ 4rj,iiFlitting the value of /‘■^/??. and q' from Eq. (2 ) in Eq. (la)„ _  , rSince the critical collisional frequency is2 mv cos 4m‘^ c^  cos  ^0 {p- jw)‘^ ^CJa)(la)( I h )2  cos 0where pi. =  —  mewe getp —p  '  (JJ—jv )-( I c )On the Polarization o f Radio-wave, etc.Using (Ic) ami (3a) :475( ? “ )  ^ ''' 1. I-’ 1 -\ hy ! L /i—jv ’ (71—jv)“ JThis equatu)ii can 1)0 deduct'd directly h’om the Appletoii-Hartree lorniula. Appleton used the light-luindcd erj-ordinatc* system ol Fig 2 and the polarization IS given hy( - J  [ -  -L- J  yT^ ‘ _ -I y 1\hyl yj l^ 2(l+a|jA) 4^(1 l-a-|-;y/y)“ JUsing oc =  p ‘“7po“. fi -  pv/p,,  ^ p , 2  =  ■inNe-l'm, y  ,7. -E(| (4) can he vntien as... (4)R - -  [ --P.X 'v v \  _  I J  / M -  ■ I .. 2]I 'hjvi ’  - K i i J  - iP  l-7'Wv)^  I (4a)l •- - W  p^ -\ liv^ ) ^ -^(V -p"- \ JP'>)Hence the limiting value is obtained by putting 71,/ — 0 (i e. jV — 0 ) in Kq. (4a)® ■ ( / “ )=- J 1 ■ i +  ‘ 1 ■ ■ ■\hyj L p —JV  ^ (p jv)“ JIt IS seen tliat Eijs (Id) and (4b) are itlentical.2. Emluatitni of the /thase-difference between ihe nounat and the abnormal Compo- nenLs of the maynrtic vector of a radio-amve at any level of the ionosphere forV <  <  VpIt was shown hy Bailey (1934) tliat the amplitude-ratios ol the normal to the abnormal components of magnetic vector are given byandvdierePy — (i j^ J — cot 00 j for the 0 -mode , f)^  =  cot 001 for the A-mode .« =  M v i + ' i ^ - v i + n(5a)(5b)(5o)476 S. K . Banerjee and S. R, Khastgir7 '  =  - 2  . M l , w“  j  a<J, =  Vc/v. da =  Vf/^<'. Jj' =  ^ 1-  =00 == phase-difference for the 0-mode.Using Eq. (5c), it can he Bho^ vn ■<knNe^... (6l^ )... (6hj\Using Eqs. (5a) and (5b) and the relation, — 1 ,mt<l>„= ± f - ) j  1 -  1»i a* ... (7a)When v<<Vc, we get from (6a), (6h) and (5 c),Y ^  Y' ^  - ... (6c)Hence ri'^ es-p'‘' -\-v^ ... (6d)Using (6d) and (7a)tan 0 0 ==: ± ^ \ f ... (7b)According to Murty and Khastgir (1960), 0(, lies in the first quadrant for the verti­cally downcoming wave m the northern heniisphci'e, hence taking the positive sign in (7b), we havetan 00 ^J ...(7c)Similarly, for the vertically downcoming radio wave in the aoutbein hemisphere ;tan 0 o«=i J  l +  .^_j V V ... (7d)From Eq. (7o), wo can draw several conclusions .(a) At the level (i.e. p' = ,0 ), the wave is plane-polarised.(b) The sense of rotation of the magnetic vector is reversed when the wave crosses the levelOn the Polarization of Radio-waves^ etc. 477(c) Since at the lower boundary of the ionosphere, p' — p  and at tlie IcTol,=  0 , the phase-difference gradually increases from zero to a certain value depending on p, v, and Vc as the wave comes down from the level, pQ^  =  to the lower boundary of the ionosphere.(d) At the level p^ '^  =  P^—W b ’[taii0 „] [cot“(?+co8ec2 ?^]3 . Effect of electron collisional frequency on the amplitude-mho at any level for v < <  Vc-Tt can be shown from the Applelon-Hartreo formulae (1927, 1929) that the amj)litude-ratio for the ordinary mode for vertically down-coming radio-wave in the northern hemisphere for zero colhsional frequency is given by(«)wherep' =  j Vc =  Ph cos dFrom Eq. (8), it can be shown .f ^±£l] = x S 'tZ 'U - / V  VcIt has been shown by Murty and Khastgir (1959) that__ __ V' 1* Vc L cos </>o sin 00 JPo =andwhere ^ . P' -Vc L 00^00 ^ sin 00(9)(10a)(1 0 b)Using — 1 , we Iiave from Eqs. (10 a), (10b)478 S, K. Banerjee and S, B. Khastgir---V 'P coa 0,j sin- j(U)s 0Q Sinllencc from Kq. (lOe)LI • /V  -I *■ u V(lOo). . .  ( 11)Using (II), (7..),[H /'o ML1 J, \/vo“ V_p'^ ... (1 1 a)and from (1 1 a) and (9) ,This means that at any levtd ol the ionosphere, the amplitude-ratio for the U-niode is lU'arly unaffected by electron collisional frequency provided the critical colli- Hjonal frequency is much larger than electron-collisional frequency. The same conclusion can lie drawn for X-mode also.U E  F  E  R  E  N 0  K SAppleton, E  V ,  1927, U .K .H I.Hailoy, V  A , 19a^l, PJul May., 19, 376Haker, W  U. and Eroon, L., 1933, Proc. T R  E  , 2 1 ,  H 03.H ftiiree, D R „  1929, P m  Vamb P hil. Soa., 25, 47M urty, Y . S. N and K hoatgir, S. PI., 1959, Proc. Nat sci, 25A , No. 5 Miu'ly, Y . S. N. and K hastg ir, IS. K  , I960 , Jour. Geo. Res,, 65, M ay Issue

On the Polarization of Radio-Wave Travelling Through the Ionosphere

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On the Polarization of Radio-Wave Travelling Through the Ionosphere

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