Group refractive index curves for radio wave propagation

Indiana. Phya. 47, 9 4 -1 1 5 (1973)

K. K. Deb

Department of Physics Suri Vidyasagar ColUege,Suri {Birbhum) [Received 8 April 1972, revised 9 May 1972)

In this paper, the variations of the group refractive index of the ionos- j)here over Calcutta with the electron number-density, in respect o f wave frequencies (i) 10 Mc/s, (ii) 3 Mc/s, (lii) 1 Mc/s and (iv) 0.6 Mc/s have been graphically shown for the four values of electron colhsional fre­

quency viz., 1/ ™ 0, V — 10“/acc, v = i/p — 5 4 8 x 10®/sec, v — lO’ /sec.

For each of the exploring wave frequencies and for each of the electron collisional frequencies the phase refractive index has been calculated and graphically shown against electron number-density. The electron number-density ranges from — 0.32 x lOVee to = 10®/cc. Tn computing the phase refractive index fi and the absorption index x fhe group refractive index ///, the general expressions for p, y, p/ given by Murty & Khastgir (1961, 1963) have been used. The following con- ciluaions have been drawn

(a) In case o f low electron number-density, the ordinary phase re­

fractive index is greater than the extra-ordinary phase refractive index for Y — p hI'P<. 1 and vice versa for Y ™ 2>hIp > 1- When the exploring wave fiequeiKjy bccomc's sufficiently largo the ordinary and the extra­

ordinary phase refractive indices have almost the same value.

(b) The curves showing the values of the ordinary and the extra­

ordinary group refractive indices for v = 10®/seo and for v = lO'^/seo are of different type.

(c) The curves showing the group refractive index for v '> vc are of different nature, when compared with the corresponding curves for p < Ug. The curves for p ~ Pc, although dissimilar in some respects to the curves for v < pc have similarities with those for p > Pc.

The observed dissimilarities between the curves for p > Pi and those for p < Pc are found both when F > 1 and F < 1.

1. Introduction

Murty & Khastgir (1961) worked out a general expression for the group refractive index of the ionosphere. Murty & Khastgir (1960) also gave a general phase- quadrant table with the help of which group refractive indices for the ordinary and extra-ordinary modes of propagation can be obtained for different exploring wave frequencies, electron number-densities and electron collisional frequencies of the ionosphere under different conditions of the magnetic field.

Gibbons & Rao (1957) obtained an analytical expression for group refractive index of the ionosphere at low frequencies with an approximation applicable

94

Group refractive index curves for radio wave propagation

through the ionosphere over Calcutta

to the Pennsylvania State University area for which the critical coUisional fre­

quency is small.

Murty & Khastgir (I960) howe/vor derived an expression for the group re­

fractive index at low frequencies without such approximation. It was shown by thorn when v is small, this expression tallied with that given by Gibbons & Rao.

Unz (1961) also derived an expression for group refractive index of the ionos­

phere for zero coUisional frequency (v — 0). Murty & lUiastgir (1962) later pointed out an error in sign in Unz’s expression derived by them.

Gibbons & Rao (1957) showed, with the help of graphs, the computed group refractive index as a function o f v, using their formula for low frequencies and for low values o f u over a range from S x lO ^ ’ic-^ to 5xl0®scc-i for various fixed values of clectron-number-deiisity (N) ranghig from 700 to 12,000 for three fre­

quencies viz, 75, 150 and 500 Kc/s.

In this paper, the variations of the group refractive index (///) of the ionosphere over Calcutta in respect of exploring wave frequencies (i) 10 Mc/s, (ii) 3 Mc/s, (lii) 1 Mc/s and (iv) 0 6 Mc/s, have been grajjhically shown. For each of the exploring wave frequencies, the calculations of phase refractive index (/n), absorption index (y), and group refractive index (//) for each of the four values of electron colli- sional frequencies lying on either side of the critical coUisional frequency over Calcutta, have been made. These graphs drawn, for the lu st time, are of practical importance, in computing /i, and /^' the general expressions for Murty &

KJiastgir (1961, 1963) have been used. The range of electron number-density is from N ^ 032 X lO^cc to ^ 100 x lO^/cc.

A reference to group refractive index curves computed by Whale & Stanley (1950) and Shinn & Whale (1952) for zero coUisional frequency for certain values o f the ratio of the g3nroniagiietic frequency of electron to the frequency o f radio­

wave is worthy o f notice in this connection.

Group refractive index curves fo r radio wave etc, 9 5

2. Formulae used eob Computation

The values o f (^) and (y) have been obtained from the formulae given by Murty & Khastgir (1963). These are

a‘ + b ^ ) ] ... (1)

... (2)

96 K. K. Deb

where a ~ cl—sji,, h — y?+ryx,7 « = p Bin r = p cos 0, p = th© ratio of the normal to the abnormal components of the magnetic vector of the wave and ^ is the phase difference between the two,

pv a _^TrNe^

p ^ m

and other notations have their usual signilicance.

It has been shown by Murty & Khastgir (1969) that

Vc L cos 96 sill <!> J

= + 1

Vc L COS 96 sin9iij cos 2<j) — a'—

and

b' = v‘^-\-p'^

and Vc — critical collisional frequency 2 cos 6

(3a|)

\

(3b)\

W

(5)

(6)

(7)

(8)

6 — the angle between the positive direction of the magnetic field and the direction of wave propagation.

Since 8 — p sin 0, we get from equation 3(a)

! = [r ta n ^ —p']

Vc

Similarly since r = p cos 0, we get from equation (3b)

(9)

r = — \y—p' cot

Vc

... (10)

Group refractive index curves fo r radio wave etc.

97

It is to be noted here that for v = 0 the above relations give (j) — 90° and henoe fi and X become indeterminate. For v = 0, the values of n and ;v' can however be computed as follows :

We know 7t^

ijL

when V = 0, <j> = 90°, s — p, r — 0, ^ — 0

so that s = ± ]

"" 7 J . ~ 2 ^ a j ^ i{f+ a )^

Since ^a — ot— s y i , siid for v — 0, 6 — 0^ and ^x can bo obtained by calculating a and h in equations (1) and (2)

The group refractive index p' has betm obtained from the general expression deduced by Murty & Khastgir (1901) viz.

Ln' Vc 2 sin 20 \ a'—cps 20 / J J / X [ - 2 “ ': ( i + 1 ^ - ) ] _j_ vccot0 _ a'p'eosec®0 / j , _ l - ^ n ' ~ - 4 b '

a' 2a'jo' vc.2 sm 20 \ a '—cos 20 / I ⁽12)

3. Computation of/Iq and

Murty & Khastgir (1960) have given phase-quadrant table according to which the phase-difference 0 between the normal and abnormal components o f magnetic vectoi- of radio wave below the ionosphere reflection level for which = p® in northern hemisphere, has been taken in the first quadrant (0 < 0 < 7t/2) for the ordinary mode and in the fourth quadrant (§;r < 0 < 27t) for the extra-ordinary mode. Proper attention has been given to this table in computing the values of Pq and pg,'.

4. Results and Discussions.

The computed values of the phase refractive index and the absorption index for four different electron collisional frequencies and for four exploring wave frequencies (i) 10 Mo/s, (ii) 3 Mc/«, (iii) I Mc/s, (iv) 0,6 Mc/s over stipulated range o f electron number-density for the ordinary and the extra-ordinary modes are shown in tables, l-(a), (b). (c) and (d) respectively.

5

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The calculated values of the group refractive index for the ordinary and the extra-ordinary modes for four different electron collisional frequencies and for the above four exploring wave frequencies over the stipulated range o f electron number-density are given in tables 2-(a), (b), (c) and (d).

Table 2a Computed values of the group refractive index for ordinary and extraordinary modes for different values N and when exploring wave

frequency —- 10 Mc/s.

V = 10“ V ^ Vc =

6.48x10“ seo-i V = 107 HOC“^

Hx 1^0 H>x flo l^x

0.32 1 001 1 007 1 006 0 9!) 1 003 1.002 1.00 1 001 1 00 1.003 1 004 1.004 1 010 1 003 1,006 1 004 .00^1

3 2 1.012 1.016 1.112 1.016 1 02 1 02 1 013 1.006^

10.0 1.039 1 061 1 080 1.05 1 038 1.044 1.03 1 05

32.0 1.138 1 191 1 007 1 10 0 99 1.184 1.065 1.052

100 1 833 1.996 1 066 0 0 96 2.057 1 370 2.48

Table 2(b) (Exploring wave frequency = 3 Mc/s)

NxlO^ V — 0 V - 10“ (Spp-i V == Vc V =,107 i

fl'x ll'r /t'o //'-F fJl-'o fl'x

0 32 1 006 1 008 1 108 1.070 1 022 1.043 1 01 0.600

1.0 1.016 1.01 1.039 0.809 1.128 1.293 1.022 0.9831

3 2 0 978 1.025 1.342 0 904 2 310 1.19 1.119 0.921

10 -8.83C 0 1.786 0.624 4 64 0.772 1.101 0 632

32 0 0 0 0.260 0.19 0.36 -0.015

100 0.30 0.08 0.09 1.00

Table 2(c) (Exploring wave frequency = 1 Mc/s).

NxiO^ V = 0 M — 10® sec“^ V = V = 1Q7 BOC“ '

lix /to' H-x //-o' llx /to' fix

0 32 0 962 0 1.125 8.78 0.892 0.906 1.002 0.661

1 0 -163.6 0 0.764 -9 9 0.9265 1.242 0,96 0.926

3.2 0.203 0.362 0,2396 -15.11 0.6292 0.2084

10 0 -1.474 0.776 --253.0 -61.4 0.4876 0.1698

32 0.677 2.69 0.3006 -6.98 1.464 --0.75

Group refractive index curves fo r radio wave etc.

Table 2(d) (Exploring wave frequency = 0.6 Mo/s).

101

Nx\Q-^

V = 10 ^0 8 0 0 -1

0.32 -60.6 1.0 -4.01

!io'

- 10''' aeo-i

f*x A*' A /

3.2 10 0 32 0

-601.3 -130.6 0 8S 0,186 1.72 0.864

2 687 1.20 1 093 0.65 0.984 1.66

0.064 -0 36 4 442 -6.66 0.44 0.44 -8.34 0 222 0 376 -0.30 o026 0.164 -1.29 -1 32 -0 279 1.16 -1 99 -4 71

with A e refractirc index and the phase refractive index with the electron nnmber-deneity over the stipulated range for both the ord^^arv

T J7, 3 7 . ⁷ LT.’S .

Fig. la

Pig. lb

102

F ig . lo

Fig. Id

Fig. 2a

Group refractive index curves for radio wave etc, 103

Fig. 2d

104 K . K . Deb

!Fig. 3 a

3b

Group refractive index curves for radio wave etc. 106

F ig. 4a

106 K. K. Deb

F ig . 4o

4.1 Na t u r e o f v a r ia t i o n o f p h a s e r e f r a c t iv e i n d e x w it h ELECTRON NUMBER-DENSITY

A. Exploring wave frequency f = lOMo/s, A = 30m, Y — < 1

P

Groujp refractive index curves fo r radio voave etc.

107

Po

For V = 0 Pq starts from the value 0.9988 at JV = 0.32 X 10* per cc and then decreases with increase in N.

starts from the value 0.9986 at N = 0.32 X 10* per oo.

then decreases with increase in N more rapidly than

For V = 10®/soc. fiQ starts from tho value unity at = 0.32 X 10* per cc and then decreases with increase in N.

Pat starts from the value unity at JV = 0.32 X 10* per cc and then decrease as N increase more rapidly than (jLq

If = Vc

= 5.48 X 10“/sec

fiQ starts from the value unity at N = 0 32 X 10* per cc and then decreases with increase in N.

starts from the value unity at N = 0.32 X 10* per oo and then decreases with increase in N more rapidly than

For p — 10’ /sec. Pq starts from the value unity at N = 0.32 X 10* per cc and then decreases with increase in N.

fig. starts from the value unity at N =s 0.32 X 10* per cc and then decreases with increase in N more rapidly than

108 K. K. Deb

B. E x p l o r i n g w a v e f r e q u e n c y / = 3 Mc/s, A = 100 m, 7 = c , \ P

N

For V = 0 Pq starts with value 0.988 at N starts from the value 0.9811

= 0.32 X 10*/cc and then de- at i\T = 0.32 X 10*/co and creases as E increases reach­

ing the zero value at ==

= 3 2 xl0 V cc.

then decreases as E increases reaching the zero value at E — 10®/co. The decrease in with the increase in N is more rapid than

V = 10®/sec Pq starts with the value 0.9880 Poi starts with the value 0.9195 at — 0 3 2 xl0 */cc and at N = 0 .3 2 xW lcc and then decreases as N increases

reaching the zero value at N

— 32 x 10^ per cc

then docroasos as N increases It attains minimum value at N ~ 10*/cc after which it increases with increasing value o f N upto N = 10®/cc and then abruptly becomes

V = ve —6.48 Pq starts with the value 0.9874 p^, starts with the value 0.9828 10®/per sec at JV = 0.32 x 10^ per cc

and then decreases as N in­

creases upto iV = 32 x 10^

per cc. It then begins to in­

crease with increase in N.

at JV' = 0.32 X 10^ per cc.

and then decreases with in­

increase in N.

V = lO’ /sec Pq starts with the value 0 986 p^^ starts with the value unity and then decreases as N in- at = 0.32 x 10^ per cc and

creases then decreases as N increases

upto = 32 x 10^/cc after which it begins to increase with increase in N.

C. Exploring wave fregnewy f ~ l Mo/s, A = 300 m, 7 = > 1 P

Group refractive index curves fo r radio wave etc. 1 0 9

Po Px

v = 0 /Iq starts with the value 0.904 at N — 0.32 X 10^/cc and then falls ofl rapidly as N increases. It becomes zero at

= 3.2x10^00.

starts with the value zero at N == 0,32 X 10* per cc and then increases as N in- cioases. Attaining maximum value at iV^ = 10* per oo it decreases and becomes zero at = 3 X 10* per oo.

V — 10®/sec Pq starts with the value 0 8925 at N = 0.32 X 10* per cc and then increases with increase in N. Attaining maximum value at JV — 10*/cc, it de­

creases as N increases upto N — 3 .2 xl0 */cc. it then rises again with increase in N

/i,j. starts with the value 1.135 at N ~ 0.32 X 10* per cc and then decreases with increase in AT up to = 10* per cc.

It then increases slightly as N increases upto N 2 Xl0*/cc. Again it decreases slightly followed by a sharp rise in value with increase in N.

Pq starts with the value 0.94 at starts with the value unity

™ 5.48 X lO^'/dcc N = 0.32 X 10*/cc and then at == 0.32 x 10* per cc and decreases with increase in N. then decreases with increase Becoming minimum at — in up to = 3.2 X 10*/oo.

10‘’/cc it increases as N in- It then increases as N in­

creases. creases.

V — 10’ /sec starts with the value 0.966 at iV = 0.32x10* per cc and then decreases as N increas­

es. Becoming minimum at

= 10®/cc. It then increases as N increases.

//a, starts with the value 0.977 at JV — 0.32 X 10* per cc and then decreases slightly as N increases upto JV — 10* per oc after which it decreases again though slightly. It then increases with increase in JV more rapidly than

110

D.

0.6 Mc/s, A = 500 m, 7 — > 1

P

N l^x

v = 0

V = 10®/sec.

starts with the value 0.66 at starts with the value 1.104

^ = 0.32x10^ por cc and at JV = 0.32x10^00 and then decreases (as ^E inoreas- then decreases as ^E increases cs) to the zero value at jV — and becomes zero at E =

3.2 x10V- 10 V -

starts with the value 0.78 at starts with the value unity jV^ = 0,32x10^ per cc and at JV“ 0 .3 2 x l0 V

fliPiTi f1nnrpn..qaq n.s N innrRn,s. tlipn Hnp.rpfl.RPfl wif.h I’nnri

then decreases as N increas­

es. Attaining minimum value at = 3.2 x 1 0 V in­

creases with increase in ^E.

then decreases with inen in

upto iV =

lO^Vcc, after which it increases'as N increases.

-5.48 X10 V o -

starts with the value 0.93 at starts with the value 0.94 at JV = 0.32 X 10^ per cc. and

decreases as ^N increases up­

to == 10® per cc after which it increases as ^N in­

creases.

N

0.32

10^/cc and de­

creases first with increase Jn N upto A ^{= WlcQ,} after which it increases as ^N in­

creases.

V = lO’/sec. ^P

starts with the value 0.94 starts with the value 0.96 at 0 .3 2 x 1 0 V ®'nd

then decreases as N increases upto ^{N =} 3.2x10^ per cc.

It then increases as N in­

creases.

at J^ = 0 .3 2 x l0 V decreases as ^N increases up­

to i\T = 10^/cc. It then in­

creases as ^N increases.

4.2 Nature o r Variation o r Group Refractive Index with Electron Number-Density

A. Exploring vm e frequency f = lOMo/s, A = 30 m, F = < 1 P

Oroup refractive index curves fo r radio wave etc.

I l l

For = 0 /to' starts from the value unity at V = 0.32 X 10* per cc and then increases at a slow rate with increase in N.

/ij,' starts from the value unity at V - - 0.32 X 10* per oc and thou increases at a relatively greater rate than as iV increases.

For V ~ 10®/boc. starts from the value unity at .V — 0.32 X 10* per co and then increases with increase in V . It becomes maximum at V — 3.2 X 10* per cc and then the value decreases slightly with increasing value of V and subsequently rises slightly as V increases upto V = 10®/oc.

starts from the value unity at N = 0.32xl0*/co and then increases at a slow rate as N increases. It becomes minimum at JV — 32 X 10*/cc after which it abruptly falls to zero at V — 10® per oo.

= 6 .4 8 x 10®/sec.

jjlq starts from the value unity fij starts from the value unity at jV = 0.32 X 10* per oc and

then increases slightly as N increases. It becomes maxi­

mum at V = 10®/cc and then decrease very slightly as N

~ 0,32 X 10* per co. and then increases rapidly as N increases.

V = lO’ /seo. pQ starts from the value unity starts from the value unity at

N = 0.32

V = 0.32 x

112 K . K. Deb

Exploring wave frequency / — 3 Mc/s A = 100 m, T = < 1 V

Pq starts with the value unity at — 0.32 X 10* per cc and then increases at a very slow rate as JV increases It he- coines maximum at — 10*

/cc after which it falls rapid­

ly as N increases. The value becomes negative at iV^ = 3.76 X 10*/cc and after attain ing maximum negative value rises rapidly to zero at ==

32xl0*/cc.

Pa;' starts with the value unity at jV — 32 X 10*/cc and remains almost constant up- to N = 10*/cc after which it increases very slightly with increase in N and subse­

quently falls to zero value at i\T = 32xl0*/cc.

V = 10®/scc. Pq starts with the value 1 108 at N — 0.32 X 10*/cc and decreases as N increases up- to = 10*/cc. it then in- in creases as N increases but attaining maximum value at N = WjGG it suddenly be­

comes zero at iV = 32 x 10*

per cc.

p j starts with the value 1 076 at = 0.32 X 10* per cc. It first decreases and then in­

creases as N increases. After attaining a maximum value at N = 3 2x10* per cc. it falls to the zero value at N

= 32 X 10* per be.

= 6 .4 8 x 10®/scc.

Pq starts with the value 1.022 p^ starts with the value 1.043 at = 0.32 X 10* per cc and

then increases as N increases It attains maximum value at — lO^’/oc after which it decreases with increase in N iipto N = 3 2 X 10* per cc.

Then it increases with in­

crease in N.

a tN = 0.32 X 10* per cc. and then increases as N increases.

Attaining maximum value at A" — 10'‘/cc it decreases with increase in N.

p — lO’ /sec. Pq starts with the value 1.01 at = 0.32 X 10* per cc and then increases at a slow rate as N increases. It attains maximum value at N — 0.32 XlO* per cc after which it decreases with increase in N.

p j starts with the value 0.5 at = 0.32 X 10* per cc and then begins to increase with increase in N. Attaining maximum value at N = 10*/cc it decreases with in­

increase in N. It attains negative value at A = 32 x 10* and then increases as A increases.

Group refractive index curves for radio wave etc, 113

C. Exploring wave frequency f ^ 1 Mc/s, A 300 in, 7 = ^ > 1 P Po

v ^ O Hq starts with the value 0.9521 at JV^ = 0.32 X 10* per cc and falls off very rapidly with the increase in N. It becoraes negative at = 0.33 X 10*

per CG. Attaining maximum negative value at N -- 10*

per cc, it incroasos to the zero value at N 3.2x10*

per cc.

starts with the value zero at A — 0.32x 10*/oc and then increases with increase in N. Attaining maximum value at A — 10*/co, it falls off to the zero value at A = 3.2 X

lOVec.

V = 10*/seo. starts w ith th e valu e 1 125 at A ™ 0 . 3 2 x 1 0 * per cc and th e n deci'oasos as A increases bec om e s n egative at A =

3 . 5 5 x 1 0 * per cc A ttain in g m a x im u m n egative valu e at

A = lO^jcc, it incrcEises and b ecom e s p o sitive at A — 84

X 10 */cc.

starts with the value 8,78 at A — 0 32 X 10*/oo and then decreases as A increas­

es. It becomes negative at A — 0.447x10* per cc and attains maximum negative value at A = 10* per cc. It then increases as A increases and becomes positive at A

= 2.985 Xl0*/cc.

P ~ Vc

« 5 . 4 8 x 10®/sec.

fiQ starts with the value 0.892 at A = - 0 32xl0*/cc and then increases very slightly as A increases. At­

taining maximum value at A — 10* cc it starts decreas­

ing but falls off very rapidly and gets negative value as N

= 3.2 X 10*/cc Attaining maximum negative value at A == 10''7cc, it increases also very sharply as A increases and becomes positive at A

= 32xl0*/cc,

/ijj' starts with the value 0,906 at A = 0.32 X 10* per cc and increases slightly as A increases. Attaining maxi­

mum value at A = 10* cc.

it falls off but loss rapidly than /if with increase in A.

It becomes negative at A

== 1.12x10* ec and attain­

ing maximum negative value at A — 10“/oo it increases sharply as A increases.

V = lO’ /sec. /if starts with the value 1.002 at A = 0.32 X 10* per ec and : uen decreases with increase in A, It becomes minimum at A = 10®/cc after which it increases with increases in N.

/if starts with the value 0 561 at A ~ — 0.32 X 10*/cc and then incroasos as A increas­

es. Attaining maximum value at A — 10*/cc. its value decreases with increase in A. It becomes negative at A = ll!'X l0*/eo.

114 K. K. Deb

D. Exploring wave frequen cy f = 0.6 Mc/s A = 600 m , Y = & > 1

P

i/ = 0

Pi!

starts with large negative value (-5 0 .5 ) at = 0.32 X 10^/co and then increases as N increases and becomes zero at iV^ = 3.2 X 10*/cc.

Px

f i j starts Avith the value (—2 38 at iV' — 0.32 X 10^/cc and then increases as N increases and becomes zero at N

= lOVoc.

V — 10®/sec. {Iq starts with very large nega­

tive value (—601.3) and then increases as N increases. Tt attains positive value at N

“ 0.9 X 10^/cc and maxi­

mum value at iV — ] 0^/cc. 11 further decreases as N in­

creases and again becomes negative at iV = 3.2xl0*/cc It attains maximum negative value at iV^ = 10’’/cc. It then increases as N increases.

p j starts with the large nega­

tive value (—130.6) at N

= 0.32 X 10^/cc and then in­

creases as N increases It becomes positive at jV' =

—0.95 X 10^ per co and maxi­

mum at N = 10^/cc. It then decreases, becomes negative at — 1.58x 10^/cc A t­

taining maximum negative value at A — 3.2xlOVcc it increases and becomes posi­

tive at A = 6.4xlO '‘/oc A t­

taining maximum positive value at = 10*^/cc, it again decreases and becomtSs nega­

tive at A = 1 26 X 10^/cc.

V = Vc

= 5.48X

pQ starts with the value 0.88 at A = 0.32 X lO^/cc and then increases as A increases.

It becomes maximum at A

= 3.2xl0^/cc and then de­

creases as A increases and becomes negative at A = 13.34 xlOVcc.

14,.J starts with the value 0 186 at A = 0.32xl0^ per cc and then increases as A increases upto A = lO^oc.

It then falls off very rapidly and becomes negative at A

= 1.19 X 10^00. Attaining maximum negative value at A = 3.2xl0^/cc it increases with increase in A and be­

comes positive at A = 13.34 xlO^/cc.

V = lO’ /sec [Iq starts with the value 1.72 at A = 0.32 X 10^/cc and then decreases as A increases Tt becomes negative at A = W loc.

/ij starts with the value 0.864 at N — 0.32 X 10^/cc and then decreases as A increses i t becomes maximum at A

= 10^/cc and then decreases with increasing value o f A . It becomes negative at A

= 20 X 10^ per co.

5. Conclusions

The following conclusions have been drawn :

1) In case of low electron number-density, the ordinary phase refractive index is greater than the extra-ordinary phase refra(5tive index for Y = < 1

V

c pr

and vic€> versa for T ~ ^ > -1 . When the exploring wave frequency becomes sufficiently large, the ordinary and the extra-ordinary phase refractive indices have almost the same value.

2) The curves showing the values of the ordinary and the extraordinary group refractive indices for v = 10®/sec and for v — lO'^/sec, are of different type.

3) The curves showing the group refractive index for v > vc are of different nature when compared with the corresponding values for v < vc. The curves for p — Vc, although dissimilar in some respects to the curves for v < Vc, have simi­

larities with those for v > vc- The observed dissiinilarities between the curves for

> Vc and those for v < vg are found both when T > 1 and T < 1.

O foup Tefractive index curves for radio wave etc*

115

6. Acknowledgement

This work has been carried out under the supervision of Professor S. R.

Khastgir, D.Se , F.N.A. 1 am indebted to him for his keen interest and constant help. My thanks are also due to ox-Principal M. N. Datta, M.A., for his interest and encouragement.

References

Gibbons J. J. & K a o 1967 Pennylvania State Umveraity Science Report N o . 9 2 ; Journal Atoms.

Terr. Phya. 11, 161.

M u rty Y . S N . & Khast& S. R . 1960a J Atmos. Terr. Phys. 17, 309.

Miu'fcy Y . S N . & K h astgir S. R . 1960b J. Gcophya. Res. 65, 1449.

M u rty Y . S N . & Kh astgir S. R . 1961 J . Atmos. Terr. Phys. 21, 65.

Murby Y . S. N . & Kh astgir S. R 1902 J . Atmos. Terr. Phys. 24, 141.

M u rty Y . S, N . & K h astgir S. R . 1963 J. Atmos. Terr. Phya. 25. 103.

Bhmn D . H . & W h ale H . A . 1962 J. Atmos. Terr. Phya. 2, 85.

TJnz H . 1961 J. Atmos. Terr. Phya. 20, 189.

W h a le H . A . & Stanley, J . P . 1960 J. Atmoa. Terr. Phya. 1, 82.

11 6

K. K. Deb

A' A X V

N e, m y

Pu H c

7

V

Vc

Appen dix. Notation and Symbols Used

— Group refractive index

— Phase refractive index

— Absorption index

— Angular frequency o f the exploring wave

_ 4^TrNe^

— Electron-number density

\

= Charge and mass respectively of an electron \

^ P Ph '

V _ eU

~ m c

— Earth’s magnetic field Velocity o f light

= 7 COB 0\yrp = y sin 0

— Angle between the direction of propagation and the positive direction of the earth’s magnetic field.

— Phase-difference between tlie normal and the abnormal compo­

nents of the magnetic vector of the radio-wave.

— Electron collisional frequency.

= Critical colhsional frequency.

6' =

- A ' - f )