Radio wave absorption in model ionospheric layers

Journal of Atmospheric and Terrestrial Physics, 1968, Vol. 30, pp. 1353-] 367. Pergamon Press, Printed in Northern Ireland

Radio wave absorption in model ionospheric layers

A. R. JAIN and C. S. G. K. SETTY Department of Physics and Astrophysics, University of Delhi, Delhi-7, India

(Received 30 October 1967)

Abshraot--Absorption suffered by a radio wave reflected in or passing through a Chapman layer approximating to either D- or E-layers at noon, for the overhead Sun, has been calculated graphically for the ordinary wave as a function of frequency for geomagnetic conditions appro- priate to Delhi (f~ = 1.20 Mc/s; magnetic dip = 42.44°). The absorption coefficients used in this calculation have been computed using the Appleton-Hartree formula. Absorption has also beeu computed using several approximate formulae in common use. Comparison between the absorptions calculated using the Appleton-Hartree formula and those other approximate formulae is made to find out the applicability of the approximations involved.

1. INTRODUCTION

ABSORPTION suffered by radio waves at a number of frequencies has been studied in the past both experimentally and theoretically. As the magneto-ionic formula given by Appleton and Hartree is too complicated to be used to interpret the observed absorption results, usually approximate formulae have been employed. Some of the common approximate formulae are listed in Table 1. The symbols and definitions used are listed in Section 2.

A summary of the observational results of various workers on frequency variation of total absorption is given in Table 2. I t is to be noticed from this table tha t the same law of frequency variation of absorption does not hold at all stations. APPLETON and PIGGOTT (1954) concluded from absorption measurements made at Slough tha t (f + f L ) -~ law was sufficiently accurate except near the critical frequencies of the E- and F-layers and below 2 Mc/s. Others have found tha t the absorption in the reflecting layer is also important and tha t the frequency variation of absorption is better represented by two terms, one which was given by Appleton and by Jaeger and another term to account for the absorption within the reflecting layer.

The object of the present work is to compute absorption suffered by radio waves at a series of frequencies incident vertically on model Chapman layers approximating to D- and E-layers when the Sun is overhead. The model Chapman layers are given in Table 3 and Fig. 1. The absorption is computed using various approximate formulae referred to by the serial numbers as listed in Table 1 and these results are compared with the absorption computed using the Appleton- Hartree magnetoionic formula. This latter formula will be referred to, hereafter, as the Exact Formula. All the computations have been made for the ordinary ray and for the geomagnetic conditions at Delhi (gyrofrequency, f• ---- 1.20 Mc/s. and dip. angle ---- 42.44°). The Exact Formula has been computed using the method of BAILEY and SOMERVILLE (1938) on the Delhi University computer IBM-1620. In case of reflection of the wave occurring within the layer, graphical integration

1353

Tab

le 1

. A

pp

rox

imat

e F

orm

ula

e

Fo

rmu

lae

No.

A

uth

or

Yea

r R

emar

ks

~e

z f~

, N.

dh

1 2m

cee

30

(£

0 -4

- f, O

L) 2

"~- p

2 B

OO

KE

R

a r

exp

(1)

q'/

'x

2 --

A

PV

LE

rOX

vo

Lv o

(~-i

-~z J

] '

4.13

3 A

(a

) (c

o 4-

wz)

2

3 A

PPL

ET

ON

19

37

4"13

3 A

(b)

wz

AX

I (a

) 4

(~ I

- a~

D 2

JA

~G

ER

19

47

AX

I (b

) 0.

) 2

A./

.f~\

5

¢t

71

J.-

=R

19

47

6 V0

----~H

El (ru

B)

¢

B 7

--

+

NA3(fMI)

(f +

/zP

8(a)

f hr O

J .X

Z(I

+

2Q

2co

tz0

) dh

o 2p

c (1

+

QIY

/.,) a

8(

b)

JAE

GE

R

1947

BIB

LE

an

d R

AW

ER

19

51

WH

ITE

HE

AD

19

56

1933

Q

uas

i-lo

ng

itu

din

al,

no

n.d

evia

tiv

e (Q

L-N

D)

1937

W

ave

~ua

ssin

g th

rou

gh

a C

hap

man

Lay

er

~av

e p

assi

ng

th

rou

gh

a C

hap

man

lay

er w

ith

a ~

1,

x=o

COL ~

0 in

3(a

)

"Wav

e pa

ssin

g th

roug

h a

Chapman

laye

r. F

unct

ion

I is tab

ulat

ed in

Tabl

e II

I of

Jae

ger'

s pa

per

I ~

4.13

3 for (~o ~

coL)

~

v o

>

¢oz

= 0

in 4

(a)

Wav

e p

assi

ng

th

rou

gh

a C

hap

man

lay

er k

=

v .

1 --

it z

2c

~

--47r

Ne-

-~ an

d Z

=

0.

~b[]

~----

is t

abu

late

d i

n /Z

2=

I -

mgoo

J ~

\ f

] T

able

II

of

Jaeg

er's

pap

er.

Wav

e re

flec

ted

wit

h i

n th

e la

yer

an

d X

=

0.

Val

ues

of

k an

d f

fz a

re s

ame

"~

as i

n 5.

F

l(f/

f•)

is t

abu

late

d i

n T

able

1 o

f Ja

eger

's p

aper

.

Fir

st t

erm

sam

e as

in

3.

Sec

on

d t

erm

is

for

no

n-d

evia

tiv

e ab

sorp

tio

n o

f a

wav

e re

flec

ted

in a

par

abo

lic

lay

er.

Der

ived

fro

m A

pp

leto

n H

artr

ee F

orm

ula

on

co

nd

itio

ns

/.t ~

>~

--

an

d

Z~

l-

-X,

/t ~

=

I--X

](1

-I-Q

xY

z)

YA

SUD

A

1963

Ass

um

pti

on

/~

~ is

av

oid

ed i

n W

hit

ehea

d's

Fo

rmu

la a

nd

val

ue

of~

t u

sed

is

1 X

1 1

+ Q

1YL)

+

z2x~

(1 +

2Q~

eot~

0)2/

t'~- ]

(1 +

~

/ .J

Dev

iati

ve

abso

rpti

on

neg

lect

ing

Ear

th's

m

agn

etic

fie

ld a

nd

on

co

nd

itio

n

(1 -

- u

S) >

~

, ,u

S ~

I m

eoeO

~.


Table 2. Emperical formulae of total absorption from the experimental results of various authors

1 3 5 5

Formula Authors ( --log p = ) Stations Remarks

1. APPLETOI~ and B/( f + f z ) 2 Slough Not valid near critical fre- PIGGOTT (1954) quencies of E- and F-layers

and below 2 Mc/s.

2. BEY~O~ and DAVIES A -t- BF(f/f~) cos Z Swansea B-Constant (1955) A-Constant absbrption in

lower layer.

3. DAWES and HAGO B Prince Rupert Frequencyrange: 2-5.2 Mc/s. ( 1955) the law holds only approx-

(f -t-ft.) ~ imately for m = 2.

4. SK~rI~ER and WRIGHT B Ibadan Frequency range of validity: (1956) (f + fz) 2-5.8 Mc/s.

5. WHITEKEAD (1957) B Slough and B and C show different (f + f z)~. + C Cambridge diurnal and seasonal varia-

tions.

6. RAG, M ~ z u l ~ u ~ and B Delhi Frequency range: 5-8 Mc/s. MITRA (1962) m = 1"1-2"4 with an

(f + fz)m average value of 1.8

7. YASUDA (1963) (a) B Central and (f + fz)2 North Europe

(b) B Kokubunj i Frequency range: (f % fz) 1.7-4.8 Mc/s.

8. R ~ A m Y R T Y and B Waltair Frequency range: 2-9 Mc/s. RAG (1964) (.f + A ) ~'~

Table 3. Model D- and E-layers

Parameter D-layer model E-layer model

.No(cm-8 ) 2 x 103 2 x 105

H(kms) 5 6

ho(kms) 85 110

• o(sec-X) 7.8 x 105 2 x 104

1356 A . R . JAr~ a n d C. S. G. K. SETTY

of absorption in the layer is carried out up to the height of reflection given by the condition X = 1.

A similar comparative study of approximate formulae with the Exact one for the phase and group refractive indices has been reported by DAVIES and Kr~G

135

125

115

E .x 105

~- es

85

75--

tO

(1961).

- /

l , , L i I I I I

Electron density, cm -3

Fig. 1. Model D- a n d E- layers .

k

P N

e

m

6

80

( 9 o ° - o )

co

COH

coL

co T

2. SYMBOLS AND DEFINITIONS

absorption coefficient

reflection coefficient

electron concentration.

electron charge.

electron mass

velocity of light

permittivity of free space

electron collision frequency

magnetic dip angle.

2~/, circular wave frequency

2~/H, circular gyrofrequency.

longitudinal component of circular gyrofrequency

transverse component of circular gyrofrequency

phase refractive index

(h - - h o ) / m reduced height


h e height of the peak of the layer

H scale height

fE critical f requency of E- layer

h r height of reflection of wave

a = 2% ]

;~ solar zenith angle,

when a ~ 1 ;

Xl = ~-~ (Cos a + S in a) - 2~/,~a 1 - i g as + O(a'~r")'

when a >~ 1 ;

x~ = 5 -~.

In formulae 2, 3, 4, 5 and 6 in Table 1,

v = ~o exp (--z)

A -- 4~N°e2 Veil m E 0 C

N o electron concentrat ion at the peak of the layer

v 0 collision f requency a t the peak of the layer

f Func t ion given by Jaeger and for (co 4- mr.) >> %, its value is 4.133,

Y r ~ YL tans 0 m l - 2 y L ( 1 _ X ) - 2 ( 1 - X )

41rNe s X - -

mgoO.)s

Y r °~T OJ

yL_~_~D__._ L 09

fD

Q1 = (1 + m l s ) 1Is - m l

m l /19.)1/~ Q2 - (1 + m12) 1/~ [(1 + - roll

1357

1358 A.R . JAIN and C. S. G. K. S~.TTY

3. RESULTS

3.1 Absorption in model D-layer Absorption in this layer has been computed for a series of frequencies using

the following formulae: (a) The Exact Formula, (b) Formula 4(a), (c) Formula 3(a), (d) Formula 3(b), (e) Formula 4(b), (f) Formula 8(a). These are plotted in Fig. 3(a). Fig. 3(b) is a replot of Fig. 3(a) on log-log scale. Figure 2. is a comparison of k(h) for f = 1.5 Mc/s. from the Exact Formula

and Formula 8(a).

II

9, ' I'i,

/ t ~L L

ii1 7 " /

~ 6

0) 5

• - / 0

I

I I I I I I I I I 70 75 80 85 90 95 I00 105 I IO

He igh t , krn

Fig. 2. Variation of absorption coefficient in D-layer at f = 1.5 Mc/s.

3.2 Absorption in model E-layer 3.2.1 .Reflection in the layer. The following formulae have been used to compute

the absorption upto the level of reflection. (a) Exact Formula (b) Formula 6 (c) Formula 8(b)

Radio wave absorption in model ionospheric layers 1359

Q.

.o

I - - 3(b)

, , ~ 8 ( o )

4,(0) " ~ . . . .

i T t 2

9"0 8 ' 0

7"0

6"0

5.0 4 '0

3 0

2'0

~ I-5

o I-0 0-9 o.s

<:{ 0"7

0 6

0 .5

0 4

0 .3

0-2

0.15 3 4 5 6

f, M c / s

(a)

Fig. S. Frequency variation of absorption in/)-layer.

- 4(0) ".~, x ',,

I I I I ~.5 2 3 4

f + fL, MC/S

(b)

A I I f 6 7 8 9

Figures 4(a) and 4(b) show k(h) for the cases (a) and (c) for f = 3 Mc/s. For the Exact Formula k(h) shows continuous increase up to the level of reflection whereas for the Formula 8(b) it shows sudden reversal near the point of reflection. In graphical integration k is taken to be equal to the value at the point of reversal up to the X = 1 level. Absorption for the cases (a), (b) and (c) are shown in Fig. 5.

3.2.2 Wave passing through the layer. In this case the following formulae have been used:

(d) The Exact Formula, (e) Formula 3(a), (f) Formula 3(b), (g) Formula 8(b), (h) Formula 5.

Figure 6 shows k(h) for cases (d) and (g) a n d f = 5 Mc/s. The integrated absorption for all the cases (d) to (h) are shown in Figs. 5 and 7.

The combined absorption for the wave passing through the D-layer and being reflected in the E-layer or passing through both the layers is shown in Fig. 8, where (-- log p)-ln is plotted against f. The three curves for f < fE correspond to cases (a), (b) and (c) of Section 3.2.1 and those for f > fE correspond to (d), (g) and (h)

1360 A . R . JAIN and C. S. G. K. SETTY

5

c

X &

8 "O

8 8

o .o .,(

60

54

,48

42

3E

3C

24

18

12

6

0

92

E x o c l _ _ ond B(b)

/ Y

L I I I I I I I I I 94 96 98 I00 102

(a)

h,

. 4 8

42

5 -~" 36

c 30

o i

X 24

8

u

.~ I Z

a 6 .~ ,

0

Exoc| - - I '

8(b) ~,./

/

hr /

I 1 l I I ~ I 102"2 102.3 102.4 102.5 i02.6 1027

Height, km

(b) Fig. 4. Var ia t ion of absorpt ion coefficient in E- l aye r a t .f = 3.0 l~Ic/s.


.o I 2.6

i 2.2

I .B

1.4

<[ I.C

0.6

0.2 I

0 8

- - 5 i

~ E x o c l 0nd 8(b) ; ( b ) ~ ~ E xoct 3(b)_.~, ,~,,,

3 ( 0 1 - - ~

f[ i

, q Ji L L [ I ~' 3 4 5 e. 7

f, Mc/s

Fig. 5. Frequency variation of absorption in E-layer (linear scale).

5 -ff

o X

~E

u

i,a

o .JD ,<

45

4.0

35

3.0

2'5

2"0

1-5

1.0

0.5 /

0

I I 9 0 I00

Exoct ! ond 8(b)

I I I I I I I I 0 IZO 130

Hei(jht, km

Fig. 6. Variation of absorption coefficient in E . l a y e r f o r f = 5 Mc/s.

1362 A . R . JAI~ and C. S. G. K. S~.TTY

==

o

<[

5 . 0 -

40 1

3 0 - -

2,0--

15

I.C

O.E

0 . 6 -

/0.4

Exoci 8(b) - - I , '

3(b)-~i '~-~- 5

31o ) ' " " ' , , , , ~

I I I I i I I i i I 0~-2 3 4 5 7 8 9 I0 t2 141618

f+fL, MC/S

Fig. 7. Frequency variation of absorption in E-layer (]og-]og scale).

I.C

O c

A 08 .9. 7 l" m 0.7

, .5 = '=' 0.6

~0 O'5 O

I 0-4

0"3

02

(I) Exoc! |ormulo

(2) S(o) for Oond 8(b) for E Ioyers

(3) 3 for D ond 6 for E Ioyers

(4) 3 for D ond 5 for IF Ioyers

{5) From Appleton ond Piggot!

I and 2

0 I Z 3 4 5 6 7 8 Frequency, Mc/s

Fig. 8. ( - - log p) 1!~ v s f , for combined absorption in D- and E-layers.


of Section 3.2.2. The straight line graph is taken from Fig. 4 of the A~PLETON and PIGGOTT paper (1954). In Fig. 9 ( -- log p) is plotted against effective frequency (f ~- fn).

4. DISCUSSION OF RESULTS 4.1. D-~ayer results

From Fig. 3a it is clear that only the Approximate Formula 8(a) given by Whitehead comes closest to the Exact Formula. The other approximate formulae

c o o. 1.5 o .o <~

8 - -

6 - -

5

4

¢n

2

0 6 - -

0 6 - -

(i) (2)

(3)

(4)

I and 2 ~ , . . - - - 4

V Exacl formula ~ '

3 for D layer 6 for E layer 3 for 0 layer .5 for E layer

I [ T I I I T I1 1.0 15 2 ~3 4 6 8 10

f÷ fL , MC/S

Fig. 9. Frequency variation of combined absorption.

with the magnetic field taken into account give values which are too small for frequencies less than 3 Mc/s. and those with the neglect of magnetic field give values which are too high for all the frequencies. Figure'3b shows that the absorption varies linearly on log-log scale for the approximate formulae while those for the Exact Formula and Formula 8(a) depart from linearity for frequencies less than 2 Mc/s, at which frequency absorption increases more rapidly. Table 4 lists analytical expressions for variation of absorption in the linear region for the various formulae.

Table 4. Empirical expressions for ( - - logp) from several formulae for D-layer

Formula No. (Table 1) Expression of" ( - - log p)

Exact l l / ( f + fL) ~'I 4 8/(f + fD ~'' 3 9 / ( f -I- fL) ~'°

8(a) 12/(f + fL) i'~

1364 A.R. JAIN and C. S. G. K. S~,TTY

4.2. E-layer results

Figures 4(a) and 4(b) show the rapid increase in absorption at f = 3 Mc/s., as the level of reflection is approached. In Fig. 4(b), drawn on an expanded scale, the absorption taking place within 500 m of the reflection level is shown. Table 5

Table 5. Absorption in E-layer (f < f~) using Exact Formula

Frequency Height of reflection Total absorption Absorption in last Me/s (Kms) (nepers) 500 m (nepers)

1.0 96.997 1.53 0.95 1.5 98.436 1.60 0.93 2.0 99.775 1.68 0.90 2-5 101.142 1.81 0.86 3.0 102.671 1.94 0.83 3.5 104.622 2.16 0.80 3.8 106.377 2.50 0.79

gives the total absorption and absorption within 500 m of the reflection level derived from the Exact Formula. I t is seen tha t the latter decreases slowly with frequency whereas the former increases rapidly with frequency. The orders of magnitude of both are the same. This result compares favourably with Whitehead's conclusion, tha t an appreciable amount of absorption occurs near the level of reflection.

In Fig. 5 for f < r E it is found tha t Formula 8(b) gives results in complete agreement with the Exact Formula. But for Formula 6 although the frequency variation of absorption is similar to tha t of Exact Formula there is progressive departure from it as frequency is decreased from the critical frequency. At f i f e ---- 0.25, the departure is 18 per cent and at f i fE = 0.5 it is 12 per cent. F o r f ~> rE, as the frequency is increased from critical frequency, the same argument holds for formulae 8(b) and 5. At (fifE) ---- 1-25 the departure is 27 per cent and at (fifE) = 1.5 it is 30 per cent. YASUDA (1963) made similar calculations and came to the same conclusions. The analytical expressions for absorption results in this case are given in Table 6.

Table 6. Emperical expressions for (-log p) from several formulae for E-layer

Formula (Table 1) Expression of ( --log p)

Exact Formula and 8(b) 110/(f -t-fL) 2'e 3(a) 26/(f -~ fL) :'° 3(b) 56/(f -p fL) ~'~

5 138/(f + / z ) 2"e

4.3. Combined absorption in D- and E-layers

Figure 8 gives combined absorption in D- and E-layers, where (--log p ) - l / ~ is plotted against f. This is conveniently compared with Fig. 4 of the Appleton and Piggott paper. The straight line graph in Fig. 8 is drawn from their Fig. 4. Although


comparison is somewhat unrealistic since the results of this paper .refer to the geomagnetic conditions at Delhi, whereas those of Appleton and Piggott refer to Slough, England, the following main features may be pointed out. The orders of magnitude of absorption for both cases are the same. The rate of increase of absorption below 6 Mc/s. from our analysis is more rapid. For frequencies near 2 Mc/s., and the critical frequency of the E-layer, absorption seems to go in the same way as observed experimentally by Appleton and Piggott.

I t is apparent from Fig. 8 that for frequencies less than fE the combined absorption in the D- and E-layers obtained from Formula 8(a) and 8(b) is in good agreement with the Exact Formula. Total absorption obtained using Formula 3 ion D-layer and Formula 6 for E-layer is also in excellent agreement with that of the Exact Formula for the frequency range 0.5 to rE"

Comparing Figs. 3 and 5 we find that with Exact Formula, for f < 2 Mc/s, D-layer absorption is greater than that of E-layer, for f near 2 Mc/s they are of equal magnitude and for f > 2 Mc/s, the E-layer absorption becomes greater. I t follows therefore that absorption in the E-layer can under no circumstances be neglected when the wave is reflected in the E-layer. Total absorption can be expressed more accurately by an expression of the type given by BIBLE and RAWER (Formula 7) than by Formula 3.

When f > rE, it is found (comparing Figs. 3 and 5) that at these frequencies E-layer absorption is greater than that of the D-layer. I t is obtained from Fig. 9 that the combined absorption in D- and E-layers according to the Exact Formula varies approximately as ( f -~ fL ) -2"64 rather than as (f W fL) -2"°° as obtained experimentally by Appleton and Piggott. This may be explained by taking the absorption in the F-layer into consideration. As the frequency increases towards critical frequency of the F-layer, absorption in F-layer, is expected to increase as in the case of deviative absorption in the E-layer, but the absorption in the D- and E-layers will tend to decrease. Hence, the effective frequency variation of absorption will be less rapid, thus decreasing the index of frequency variation law, bringing it closer to the experimental value. It follows from this that when the frequency range is close to the F-layer critical frequency the index may be expected to be lower than 2 as in fact observed by RAo et al. (1962). Further it may be stated here that when the D-layer absorption becomes important, as in winter, the index may be nearer to 2. (RAo et al. see their Figs. 1 and 2, p. 247).

5. CONCLUSIOI~S

Following conclusions may be drawn with reference to Tables 7-10, which summarise the results.

Table 7. Percentage error of absorption in D-layer computed from approximate formulae

Frequency Formula 8(a) 3(a) 3(b) 4(a) 4(b) Mc/s no.

1.O -~ 15 - -4I ÷89 --44 ~63 2.0 T4 --16 ÷65 --23 -I-58 3.0 ~-3 --8 -t-48 --9 -I-45 6.0 ~ 2 <2 -~26 ~2 ~26

1366 A . R . JA~N and C. S. G. K. SETTY

Table 8. Percentage error of absorption in E-layer computed from approximate formulae

Frequency Formula 8(b) 6 5 3(a) 3(b) Mc/s no.

1"0 <2 +18 - - - - - - 2"0 <2 +12 - - - - - -

3 " 8 < 2 < + 5 - - - - - -

4 " 4 <1 - - +15 --50 --31 5"0 <1 - - +27 --30 --5 6 " 0 < 1 - - + 3 0 - - 2 0 + 6

Table 9. :Percentage error of combined absorption in D- and E-layers at a series of frequencies computed from the Exact Formula

Frequency Absorption in D-layer Absorption in E-layer Me/s (%) (%)

i '0 75 25 2"0 44 56 3"0 25 75 3"5 19 81 4"5 16 84 5"0 20 80 6"0 21 79

Table 10. Percentage error of combined absorption in D- and E-layers using approximate formulae

Frequency Formula 3(a) for D-layer Formula 8(a) for D-layer Me/s and 6 for E-layer and 8(b) for E-layer

1-0 - 2 6 +11 2.0 +1 +1.3 3.0 +4 +1 3.8 +1 0 5.0 +17 0 6.0 +20 0

a. Absorption in D-layer. F o r m u l a 8(a) gives abso rp t ion wi th in 4 pe r cent , F o r m u l a 3(a) wi th in 16 per cent and F o r m u l a 4(a) wi th in 23 per cent a c c u r a c y for f requencies g rea te r t h a n 2 Mc/s. Below 2 lVIc/s the error increases rap id ly .

b. Absorption in E-layer. The resul ts are s u m m a r i s e d in Tab le 8. F o r m u l a 8(b) gives 2 per cent accu racy in the comple te f r equency range. F o r f < fE a n d f > 1.25 fE F o r m u l a e (6) and 3(b), respect ive ly , seem to give reasonab le accuracy .

e. Combined absorption in D- and E-layers. Tab le 9 gives re la t ive i m p o r t a n c e of D- and E - l aye r absorp t ions . F o r f < 2 M e / s , D- l aye r abso rp t ion is p r e d o m i n a n t . F o r f > 2 Mc/s., E - l aye r abso rp t ion becomes increas ingly i m p o r t a n t .

Tab le 10 shows t h a t F o r m u l a e 8(a) a n d 8(b) r e spec t ive ly fo r D- a n d E - l aye r s give good accu racy for f > 1 Mc/s. F o r m u l a e 3(a) and 6 give good a g r e e m e n t w i th the E x a c t F o r m u l a in the in t e rva l 2 < f < 5 (Mc/s).

d. Frequency variation of combined absorption. Refer r ing to Fig. 9, abso rp t ion in


the interval 1.8-3 Mc/s the f requency var ia t ion m a y be represented a~proximate ly b y ( f - t-fz) -1'5 law. I t is in fac t represented be t te r b y an expression of the t y p e given b y BIBLE and RAWER (Table 1, F o r m u l a 7). F o r / > 5 Mc/s., ( f -t- fz) -~'8 law fits approximate ly , when the F - l aye r absorpt ion is no t t aken into account . As f approaches the F - l aye r critical f requency the index of f requency var ia t ion law m a y be expected to decrease (see Discussion).

Acknowledgements--The authors wish to thank Dr. KE~-m~T~ DAVIES, ESSA Boulder Lab- oratories, U.S.A. for his comments and suggestions and Prof. R. C. M~zum)XR, Head of the Department of Physics and Astrophysics for his encouragement. Thanks are also due to Mr. M. K. VYAW~A~E for his assistance in computations.

The research reported in this paper was supported by a PL-480 Grant through the iN-BS and ESSA Laboratories, The Department of Commerce, U.S.A. under contract NBS(G)-44. One of us (A. R. J.) is indebted for the award of a Fellowship under the PL-480 Project.

DEFERENCES

APPLETON E.Y. 1937 APPLETOI~ E. V. and PIGGOTT W . R . 1954 BA~EX V. A. and SO~ERV~.T.~. J .M. 1938 BE~-~ON W. J. G. and DAvr~.S K. 1955

BIBLE K., PAUL A. and RAWE~ K. 1951 BOOER H . G . 1935 DAVrES K. and HAOG E . L . 1955 DAWES K. and KInG G. A.M. 1961 JAEGER J .C. 1947 RA_MA~AM-0-RTY Y. V. and RAO B.R . 1964 RAO M. K., ~ A R S. C. and MITRA 1962

S.N. S K r m ~ N. J. and W~mHT R . W . 1956 Wm.I,:S~AD J . D . 1956 W~a'I'~E~u J . D . 1957 YASUDA J.

Proc. R. Soc. A162, 451. J. Atmosph. Terr. Phys. 5, 141. Phil. Mag. 26, 888. Physics of Ionosphere, 40,

Society, London. J. Atmosph. Terr. Phys. 2, 51. Proc. R. Soc. A150, 267. J. Atmosph. Terr. Phys. 6, 18. J. RCS. NBS 65D, 323. Proc. Phys. Soo. 59, 87. J. Atmosph. Terr. Phys. 26, 849. J. Atmosph. Terr. Phys. 24, 245.

J. A$mosph. Terr. Phys. 9, 103. J. Atmosph. Terr. Phys. 9, 276. J. Atmosph. Terr. Phys. 10, 12.

Physical

1963 J. Radio Rcs. Labs. (Japan) 10, 213.

Documents

Radio wave absorption in model ionospheric layers