Variation of Transmission in the Ionosphere

R . Misra

Contai P, K. College, Midnupore, West Bengal AND

B. Chakravarty

Depit. of Phgsics, Indian Institute of Technology, Kharagpur, West Bengal

{Beceived G March 1973)

TJio valuos of non-doviative and doviative absorptions vary from region to regioji depending upon eltK^tron density, totaJ particle density, and tc'ni- peratiire of tlio region, l^esent work deals with the variation o f ab­

sorption, caleulat(vi from different^ formulae, with altitude ranging from 60 km. to 200 km., using 5 MHz weaves incidejit vertically, for a fixed value o f y (~ 28°), th(^ solar zcmith angle. The variations of absorption are presented l^y graphs.

1. Introduction

Tlie absorption suffered by a radio w ave in traversing a distance 8 tlirough an ionizcni region is given b}^

Indian J. Phys, 48, 406-411 (1974)

Variation of transmission in the ionosphere

1 = exp ^ — J Kds"^ , (1⁾

where 7 and /j, are respecively t}i.e power received and incident on the region responsible for absorption, K is the co-efficient o f absorption, and ds is an element of path length. Calculation of total absorption is essentially the evaluation of J kds which includes factors like, particle density, temperature, electron density etc.

2. Calculation and Results

During the process of transmission a wave may penetrate a region if its frequency be greater than the critical frequency o f that region. This critical frequency depends upon the electron density o f that region and is given by

eW_max

rrm ... ⁽²⁾

Where c and m are the charge and mass o f the electron and Nmax i® the m axim um number o f electoons per c.o. o f the region.

For any wave travelling through a region in the ionosphere non-deviative al)sorption occurs if the frequency of the wave he much greater than the critical frequency of the region while deviativo absorption occurs for waves of frequency slightly greater than the critical frequency o f the region concerned.

After penetrating the region the wave will ultimately be reflected from a region where the frequency o f the wave will fall short o f the critical frequency and it will return to earth by traversing each region twice in its passage.

I f V bo the value o f collision frequency of particles with electrons at a height z above the datum level and bo its value at z = 0, then

V * ,

whence Z

=

(3)

(4) whore h is the average height o f the region above eartJi’s surface; /(.„ the Ixeight of the reference level above the earth’s surface and H, the scale height given by

- (S) whore R in the molar gas coiifltani; T, tlie absolute tempt^rature of the region concemod; M, the moan molecular weight of the constituents of the region; g, the acceleration due to gravity. The value o f v may bo calculated by the formula given by Nicolet (1963) and used by Chapman & Little (1967)

i^ = 6.4xlO-^<»wT^ ... (6)

where n is the total particle density of the region concerned. Wo also know that

/o*

: - (7)

who 0 is tho electron density at the level of maximum electron production at 0 and is coimocted to Nmax by

Nmao = No c o e i x , - W

Hence from eqs. (2), (7) and (8) /# and/c are rolafrxl by the formula

fo^

coa*

₍₉₎

The values o f total absorption (both deviativo and non-deviative) could be calculated from different formulae as shown below :

I. Tho total absorption due to double passage o f any wave through a region may be given by the formula as used by Jaeger (1947)

(10)

Using relation (9) this may be written as

^ c sec X f

4 0 8 R . M isra and B . C hakravarty

(11)

The calculated values of absorption for single passage of the wave are shown by curve I in figure 2.

Fig. 1. Plot of Ni^ x against h in kmH

IT. At lower altitudes the value of v is generally high. Hence the values of absorption at those regions for singki passage of the wave through it could be calculated by the formula

J me i fi{47T^p-\-p^) ⁽1 2)

The values of absorption calculated at different altitudes are presented graphically by curve IT of figure 2.

III. As the altitude increases the value of v® becomes smaller and smaller becoming negligible for much higher regions. Hence v® may be neglected in com­

parison with (27t/)® in eq. (12) for these regions. In such cases the total absorption for single passage of the wave will be given by

= „ - V ( - *• (>»'

J m e (2 77/ ) * J n

The integral in eq. (13) is evaluated in two ways

(i) By graphical method-here the product o f Nv is plotted against height as shown in figure 1 and the area under the curve gives the value o f the integral within the limit for which absorption is to be ealoulated.

(ii) It is evaluated for a particular region hy the direct multiplication of the mean values o f N and v with da, considering the values of N, and v to be constant over the finite value o f da.

The calculated values o f absorption by the above two methods are given in curves I, TIA and IIIB o f figure 2 respectively.

Aprtrvoim

Fig. 2. Variation of absortion with altitudes.

IV. From magneto-ionic theory it was shown by Ratcliffe (1962) that the absorption per unit path o f the wave is given by

(14)

where fi is the re& aotive index o f the region.

Rawer has show n th at the value o f /i is given b y

;t» = l . /o* (16)

4 10 R . M isra and B . C hakravarty

where is the g³aromagnetic frequency due to earth’s field in that region. Neg­

lecting fff in com parison with / , Rawer puts finally.

f 2

A fter some sim plifications (14) becom es _/c® sec* X k = V

(16)

(1'

Taking regions o f finite thickness and supposing tliat N, v ote. remain constant in that region , the value o f k m ay be m ultiplied b y the tliickness o f the region under consideration and the values o f absorption calculated. Th calculattKl values are presented in figure 3.

Fig. 3. Variation of absorption with altitudes.

3. DiscrssioN

The values o f absorption are calculated taking N, v, H etc. from R ocket Pannel data (1962) and from Chapman & Little (1957). The values o f absorption vary for regions at different altitudes depending upon the values o f N, v, H etc. o f that region. The value o f J ^+0kds is found out with mean values o f the parameters

h

and plotted against the mean height o f the regicm i.e. h + 5 . I t is seen from the graph th a t aU o f them have almost similar features, e.g. m axim um absorption ooouring at about 90 kms. The original Jaeger’s form ula was basioally derived

for deviative loss. But since the approximation /e//-+ 0 is made, the formula is reduced to eq. (10) and as the condition/c < < / is satisfied, eq. (10) may be used for non-doviative loss which has been pointed out by Ratcliffe (1962). Eq. (13) generally applies to altitudes above 80 kms., where the condition of derivation of it may be applied, but it is normally used by many workers for lower altitudes also. Eq. (12) may be reduced to eq. (13) only if v® < < (27

/)® which is the case for higher altitudes. This could also be seen from figirre 2 that at higher altitudes v®<<(2ff/)® and the curve II coincides with the ourve III. Eq. (14) was mainly derived for deviative loss only. But as at lower altitudes the value of fe < < / and the value of ft do not appreciably alter from (1) and the condition of non-deviativo loss is satisfied. Under such conditions eq. (14) may be approxi­

mately applied to calculate non-deviative loss idso. Thus we see that or a transmitting wave non-doviative absorption occurs at lower altitudes but at lugher altitudes as the value of/c approaches / the absorption becomes deviative.

It may be noted that the values of absorption calculated from eq. (11) are much higher than those from other formulae as is evident from the graphs also.

The regions for this difference is not clearly understood and is under further investigations.

Bevebekoes

Chapman S. Little C. G. 1967 Jr. Atmos, and Terr. Phys.. 10, 20.

Jaeger J. 0. 1947 Proc. Phys. Soc., 59, 87.

Nicolet M. 1953 J. Atmos. Si Terr. Phys, 3, 200.

Ratcliffe J. A. 1962 The magneto-ionic theory and its application to the Ionosphere pp. 165-116.

Rawer Karl The Ionosphere

Rocket Pannel 1952 Phys. Rev. 88, 1027.