Pramhoa, Vol. 7, No. 6, 1976, pp: 385-388, @ Print~ in India.

Excitation of multilayered plasma columns with the ring of magnetic currents

SUBHASH CHANDRA SHARMA and J S VERMA Plasma Research Division, Department of Physics, Birla Institute of Technology and Science, Pilani 333031

MS received 30 April 1976; in final form 28 July 1976

Abstract. The excitation of gaseous plasma column having semiconductor plasma columns on either side is studied with the excitation source being the ring of magnetic currents. The whole structure being cylindrical i n shape, contains the conductor along its axis. The effect of radii of all the columns including that of the ring on radiation pattern, is studied which shows a peak of maximum radiation in a certain direction along with some other less ntense peaks. In most Cases the peak occurs roughly at 61 ° at which fine structure is given. Also three intense peaks of radiation occur when radius of the plasma (outer semiconductor)column is 0.058 m.

Keywords. Plasma; ring source; leaky waves; radiation field.

1. Introduction

Excitation of the plasma columns with the help of sources of electric and magnetic currents has been studied by various workers (Tamir and OliIxer 1962, Gupta and Siagh 1967, Dhani Ram and Verma 1972, Sharma e t a l 1975 a, 1975 b). Such problems find application in guided and enhanced radiation modes. We consider here only the radiation mode. Bachynski (1967) and Ram Chandra and Verma (1976) have reviewed the characteristics of various types of excitation sources in and outside plasmas. Inside the plasma the presence of the source appears a bit difficult from the experimental point of view. In the present theoretical study,, we have therefore taken the source as situated in ff.e air so as to be more closer on experimental side.

2. Analysis

We have studied the semiconductor plasma column (radius c), gaseous plasma column (radius d) and semiconductor p_lasma column (radius e) while excited by a ring of magrteticcurrertts (radius a)which is assumed t o be situated in the air (radius b). The geometry consists of a central conductor along its axis of radius a 1 (al < b < c < d < e). The source is assumed to be situated at z = 0 plane. This geometry is depicted in figure 1. Following Dhani Ram and Verma (1972), one cart arrive at the following solutiorts for different radial zones for first asymmetric mode in cylindrical coordinates.

h x = A1J1 (Vop) + B 1 Y a (Vop) a x < p < a.

h H = A2JI (Vop) + B z Y 1 (vop) a < p < b

P - -3

(l) (2)

385

386 Subhash Chandra Sharma and , I S Verrna

CENTRAL

FREE SPACE CONDUC'rOR or ;~AmUS a t

2 , L/ / s 1 i?::e'..~'-':,.'~':.~ :'. ~':'~:'::-~.;~.'~ /

- . ~ K I I I ~'~-----Im,..Z A~, 'L

AIR COLUMN[,~a.~------RING SOURCE OF . . . . . . . . . . PI . . . . . . . RADIUS ~,1'

AIR COLUMN I ~'.-:rT,':'~"..'~..r ,~.::-.',- ",:.:'~ ~.,.. ..... ; ,...'-~.. . . . . . . .,. , . , t.;~,~;. 2

MAGNETIC RING SOURCE FREE SPACE ,Uo,C 0 ,~

- 0 P L A N E S E C T I O N AT -E.=O

Figure 1. column. Region 2: Gaseous plasma column.

h TM = A3JI (vzp) + Bz Y~ (v~) b < p < c

h', = "4,]1 (v p) + "4Y (v p) c < p < d

hv = As J1 (vsP) + B5 Y1 (v~p) d < p < e

h v' = A ~ H 1 (1) (Vop). e < P-

Geometry of the problem analysed. Region 1: Semiconductor plasma

(3) (4) (5) (6)

Here h stands for the fourier transform o f / / ¢ . J , , Y, and H, (1) are respec- tively the Bessel's function of first kind, second kind and Hankel's function of first kind of n-th order.

vo ~ = ko "~ - - k , 2, vi z = k02¢.~ - - k , 2, vl 2 = ko2Et - - k , ~

and

ko z = W~ #o¢o.

Here rv and k, are respectively source frequency and propagation constant. The free space permeability and permittivity are /z0 and c0 respectively. ~ and ~ stand for the relative permittivity of semiconductor and g~seous plasma columns respectively. Gaseous plasma colmun is supposed to be lossless while semi- conductor plasma column is assumed to be lossy. Following Dhani Ram and Verma (1972), one can find out the magnitude o f the amplitude o f the radiation field, i.e., [ "46 ] (k, = ko sin 0) with the help of the steepest Descent method.

The values of [ "4~ ] have been computed using an IBM-1130 computer against various values of aT, a, b, c, d, e and gaseous plasma frequency (w~).

3. Conclusions

The amplitude of the radiation field is calculated for the values of the parameters e.g., w = 2zr × 1011 rad sec -1, wpl = 2 x 10 TM rad sec -1, semiconductor plasma frequertcy w,s = 3 x 1013 rad/sec, collision frequency of semiconductor plasma column = 10 lz rad sec -1, a 1 = 0"001 m, a = 0" 185 m, b ----- 0"025 m, c = 0"035 m, d = 0" 045 m, e = 0" 055 m. The general behaviour of the field pattern is given irt figure 2. These plots show the zigzag variation of amplitude of the field but in

Plasma excitations 387

I 0 i

B

g

c 10

.J u.i E

z O -I

I

w o

:7

<

x 16

I F'; i • I I I t l I I I

t l I l " I / t I I I i

I I I i I I I I I i i "" ~

f t

/

J /

I I 1 L 1 1 1 i f I V I I I i . 6 18 30 42 54 66 78 90

e ( in degrees }

Figure 2. Radiat ion field for the following parameters : - - b = 0 . 0 2 8 m , al = 0.001 m, e = 0 . 0 3 5 m , d = 0 . 0 4 5 m , e = 0 . 0 5 5 m . _ M _ c = 0 - 0 3 8 m , al = 0.001 m, b = 0 . 0 2 5 m , d ~ 0 . 0 4 5 m , e = 0 . 0 5 5 m .

Table 1. F ine s tructure of the radiat ion peak

Direct ion of the Amplitude of the radiat ion peak Value of the parameters radiat ion field

(in degree) (in relative units)

61. 63330 wvl = 3 x 101° lad sec -1 13747.8000

61. 62660 b = 0.028 m 12040.8800

61. 62660 b = 0.028 m, c = 0 • 038 m 41519.0500

61. 63330 10399.0500

61. 83300 e = 0.058 m 10156.7200

63- 39320 103. 8167

61- 63330 d = 0.048 m 1659. 2700

Values of parameter unless quoted in the table are a x = 0.0001 m, a = 0.0185 m, b = 0 . 0 2 5 m , e = 0 . 0 3 5 m , d = 0 . 0 4 5 m , e = 0 . 0 5 5 m , w = 2 7 r x 10 TM rad sec -1, wpl = 2 × 10 l° t a d sec -1, w~ = 3 x 10 is rad sec -1.

388 Subhash Chandra Sharma attd J S Verma

all cases a peak. of maximum intense radiation field occurs and this peak is always noticed in the direction around 61 °. Only for e = 0"058m three peaks occur. The fmo structure of these peaks are depicted in table 1, which clearly shows that the strongest peak occurs at 61"6266 ° for the values o f b = 0 " 0 2 8 m and c = 0"038 m.

The results presented here are purely theoretical and the explanation for such a type of radiaton mode is provided by Tamir and Oliner (1962)with the help of leaky wave excitation on the plasma columns. The physical realization of the geometry studed here is also not difficult. Occurrence of peak of maximum radiation in a certain direction may in principle be useful to send the enhanced radiations in a preferred direction.

Acknowledgements

One of us (SCS) is indebted to CSIR (New Delhi) for a research fellowship. The help rendered in computation by the [PC staff of the Institute is gratefully acknowledged. The authors also thank the referees for useful comments.

References

Bachyaski M P 1967 RCA Review 28 111 Dhani Ram and Verma J S 1972 Indian J. Pure Appl. Phys. 10 716 Gupta K C and Singh A 1967 Int. J. Electron. 23 323 Ram Chandra and Verma J S 1976 (to be published) Sharma Subhash Chandra, Ram Chandra and Verma J S 1975 a Indian J. Pure Appl Phys. 13 829 Sharma Subhash Chandra, Ram Chandra and Vcrma J S 1975 b Indian J. Radio Space Phys.

4 289 Tamir T and Oliner A A 1962 IRE Trans. Antenna Propag. AP-10 55