INFLUENCE OF DISSIPATIVE PROCESSES ON THE PROPAGATION OF GUIDED ELECTRON PLASMA WAVES ON A PLANAR PLASMA SLAB

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INFLUENCE OF DISSIPATIVE PROCESSES ON THE PROPAGATION OF GUIDED ELECTRON PLASMA

WAVES ON A PLANAR PLASMA SLAB

P.K. Cibin

To cite this version:

P.K. Cibin. INFLUENCE OF DISSIPATIVE PROCESSES ON THE PROPAGATION OF GUIDED

ELECTRON PLASMA WAVES ON A PLANAR PLASMA SLAB. Journal de Physique Colloques,

1979, 40 (C7), pp.C7-599-C7-600. �10.1051/jphyscol:19797290�. �jpa-00219279�

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JOURNAL DE PHYSIQUE CoZZoque C7, szcppZQment au n07, Tome 40, JuiZZet 1979, page C7- 599

INFLUENCE W OISSIPATM PROCESSES ON THE PROPAGATION OF GUIDED ELECTRON PLASMA WAVES ON A PLANAR PLASMA SLAB

P.K. Cibin.

Boris ~ i d r i z I n s t i t u t e of NucZear Sciences, Beograd, YugosZavia.

The aim of this paper is to obtain the propagation and attenuation characteristics of guided electron plasma waves propagating on a planar plasma slab placed between di- fferent dielectrics in the presence of dissipative processes.

We consider a planar plasma slab of ufii- form density,thickness a and with the boundary planes parallel to X-Z plane.

We describe plasma by equivalent permittivity

and neighbouring dielectrics by

E ~ = Aexp (-By+ jay) + B ~ x P ( B Y - ~ ~ Y ~ x

[

The boundary conditions (continuity of tangential components of electric and magnetic field), with the condition that the electric and magnetic field must be finite everywhere, form set of four linear homoge- neous equations for the four constants of integration. The requirement that nonzero solution of this set should exist, yields the dispersion relation

It is evident that the propagation coe- E ~ = E ~ ~ - ~ E ~tg ~ = E ~ ~ ( ~ - ~(2) fficient

B

and the attenuation coefficient

a can be given by E ~ = E ~ ~ - (1-j tg 62) ~ E ~ ~ = E ~ ~ (3

( E ~ - E ~ ) ( E -E 1 2 P where tg d l and tg 62 are loss tangents of ^B= -In

2a ( E +E

B

( 6 2 + ~ p ) the dielectrics, w, up and v are operating, 1 P

plasma and collision frequency, respectively.

In the presence of dissipative processes, guided electron plasma waves must attenuate /1-3/ and Z dependence of electromagnetic fields must be given in $he form exp(-az

-

j B z ) , where a and

B

are the attenuation and propagation coefficients respectively. The introduction of this dependence into Maxwe- ll 's equations yields

where ko is the wavenumber in the free spa- ce, E~ the permittivity of free space and E, the relative dielectric constant.

In the slow-wave limit /1/ we can assume that

ja+j~/~*I w

~ € 1

^{( 6 )}

and then the general solution of eqn.(4) is

d aJ

Fig. 1

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797290

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If the imaqinary parts of the permitti- vities are much smaller in magnitude than the respective real parts, the propagation coefficient $ reaches the maximum values at the resonance conditions

E =-E and E = - E

pr lr pr 2r' (1 1)

and these values are given by

v

For the lower resonance frequency the attenuation coefficient a is equal to n/4aI and for higher resonance frequency is equal to 3a/4a. Between the resonances the propagation coefficient reaches the minimum value for

This minimum value is given by

In this case the attenuation coefficient is equal to s/2a.

The normalised propagation and attenuation characteristics are plotted for vari- ous ratios of collision and plasma frequency and ~~,=15. ~ ~ ~ tg = 61=tg 62=0, in 3 , fig. 1.

REFERENCES

/1/ A.W.Trivelpiece, R.W.Gould, J.Appl.Phys. v.30 (1959) 1784, /2/ P.J.B.Clarricoats, A.D.Olvef, J . S . L .

Wong, Proc. IEE, v.113 (1966)755, /3/ B.~.AniEin, Fizika, v.1(1968)69,