Interstellar Communication [in Russian], Nauka, Moscow (1969). V. I. Siforov, "Some problems of finding and analyzing radio emission from other civilizations, ...
LITERATURE 1o
2.
3~
4. 5. 6. 7. 8.
CITED
L. M. Gindilis, S. A. Kaplan, N. S. Kardashev, et al.~ Extraterrestrial Civilizations: Problems of Interstellar Communication [in Russian], Nauka, Moscow (1969). V. I. Siforov, "Some problems of finding and analyzing radio emission from other civilizations, n in: Proceedings of All-Ufiion Symposium on Extraterrestrial Civilizations, Byurokan [in Russian], Akad. Nauk ArmSSR (1965)~ L. M. Gindilis, Izd. Vyssh. Uchebn. Zaved., Radiofiz., 1_6.6,No. 9, 1448 (1973). J. M. Wozencraft and I. M. Jacobs, Principles of Communication Engineering, Wiley-lnterscience (1965) A . N . Dukhovner, Signals and Signal Conversion in L i n e a r Circuits [in Russian], SZPI (1970}. A . N . Dukhovner, Izv. Vyssh. Uchebn. Zaved., Radio61ektron., 16, No. 8, 92 (1973). A . N . Dukhovner, " T r a n s m i s s i o n of radio signals to e x t r a t e r r e s t r i a l civilizations," Ref. Zh. Obshch. Vopr. Issled. Kosmich. P r o s t r a n . , 7, Abs. 7, 62.364 (1974). G . V . Glebovich and I. P. Kovalev, Broadband T r a n s m i s s i o n Lines for Pulse Signals [in Russian], Soy. Radio, Moscow (1973).
LINEAR
TRANSFORMATION
IN I N H O M O G E N E O U S A.
A.
Zharov
OF
ELECTROMAGNETIC
ISOTROPIC and
I.
G.
PLASMA
WAVES
LAYERS
Kondrat'ev
UDC 538.576.2
The authors d i s c u s s the effect of spatial dispersion in plasma on the reflective c h a r a c t e r i s t i c s of inhomogeneous resonant plasma l a y e r s that differ in the way in which the permittivity e p a s s e s through z e r o . It is shown that, when there is spatial dispersion, complete s c r e e n i n g does not o c c u r and part of the energy leaks through the layer. Using the example of a quadratic l a y e r , it is shown that, when e has a z e r o of o r d e r higher than the f i r s t , the t r a n s f o r m a t i o n of the energy of the incident field into longitudinal (plasma) waves is nonresonant in nature (there is no resonant absorption). As shown in [1], inhomogeneous isotropic plasma l a y e r s - x 0 _< x - x 0 in which the permittivity has the distribution
e(x) = (-- 1)m xm/x~
(nz > 1)
(1)
(losses being ignored) a r e ideal s c r e e n s for t r a n s v e r s e magnetic waves (or TM waves with r e s p e c t to the x direction); s o - c a l l e d resonant s c r e e n i n g o c c u r s . The entire region lying behind the plane in which e p a s s e s through z e r o is screened: E---- H--=0
(x>0).
(2)
When there a r e l o s s e s in the plasma, complete s c r e e n i n g does not o c c u r and part of the e n e r g y p a s s e s through the layer. It is of i n t e r e s t to determine the way in which the field v a r i e s under condition (1), allowing for spatial dispersion resulting f r o m t h e r m a l motion of the particles. This is the topic to be taken up in this s h o r t paper. In so doing, we have been able to resolve the h e r e t o f o r e open question of the t r a n s f o r m i n g properties of r e s o n a n t regions of inhomogeaeous plasma in which e has a z e r o of o r d e r higher than the f i r s t (see s u r v e y s [2-4]). w A s s u m e as follows that a plane TM electromagnetic wave is incident f r o m a vacuum on plasma l a y e r (1) *: Hy = 1 e x p ( - - i % k o x - iTleoz), *The p r a c t i c a l rationalized s y s t e m of units is employed; e 0 and ~0 are the permittivity and permeability of a vacuum and e is the relative permittivity of the plasma. The time dependence is taken in the f o r m e iwt. S c i e n t i f i c - R e s e a r c h Institute of Radi0physics. T r a n s l a t e d f r o m Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 20, No. 10, pp. 1474-1478, October, 1977. Original a r t i c l e submitted April 8, 1976; r e v i sion submitted April 26, 1977.
1014
0033-8443/77/2010-1014507.50 9 1978 Plenum Publishing Corporation
(3)
E~ = --- Zo% exp (-- i % k o x - iTkoZ), E~ = Z o 7 exp (-- i % k o x -- i'~.koZ),
where a 0 = f i - - - ~ -~, k0 = w e4-~0~, Z 0 = ~ . A s s u m i n g the dependence on the z coordinate of the field within the l a y e r to be d e s c r i b e d by the multiplier exp (-iyk0z), and omitting this multiplier in what follows, we witl have the following e x p r e s s i o n s f o r the components of the field in the l a y e r in the quasihydrodynamic a p p r o x i mation (see, e . g . , [5]): d d an Hy dx dHy 1 dx dE._x. (4)
as---z- ~ - ~ r
dx
+kg(~--~)H'=--'~'~Z0~---?~
- -ax - i - + ko~ (~ _ .~ o~, E~ =
where/3,~ = v,~/c 2 = ~r of the electron).
Zo
=
dx'
_
dHy
~r
(4,) d Ex
(4")
c2 0r is B o l t z m a n n ' s constant, T o is the plasma t e m p e r a t u r e , and m 0 is the m a s s
Even the solution of homogeneous equation (4) with a(x) in the f o r m (1) runs into c e r t a i n difficulties, as noted in [1]; these difficulties e s s e n t i a l l y have yet to be o v e r c o m e . In what follows, t h e r e f o r e , we will c o n s i d e r l a y e r s with permittivity en(X) , w h i e h d i f f e r s somewhat f r o m (1)(est(X)): ~n(X) = o ~t(x) + | iJT
(5)
(the s u b s c r i p t n will be henceforth omitted).* F o r the "new" l a y e r s homogeneous equation (4) coincides (T2(1 - ~ ) ~ y2n) with the c o r r e s p o n d i n g equation in the absence of spatial dispersion. This p e r m i t s us to a s s e r t that, in o r d e r to find a c o r r e c t solution for the problem in question, we can use the s a m e artificial p r o c e d u r e as in the ease of a "cold" plasma (see [1, 6] for details); specifically, we can replace the actual distribution e(x) by the auxiliary distribution , r-
~(x) = ~
(-
1)"7 x"/x'g
+ (- i)"x?/xy
(
- xo..
