Sum1mary
Starting from Maxwell’s equations, a theoretical investigation of the propagation of a quasi-staticE-mode in a longitudinally magnetized plasma slab is made. A transmission-line equation is obtained for the electric field and the Ritz-Rayleigh variational method is used to minimize the error over the cross-section of the slab, when a trial function for the field distribution in the plasma is assumed. A parabolic distribution is taken as an analytical model for the electron-density profile in the cross-section, and the electron density is supposed to vanish at a point outside the plasma slab; in the limit for the zero point to go to infinity, uniform case-equations are recovered. Under these conditions, a dispersion relation is derived and dispersion curves are calculated and plotted for some numerical cases of interest. In the homogeneous case a comparison is made between the approximate solutions and the exact solutions.
Riassunto
Si studia la propagazione di un modo TM in una « slab » di plasma magnetizzato longitudinalmente. Si è supposta una distribuzione parabolica per la non uniformità trasversale della densità elettronica. Si sono calcolate le curve di dispersione applicando il metodo Ritz-Rayleigh. Il tracciamento di queste curve è stato effettuato per alcuni casi interessanti.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- x, y, z :
-
co-ordinate axes, as in Fig. 1
- E :
-
electric field of the propagating wave
- H :
-
magnetic field of the propagating wave
- E zp(u):
-
cross-sectional distribution of the longitudinal electric field component inside the plasma
- E zv(u):
-
cross-sectional distribution of the longitudinal electric field component outside the plasma
- E 0,E 1 :
-
amplitude constants ofE zp(u)
- β :
-
longitudinal propagation constant
- u :
-
βx
- 2d :
-
slab thickness
- 2D :
-
distance between outside parallel metal plates
- l :
-
value of |x| (>d) at which the electron density is zero
- B 0 :
-
longitudinal static magnetic field
- \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \in } \) :
-
dielectric constant tensor
- ε 1,ε 2,ε 3 :
-
dielectric constant tensor components
- μ 0 :
-
free space permeability
- δ :
-
βd
- Δ :
-
βD
- λ :
-
βl
- f(u):
-
cross-sectional, symmetric distribution of the electron density, normalized so thatf(0)=1
- L :
-
second-order linear differential operator
- μ :
-
λ/δ
- μ :
-
parameter characterizing the cross-sectional inhomogeneity (>1)
- ω :
-
angular frequency of the propagating wave
- ω b :
-
electron cyclotron angular frequency at theB 0 field
- ωp0 :
-
plasma angular frequency at thex=0 center of the slab,X 0=ωp0 2/ω2=1/ω2,Y 2=ω b 2/ς2,a=ω b 2/ωp0 2, τ=1−(1-Y 2)/X 0, τ0=1−1/X 0.
References
G. A. Postnov:Radio Engin. and Elec.,10, 63 (1960).
S. S. Jha-Kino:Journ. of Elec. and Cont.,14, 167 (1963).
V. L. Granatstein:A First-Order Perturbation Expression for Inhomogeneous Plasma Guides. Paper presented at the meeting of the American Physical Society, Division of Plasma Physics, San Diego, Cal. (November 1963).
V. Y. Kislov andE. V. Bogdanov:Proc. of the Symposium on Electromagnetics and Fluid Dynamics of Gaseous Plasma (New York, 1961).
Author information
Authors and Affiliations
Additional information
This work has been sponsored by the Cambridge Research Laboratories, OAR through the European Office, Aerospace Research, United States Air Force under Contract AF 61(052)-145.
Rights and permissions
About this article
Cite this article
de Santis, P. Quasi-static waves in inhomogeneous magnetoplasma slabs. Nuovo Cim 35, 823–837 (1965). https://doi.org/10.1007/BF02739345
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02739345