An approximate theory of electromagnetic wave propagation in a weakly relativistic plasma

Abstract

An approximate analysis of different types of electromagnetic wave propagation in a weakly relativistic electron plasma is presented. The particular case of wave propagation near the cold plasma cut-offs is considered, and possible applications of the results to diagnostics of magnetospheric parameters are discussed. It is pointed out that wave propagation near plasma resonances in some cases requires relativistic consideration, especially for extraordinary waves. Almost parallel right- and left-hand polarized waves as well as almost perpendicular ordinary and extraordinary wave propagation are considered in detail. It is shown that, in the vicinity of certain frequencies, relativistic effects on the refractive index of these waves cannot be disregarded even when the electron energy is quite small. The problem of wave energy focusing along and perpendicular to the magnetic field is considered with relativistic effects taken into account.

Almost perpendicular electromagnetic wave transformation in a weakly relativistic inhomogeneous plasma

“…FIGURE 1. Schematic presentation of the co-ordinate systems used by Sazhin (1987) (a) and in this paper (6).…”

“…The analysis of (1) appears to be simplest when we adopt the co-ordinate system presented in figure 1 (b) and assume that all the parameters vary along the z axis only. In such a case (1) can be simplified to 2where i x and i are unit vectors in the x and y directions respectively, e' is the dielectric tensor in the system shown in figure 1 (b) which is related to the corresponding tensor e in the system shown in figure 1 (a) (considered by Sazhin (1987)…”

“…Electromagnetic wave transformation 233 Equations (4)-(6) are rather general and can be applied to different models of wave propagation. Like Sazhin (1987), we ignore ion effects and take the electron distribution function in the form whereP|i (1) is the relativistic momentum in the direction parallel (perpendicular) to the magnetic field, 2> 0 | | (±) = w \\(L) m o> w \\ ar *d W L a r e t n e thermal velocities in the corresponding directions, m 0 is the electron mass at rest, and j = 0,1,2, -Also following Sazhin (1987) we can define the parameter /? as where FT and Q o are the electron plasma frequency at rest and the electron gyrofrequency at rest, respectively.…”

“…The corresponding plots M>||/C versus Y = O 0 /w for different n / Q 0 and A e are presented in figure 2. The curves are shown only for those values of Y for which the expressions for N lex and i^l or are valid (see Sazhin 1987). In particular, we assume that -^lex(or) differs by less than 30 % from the corresponding cold plasma value.…”

“…In our recent paper (Sazhin 1987) we derived several approximate formulae for electromagnetic wave refractive indices in a weakly relativistic homogeneous plasma. These formulae can also be applied to the case of wave propagation in a weakly inhomogeneous plasma, when the characteristic scale of inhomogeneity is well above the wavelength; here we apply them to the problem of electromagnetic wave transformation in an inhomogeneous plasma.…”