Electron Cyclotron Electromagnetic Instabilities in Weakly Relativistic Plasmas

Abstract

The relativistic dispersion relation of whistlers is solved for weakly relativistic plasmas. The solution takes into account various deviations from a Maxwellian distribution found in laboratory plasmas, namely, pressure anisotropy, loss cone, and cold plasma. The relativistic effects are shown to be strongly stabilizing even for low temperature plasmas when the density is such that ωp2/ωc2≪0.25. The spectrum of unstable waves is also shifted toward smaller frequencies.

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

“…Expressions of Sazhin et al (1981) corresponding to (2.13)-(2.14) contain algebraic mistakes unless A e = 1, or 6 = 0, or 6 = \n. These mistakes influence the numerical coefficients of some formulae of our subsequent publications (Sazhin 1981, 19826;Majewski & Sazhin 1984) which were founded on the results of Sazhin et al (1981) unless A e = 1, or 6 = 0, \n for an arbitrary A e . However, their conclusions remain unchanged when the non-relativistic approximation is valid.…”

“…The equations for wave propagation within this model appear to be much more complicated than those for the cold plasma model, and are in most cases analysed by numerical methods (see, for example, Scharer & Trivelpiece 1967;Tokar & Gary 1985). In contrast to these papers, Sazhin et al (1981), Sazhin ( , 1982aSazhin ( , b, 1985aSazhin ( , b, 1986a and Majewski & Sazhin (1984) attempted to present an approximate theory of wave propagation within this model which would be simple enough for concrete applications but would take into account all the essential features of the phenomenon. The third model is the most general one and is based on the relativistic kinetic equation (Baldwin, Bernstein & Weenink 1969).…”

Relativistic and non-relativistic analysis of whistler-mode waves in a hot anisotropic plasma

“…An alternative approach to the theory of whistler-mode waves in a hot plasma has been based on the so-called weakly relativistic approximation, which uses the condition (1) with terms of order w 2 /c z taken into account, allowing substantial simplification of the general relativistic wave dispersion equation (see e.g. Shkarofsky 1966;Jacquinot & Leloup 1971;Sazhin 1987a). However, even this relatively simple weakly relativistic whistler-mode dispersion equation is much more complicated than the non-relativistic dispersion equation, and its applications have been very limited (Jacquinot & Leloup 1971;Wingle 1983;Robinson 1987a).…”

“…In the limit as r-+ 0, but keeping terms of the order of r, we can write an approximate solution of (10) as (Jacquinot & Leloup 1971;Sazhin 1987a, b) …”

“…Shkarofsky 1966;Jacquinot & Leloup 1971;Sazhin 1987 a). However, even this relatively simple weakly relativistic whistler-mode dispersion equation is much more complicated than the non-relativistic dispersion equation, and its applications have been very limited (Jacquinot & Leloup 1971;Wingle 1983;Robinson 1987 a).…”