MHD Waves and Instabilities in Two-Component Anisotropic Plasma
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E PLASMA
MHD Waves and Instabilities in Two-Component Anisotropic Plasma N. S. Dzhalilova and S. Sh. Huseinova,* a
Shamakhy Astrophysical Observatory, Azerbaijan National Academy of Sciences, Pirkulu, Shamakhy district, AZ5626 Azerbaijan *e-mail: [email protected] Received October 22, 2018; revised December 17, 2018; accepted December 20, 2018
Abstract—Based on the 16-moment MHD transport equations, the propagation of linear waves in an anisotropic homogeneous cosmic plasma is considered. A general dispersion relation is derived with allowance for two plasma components (electrons and protons) and heat flux along the magnetic field. This dispersion relation is a generalization of the previously studied cases of one-component (ion) plasma. The case in which the effects associated with the heat flux are ignored is analyzed in more detail. In the limit of longitudinal propagation, the wave modes fully consistent with the modes known in the low-frequency kinetic theory of collisionless plasma are classified. Firehose and mirror instabilities are analyzed. It is shown that taking into account the electron component modifies the growth rates and thresholds of instabilities. DOI: 10.1134/S1063780X19060047
1. INTRODUCTION Since the measured parameters of highly rarefied magnetized space plasmas (e.g., solar and stellar winds, star coronas, star disks, the ionosphere and magnetosphere of planets, and interstellar medium) are macroscopic, the MHD description of such plasmas is preferable. The derivation of a closed set of MHD equations for collisionless plasma runs into difficulties. The main difficulty is related to the truncation of the infinite chains of equations for the moments of the distribution functions. This requires additional physical justification, as well as a specific type of the particle velocity distribution. Classical examples of such equations describing plasma as a fluid are the Chew–Goldberger–Low (CGL) equations [1] and the 16-moment transport equations [2, 3], derived for a bi-Maxwellian plasma with a zero Larmor radius. The main advantage of the 16-moment MHD transport equations in comparison with the CGL equations is that they take into account the heat flux along the magnetic field. In contrast to the CGL equations, the 16-moment equations give a correct expression for the threshold of mirror instability, which is identical to the result predicted by the lowfrequency kinetic theory [4, 5]. A disadvantage of the MHD descriptions of plasma in comparison with the kinetic one is that it considers small wavenumbers k < ω pp /c (where ω pp is the proton plasma frequency and c is the speed of light). In a number of papers,
MHD instabilities were modified with allowance for a finite Larmor radius (see, e.g., [6, 7]). In the previous works, we developed the theory of MHD instabilities based on the 16-moment equations [4, 5, 8, 9]. In those works, the results were obtained for an ion plasma. The role of electrons was reduced only to the maintenance of plasma quasineutrality. Strictly speaking, the contr
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