Low-Frequency Wave Instabilities in Magnetized Collisional Plasma with Longitudinal Electric Field and Weak Inhomogeneity of Density

Abstract

In the framework of linear approximation of the perturbation theory the conditions have been considered for the onset and development of the low-frequency wave instabilities for the plasmas in the external magnetic field as well as in the weak quasistatic electric field, both being parallel. It is assumed that the pair Coulomb collisions are described by the model integral of Bhatnagar-Gross-Krook. Inhomogeneity of plasma density is supposed to be “one-dimensional”. For the case of long-wave perturbations which propagate almost perpendicular to the external magnetic field, it has been shown that under some additional physical conditions, the dispersion relation is the polynomial of the fourth order with respect to the reduced frequency. This equation is solved through the Euler method. Two among four roots obtained turn out to be unstable with respect to the small perturbations. For the case of weak density inhomogeneity, when ion cyclotron radius is much less than mean characteristic size of inhomogeneity, the expressions for the instability growth rates have been obtained. Numerical simulation on the basis of the obtained formulas has been performed for the values of main plasma parameters (density, temperature, magnetic field amplitude, etc.) which are typical for the flare atmosphere in the solar active regions. It turns out that instability of the one of mentioned roots has clearly expressed threshold character, i.e. it arises at the certain value of slowly increasing amplitude of the weak electric field.