ABSTRACT
This chapter discusses the basic equations of the theory of small-scale instabilities in a finite–β plasma allowing for magnetic-field curvature. It considers the equilibrium of a collisionless plasma. The chapter explains the local permittivity of such a plasma. It also considers the two-fluid description of small-scale interchange perturbations in a plasma cylinder. In contrast to the case of a rectilinear magnetic field, in the case of a curvilinear magnetic field, there exist branches of hydromagnetic perturbations with frequencies higher than the drift frequencies. The problem of allowing for the curvature effects in the theory of plasma instabilities has a long history. In the case of a weakly inhomogeneous magnetic field one can construct one more constant of motion, namely, the magnetic moment. The chapter shows that in the absence of magnetic-field curvature, the dispersion relation for low-frequency long-wavelength perturbations splits into two dispersion relations corresponding to the inertial and inertialess oscillation branches.
