Magnetic instabilities in collisionless astrophysical rotating plasma with anisotropic pressure

A technique is developed for analytical study of instabilities in collisionless astrophysical rotating plasma with anisotropic pressure that may lead to magnetic turbulence. Description is based on a pair of equations for perturbations of the radial magnetic field and the sum of magnetic field and perpendicular plasma pressures. From these equations, a canonical second-order differential equation for the perturbed radial magnetic field is derived and, subsequently, the dispersion relation for local perturbations. The paper predicts two varieties of hybrid instabilities due to the effects of differential plasma rotation and pressure anisotropy: The rotational-firehose and rotational-mirror ones. When the gravitation force is weak compared with the perpendicular pressure gradient, a new family of instabilities (the pressure-gradient-driven) is revealed.