Magnetorotational instability in a collisionless plasma with heat flux vector and an isotropic plasma with self-gravitational effect

The linear stability of a differential rotating magnetized plasma is analyzed in the collisionless approximation along with heat flux vector. The dispersion relation is derived and simplified cases are discussed with instability criteria presented. Anisotropic pressures are shown to not only alter the classical instability criterion but also induce new unstable regions. The shear rotating instability in a collisional magnetized plasma with a scalar kinetic pressure in the presence of self-gravitational effect is then considered. Three cases are discussed specifically according to the general dispersion relation. The effects of Jeans term and compressibility on the local shear instability induced by differential rotation are examined and the analytic instability criteria are presented.