The kinetic theory of quasi-stationary collisionless accretion disc plasmas

Astrophysical plasmas in accretion discs are usually treated in the framework of fluid or MHD approaches but there are some situations where these treatments become inadequate and one needs to revert to the more fundamental underlying kinetic theory. This occurs when the plasma becomes effectively collisionless or weakly-collisional such as, for example, in radiatively inefficient accretion flows onto black holes. In this paper, we lay down the basics of kinetic theory in these contexts. In particular, we formulate the kinetic theory for quasi-stationary collisionless accretion disc plasmas in the framework of a Vlasov-Maxwell description, taking the plasma to be non-relativistic, axisymmetric, gravitationally-bound and subject to electromagnetic fields. Quasi-stationary solutions for the kinetic distribution functions are constructed which are shown to admit temperature anisotropies. The physical implications of the theory are then investigated and the equations of state and angular momentum conservation law are discussed. Analysis of the Ampere equation reveals the existence of a quasi-stationary kinetic dynamo which gives rise to self-generation of poloidal and azimuthal magnetic fields and operates even in the absence of turbulence and/or instability phenomena.