Abstract

A fundamental problem in theoretical astrophysics concerns the phenomenology of plasmas arising in the vicinities of compact objects. In this talk the case of magnetized accretion disk plasmas is considered. The issue is addressed in the framework of kinetic theory. In particular, a theoretical treatment is presented of Vlasov-Maxwell equilibria for cases where a collisionless plasma is acted on by gravitational and electromagnetic fields. It is pointed out that there exist asymptotic kinetic equilibria represented by generalized bi-Maxwellian distribution functions and characterized by temperature anisotropy and primarily toroidal differential rotation. An exact analytical solution of the stationary Vlasov equation is obtained, based on the conservation laws of single-particle dynamics. It is shown that kinetic equilibria of this type are able to sustain both toroidal and poloidal electric current densities, the latter being produced by temperature anisotropy via finite Larmor-radius effects. This leads to the existence of an equilibrium kinetic dynamo effect resulting in the self-generation of both poloidal and toroidal magnetic fields. Remarkably, the toroidal component arises even without any net radial accretion or turbulent flows. Conditions for the occurrence of these equilibria are discussed. The theory developed allows the analytical construction of asymptotic stationary solutions of the MHD fluid equations