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

The kinetic theory of quasi-stationary collisionless accretion disc plasmas