  This paper is concerned with the kinetic treatment of quasi-stationary
axisymmetric collisionless accretion disc plasmas. The conditions of validity
of the kinetic description for non-relativistic magnetized and
gravitationally-bound plasmas of this type are discussed. A classification of
the possible collisionless plasma regimes which can arise in these systems is
proposed, which can apply to accretion discs around both stellar-mass compact
objects and galactic-center black holes. Two different classifications are
determined, which are referred to respectively as energy-based and magnetic
field-based classifications. Different regimes are pointed out for each plasma
species, depending both on the relative magnitudes of kinetic and potential
energies and the magnitude of the magnetic field. It is shown that in all
cases, there can be quasi-stationary Maxwellian-like solutions of the Vlasov
equation. The perturbative approach outlined here permits unique analytical
determination of the functional form for the distribution function consistent,
in each kinetic regime, with the explicit inclusion of finite Larmor
radius-diamagnetic and/or energy-correction effects.
