  A theoretical treatment is presented of kinetic equilibria in accretion discs
around compact objects, for cases where the plasma can be considered as
collisionless. The plasma is assumed to be axi-symmetric and to be acted on by
gravitational and electromagnetic fields; in this paper, the particular case is
considered where the magnetic field admits a family of toroidal magnetic
surfaces, which are locally mutually-nested and closed. It is pointed out that
there exist asymptotic kinetic equilibria represented by generalized
bi-Maxwellian distribution functions and characterized by primarily toroidal
differential rotation and temperature anisotropy. It is conjectured that
kinetic equilibria of this type can exist which are able to sustain both
toroidal and poloidal electric current densities, the latter being produced via
finite Larmor-radius effects associated with the temperature anisotropy. This
leads to the possibility of existence of a new kinetic effect - referred to
here as a \textquotedblleft kinetic dynamo effect\textquotedblright\ -
resulting in the self-generation of toroidal magnetic field even by a
stationary plasma, without any net radial accretion flow being required. The
conditions for these equilibria to occur, their basic theoretical features and
their physical properties are all discussed in detail.
