  A kinetic treatment is developed for collisionless magnetized plasmas
occurring in high-temperature, low-density astrophysical accretion disks, such
as are thought to be present in some radiatively-inefficient accretion flows
onto black holes. Quasi-stationary configurations are investigated, within the
framework of a Vlasov-Maxwell description. The plasma is taken to be
axisymmetric and subject to the action of slowly time-varying gravitational and
electromagnetic fields. The magnetic field is assumed to be characterized by a
family of locally nested but open magnetic surfaces. The slow collisionless
dynamics of these plasmas is investigated, yielding a reduced gyrokinetic
Vlasov equation for the kinetic distribution function. For doing this, an
asymptotic quasi-stationary solution is first determined, represented by a
generalized bi-Maxwellian distribution expressed in terms of the relevant
adiabatic invariants. The existence of the solution is shown to depend on
having suitable kinetic constraints and conditions leading to particle trapping
phenomena. With this solution one can treat temperature anisotropy, toroidal
and poloidal flow velocities and finite Larmor-radius effects. An asymptotic
expansion for the distribution function permits analytic evaluation of all of
the relevant fluid fields. Basic theoretical features of the solution and their
astrophysical implications are discussed. As an application, the possibility of
describing the dynamics of slowly time-varying accretion flows and the
self-generation of magnetic field by means of a \textquotedblleft kinetic
dynamo effect\textquotedblright\ is discussed. Both effects are shown to be
related to intrinsically-kinetic physical mechanisms.
