Magnetic fields are a distinctive feature of accretion disc (AD) plasmas around compact
objects (i.e., black holes and neutron stars) and they play a decisive role in their dynamical
evolution. Of particular interest for the structure of ADs and their dynamical
properties is the interaction between the magnetic field and the accreting plasma. The
magnetic field can modify the velocity profile of the disc introducing species-dependent
rotational frequencies. Moreover, from the microscopic point of view, the same field is
a natural source of phase-space anisotropies, allowing for the existence of characteristic
symmetries, which influence the dynamics of charged particles in the AD plasma. These
features are important both for the kinetic description of AD plasmas and their influence
on the collective plasma interactions. In this paper, basic issues concerned with the origin
and structure of magnetic fields in collisionless astrophysical AD plasmas are discussed,
with particular reference to the stationary dynamo phenomenon, which leads to the selfgeneration
of the magnetic field appearing in these systems. More precisely, the problem
is addressed here of the generation of both the poloidal and toroidal components of the
AD magnetic field as a consequence of plasma currents produced purely by diamagnetic
collisionless kinetic mechanisms, which are characterized by a slow-time variation.
