The large-scale features and dynamics of many objects in the
Universe depend very strongly on how small-scale turbulence
affects the transport properties of astrophysical plasmas.
This critical transport problem has so far mostly been studied in
the fluid MHD framework, whereas many turbulent magnetized
astrophysical plasmas, such as the solar wind, the intracluster
medium or plasma accreted onto black holes are thought to be only
weakly collisional. How the couplings between turbulence and kinetic
processes affect transport and magnetic field generation in this kind
of environment is very poorly understood at the moment. In weakly
collisional, high-beta magnetized plasmas, a suspected very
important effect is that large-scale, field-stretching motions,
by generating pressure anisotropies with respect to the local field,
trigger extremely fast mirror and firehose instabilities at microscopic
scales comparable to the ion Larmor radius.
As a first step towards understanding the dynamical macroscopic
consequences of these instabilities, we present a kinetic theory
of the nonlinear development of the parallel firehose instability
with finite Larmor radius effects. We show that this process leads to a
significant modification of the local magnetic field geometry and that any firehose-unstable pressure
anisotropy evolves nonlinearly towards its
critical value for instability in the course of the process. We finally discuss
the possible consequences of this evolution for turbulence and magnetic
field generation in weakly collisional astrophysical plasmas.