  The turbulent amplification of cosmic magnetic fields depends upon the
material properties of the host plasma. In many hot, dilute astrophysical
systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity
of particle--particle collisions allows departures from local thermodynamic
equilibrium. These departures exert anisotropic viscous stresses on the plasma
motions that inhibit their ability to stretch magnetic-field lines. We present
a numerical study of the fluctuation dynamo in a weakly collisional plasma
using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous
(Braginskii) stress. When the stress is limited to values consistent with a
pressure anisotropy regulated by firehose and mirror instabilities, the
Braginskii-MHD dynamo largely resembles its MHD counterpart. If instead the
parallel viscous stress is left unabated -- a situation relevant to recent
kinetic simulations of the fluctuation dynamo and to the early stages of the
dynamo in a magnetized ICM -- the dynamo changes its character, amplifying the
magnetic field while exhibiting many characteristics of the saturated state of
the large-Prandtl-number (${\rm Pm}\gtrsim{1}$) MHD dynamo. We construct an
analytic model for the Braginskii-MHD dynamo in this regime, which successfully
matches magnetic-energy spectra. A prediction of this model, confirmed by our
simulations, is that a Braginskii-MHD plasma without pressure-anisotropy
limiters will not support a dynamo if the ratio of perpendicular and parallel
viscosities is too small. This ratio reflects the relative allowed rates of
field-line stretching and mixing, the latter of which promotes resistive
dissipation of the magnetic field. In all cases that do exhibit a dynamo, the
generated magnetic field is organized into folds that persist into the
saturated state and bias the chaotic flow to acquire a scale-dependent spectral
anisotropy.
