  Recent laboratory experiments with laser-produced plasmas have observed and
studied a number of fundamental physical processes relevant to magnetized
astrophysical plasmas, including magnetic reconnection, collisionless shocks,
and magnetic field generation by Weibel instability, opening up new
experimental platforms for laboratory astrophysics. We develop a fully kinetic
simulation model for first-principles simulation of these systems including the
dynamics of magnetic fields---magnetic field generation by the Biermann battery
effect or Weibel instability; advection by the ion flow, Hall effect, and
Nernst effect; and destruction of the field by dissipative mechanisms. Key
dimensionless parameters describing the system are derived for scaling between
kinetic simulation, recent experiments, and astrophysical plasmas. First,
simulations are presented which model Biermann battery magnetic field
generation in plasmas expanding from a thin target. Ablation of two neighboring
plumes leads to the formation of a current sheet as the opposing
Biermann-generated fields collide, modeling recent laser-driven magnetic
reconnection experiments. Second, we simulate recent experiments on
collisionless magnetized shock generation, by expanding a piston plasma into a
pre-magnetized ambient plasma. For parameters considered, the Biermann effect
generates additional magnetic fields in the curved shock front and thereby
increases shock particle reflection. Both cases show the importance of kinetic
processes in the interaction of plasmas with magnetic fields, and open
opportunities to benchmark these important processes through comparison of
theory and experiments.
