  We present results of a 2D3V kinetic Vlasov simulation of the Weibel
instability. The kinetic Vlasov simulation allows us to investigate the
velocity distribution of dilute plasmas, in which the effect of collisions
between particles is negligible, and has the advantage that the accuracy of the
calculated velocity distribution does not depend on the density of plasmas at
each point in the physical space. We succeed in reproducing some features of
the Weibel instability shown by other simulations, for example, the
exponentially growing phase, the saturation of the magnetic field strength, the
formation of filamentary structure, and the coalescence of the filaments.
Especially, we concentrate on the behavior of the filaments after the
saturation of the magnetic field strength and find that there is a kind of
quasi-equilibrium states before the coalescence occurs. Furthermore, it is
found that an analytical solution for stationary states of the 2D3V
Vlasov-Maxwell system can reproduce some dominant features of the
quasi-equilibrium, e.g, the configuration of the magnetic field and the
velocity distribution at each point. The analytical expression could give a
plausible model for the transition layer of a collisionless shock where a
strong magnetic field generated by the Weibel instability provides an effective
dissipation process instead of collisions between particles.
