Nonlinear relaxation of the hydrodynamic Weibel instability in collisional plasma

The model of rotational anisotropic electron hydrodynamics (RAEH) was recently developed by Bychenkov et al. in order to describe self-consistently the rotational structures in a plasma with an anisotropic electron energy distribution. In the present treatment the authors include in the RAEH model a treatment of the electron collisional dissipation, i.e., effects such as magnetic viscosity, pressure isotropization, and Joule heating of a plasma by the rotatoinal currents that develop. Electron collisions are taken into account in the model of RAEH. A numerical simulation of the nonlinear relaxation of the Weibel instability is carried out using the RAEH equations. The effect of collisional dissipation on the evolution of the quasistatic magnetic field and the components of the stress-energy tensor is studied. The dependence of the electron collision frequency is studied for the rate of maximum conversion of thermal anisotropic electron energy into the electromagnetic energy of pulsations