Nonlinear analysis of Coulomb relaxation of anisotropic distributions

The bi‐Maxwellian model is employed to study the time evolution of anisotropic distributions resulting from Coulomb collisions. The rate of change of temperatures caused by like‐particle collisions is described by a single ordinary differential equation for E, where E=T⊥/T∥. It exhibits a logarithmic singularity in the limit E→0, expressing the velocity space geometry and nonlinearity in the collision operator. The temporal relaxation is compared with a numerical solution of the nonlinear Fokker–Planck equation and is found to be insensitive to changes in the collision operator in the case of E>1. For E<1, however, the relaxation toward thermal equilibrium turns out to be dependent on the chosen model. The influence of unlike‐particle collisions is also investigated.