Formation of Maxwellian Tails

Using two models, we study the relaxation to a Maxwell distribution in the context of classical kinetic theory. For the first model, an exact solution of the nonlinear Boltzmann equation is derived. For the second model, an asymptotic solution exhibits the remarkable feature of a transient tail population sometimes much larger than the equilibrium Maxwell distribution. This phenomenon may be of importance for calculating rates of fast chemical reactions and for controlled thermonuclear fusion.