Relaxation of a Lorentz Gas with a Repulsive r—s Force Law

The relaxation of a Lorentz gas (dilute light particle subsystem in a heavy particle heat bath) has been studied for a repulsive r—s central force law interaction between the light and heavy particles. The Fokker—Planck equation for the velocity distribution functions of the light particle subsystem has been solved numerically for s=5, 9, 13, 21, and ∞ for various initial conditions. The dependence of the rate of relaxation and of the form of the time-dependent velocity distribution function on the force law parameter s is discussed in light of the above results.