The failure of the scattering angle cutoff for Coulomb interactions

Abstract

Careful study of the collision frequency for Coulomb interactions indicates that the traditional practice of making cutoff on a scattering angle is a failure. The only complete cutoff should be on velocity change. After making the velocity change as an independent variable, we obtain more satisfactory physical results for both Coulomb interactions and hard-sphere interactions. These physical results include collision frequency, dynamical friction coefficient, diffusion coefficients, energy exchange frequency, and arbitrary high-order Fokker–Planck coefficients. New special functions, Ql(k,u), are obtained for the expression of the arbitrary order Fokker-Planck coefficients for both Coulomb interactions and hard-sphere interactions. The combined results establish a valuable relationship between Coulomb interactions and hard-sphere interactions with a parameter α. The special functions, Ql(k,u), have some interesting properties which make it possible to analyze arbitrary order Fokker-Planck coefficients easily for the first time. A new constant D0 is introduced to replace Couloumb logarithm in the precise calculation of plasma equilibrium time. This new constant D0 is related with Arrhenius exponential constant defined in the collision theory for chemical reaction rate. A physical term H is proposed as the accumulative measure of a force to unify the concept of collision strength.