Theory of collision algorithms for gases and plasmas based on the Boltzmann equation and the Landau-Fokker-Planck equation

A time-explicit formula that describes the time evolution of velocity distr ibution functions of gases and plasmas is derived from the Boltzmann equati on. The formula can be used to construct collision simulation algorithms. S pecialization of the formula to the case of the Coulomb interaction shows t hat the previous method [K. Nanbu, Phys. Rev. E 55, 4642 (1997)] for a Coul omb collision simulation is a solution method of the Landau-Fokker-Planck e quation in the limit of a small time step. Also, a collision simulation alg orithm for multicomponent plasmas is proposed based on the time-explicit fo rmula derived.