Grad–Fokker–Planck plasma equations. Part 1. Coffision moments

Thirteen moments are taken of the collision term in the Boltzmann–Fokker– Planck equation for a multi-species, multi-temperature, hot plasma, following the method first developed by Grad for neutral gases. The collision integrals are evaluated for each colliding species pair. These integrals give, in particular, the rate of exchange of momentum and energy produced by collisions. The set of integrals may be combined with moments of the remaining terms in the Boltzmann equation to give thirteen moment equations for each species of particle. To complete the calculation, extensive use was made of the symbolic computer language REDUCE.