Nonlinear Landau Collisions Without Collision Tensors

Abstract

Far-from-equilibrium plasmas require nonlinear Coulomb collisions, but direct three-dimensional Hermite discretization of the Landau operator needs an impractical dense tensor. By porting quantum chemistry Coulomb-integral methods, we reduce the six-dimensional integrals to one-center Coulomb moments and separable exponential-sum contractions. This gives a four-order-of-magnitude working-memory reduction and enables nonlinear relaxation tests. Numerical simulations preserve invariants and show that finite-basis linearization changes relaxation and produces a fourfold angular error.

6 pages, 3 figures