Efficient calculation of degenerate atomic rates by numerical quadrature on GPUs

Abstract

The rates of atomic processes in cold, dense plasma are governed strongly by effects of quantum degeneracy. The electrons follow Fermi–Dirac statistics and their high density limits the number of quantum states available for occupation after a collision. These factors preclude a direct solution to the usual rate coefficient integrals. We summarize the formulation of this problem and present a simple, but efficient method of evaluating collisional rate coefficients via direct numerical integration. Numerical quadrature has an intrinsically high level of parallelism, ideally suited for graphics processor units. GPUs are particularly suited to this problem because of the large number of integrals which must be carried out simultaneously for a given atomic model. A CUDA code to calculate the rates of significant atomic processes as part of a collisional-radiative model is presented and discussed. This approach may be readily extended to other applications where rapid and repeated evaluation of many integrals is required.