Compute simulation-based criteria for validity of the diffusion approximation in the stationary method

Determine how to calculate, directly from numerical test-particle simulations, the criteria of Kaiser et al. (1978) that specify where the diffusion approximation is valid for the stationary pitch-angle diffusion equation with continuous injection and absorbing boundaries.

Background

Method M5 (the stationary solution approach) requires continuous injection at a source pitch angle and absorbing boundaries. It is not valid close to the source because the distribution may not be diffusive and the derivative may be discontinuous. While Kaiser et al. (1978) provided criteria for where the diffusion approximation is valid, the current paper highlights the lack of a clear procedure to evaluate these criteria from simulation data.