COMPARISON OF 3 NUMERICAL TREATMENTS OF CHARGED-PARTICLE TRANSPORT

The treatments invoked direct finite-difference solutions of the funda mental equation for rectilinear transport, solutions of the matrix for m of the transport equation in terms of Fourier integrals, and Monte C arlo simulations, which kept track of approximate to 6.4 x 10(7) parti cles. Variables selected for comparison were the first four coefficien ts in the expansion of the distribution function in terms of scatterin g eigenfunctions. These coefficients embody detailed information not o nly about isotropic density but also about the lowest order anisotropy , which controls diffusion, and about two higher order anisotropies, w hich control dispersion. Finite-difference and Fourier methods gave re sults in better agreement with each other (deviations for each coeffic ient of approximate to 0.1% for Vt/lambda > 1) than with results of Mo nte Carlo simulations (deviations of approximate to 0.1% for Vt/lambda > 1). However, the latter deviations are essentially those expected f rom statistical fluctuations. To obtain deviations as small as the for mer ones, great care must be taken to compute parameters accurately an d to derive from finite approximations results that accurately represe nt those of the continuous formulation. To document precautions that l ead to accurate results, computations and extrapolations invoked durin g the comparison are described in detail.