An Extended First Collision Source Method for Electron Beam Source Problems

Beam source problems are difficult to treat numerically because of the associated singularities in angle and space. For electrons, conventional first collision source techniques offer little help because the cross sections are so large and anisotropic that the first collision source and original source are not very different. By extending the definition of the uncollided flux to include particles that have not deviated significantly from the original beam direction, an extended first collision source is obtained that is smooth enough for use in S_N codes. Through the use of effective cross sections, the extended first collision source is determined using standard first collision source techniques. The effective cross sections model electron transport with a reduced number of collisions, but larger deflections per collision. These qross sections are generated using a brute-force S_N solution of the space-independent Spencer-Lewis equation on a restricted cone of directions, centered about the beam direction. Several sample calculations are given.