One dimensional beam transport

Abstract

Approximations to the transverse integrated scalar flux for a particle beam, whose corresponding angular flux satisfies the one dimensional transport equation, are developed under the assumption that the angular distribution remains peaked about the original beam direction. Asymptotic expansions, in the form of a power series in z q + , are obtained by scaling appropriately small terms in the transport equation. Similar results are also generated by developing a truncated hierarchy of (1 -p)n-moments of the angular flux. A low order truncation is shown to be sufficient to obtain the scalar flux with a high order error. Although formally different, all methods are seen to yield the same asymptotic expansion of the scalar flux. This is not unreasonable as all methods exploit the same feature of the solution, namely, that highly forward peaked scattering results in an initially peaked distribution remaining peaked.

A Priori Error Estimates and Computational Studies for a Fermi Pencil-Beam Equation

“…Previous numerical approaches are mostly devoted to the study of the one-dimensional problem see, e.g. [12] and [15].…”