Pencil-beam approximation of stationary Fokker-Planck

TL;DR

This paper rigorously compares three models for stationary Fokker-Planck equations in narrow beam scenarios, providing error estimates and analyzing well-posedness in a half-space setting.

Contribution

It offers a detailed approximation analysis and error estimates for ballistic, Fermi pencil-beam, and Fokker-Planck models in a rigorous mathematical framework.

Findings

Error estimates in 1-Wasserstein sense for model approximations

Well-posedness and regularity results for Fokker-Planck with singular sources

Comparison of models in half-space geometry

Abstract

Solutions of stationary Fokker-Planck equations in the narrow beam regime are commonly approximated by either ballistic linear transport or by a Fermi pencil-beam equation. We present a rigorous approximation analysis of these three models in a half-space geometry. Error estimates are obtained in a 1-Wasserstein sense, which is an adapted metric to quantify beam spreading. The required well-posedness and regularity results for the stationary Fokker-Planck equation with singular internal and boundary sources are also presented in detail.