Characteristic Sweeps and Source Iteration for Charged-Particle Transport with Continuous Slowing-Down and Angular Scattering

TL;DR

This paper introduces a semi-analytic deterministic method for charged-particle transport that combines characteristic sweeps with source iteration, enabling efficient and accurate simulations of complex phenomena like Bragg peaks and secondary fragment effects.

Contribution

The work develops a novel framework integrating characteristic-based directional sweeps with fixed-point source iteration for charged-particle transport, including rigorous convergence analysis and error bounds.

Findings

Validated characteristic sweep against exact ballistic benchmark.

Demonstrated fixed-point convergence for forward-peaked scattering.

Simulated Bragg peak localization and secondary fragment effects.

Abstract

We develop a semi-analytic deterministic framework for charged-particle transport with continuous slowing-down in energy and angular scattering. Directed transport and energy advection are treated by method-of-characteristics integration, yielding explicit directional sweeps defined by characteristic maps and inflow data. Scattering is incorporated through a fixed-point (source-iteration) scheme in which the angular gain is lagged, yielding a sequence of decoupled directional solves coupled only through angular sums. The method is formulated variationally in a transport graph space adapted to the charged particle drift. Under standard monotonicity and positivity assumptions on the stopping power and boundedness assumptions on cross sections, we establish coercivity and boundedness of the transport bilinear form, prove contraction of the source iteration under a subcriticality condition and derive a rigorous a posteriori bound for the iteration error, providing an efficient stopping criterion. We further analyse an elastic discrete-ordinates approximation, including conservation properties and a decomposition of angular error into quadrature, cone truncation and finite iteration effects. Numerical experiments for proton transport validate the characteristic sweep against an exact ballistic benchmark and demonstrate the predicted fixed-point convergence under forward-peaked scattering. Carbon-ion simulations with tabulated stopping powers and a reduced multi-species coupling illustrate Bragg peak localisation and distal tail formation driven by secondary charged fragments.