Subspace Approximation to the Focused Transport Equation. II. The Modified Form

TL;DR

This paper introduces a conservative form of the focused transport equation for energetic particle transport, employing a subspace method for efficient analytical and semi-numerical solutions, improving computational speed over traditional methods.

Contribution

It presents a modified, norm-conserving form of the focused transport equation and applies a subspace method for faster analytical and semi-numerical solutions.

Findings

The modified equation conserves particle number.

The subspace method enables faster solutions.

Semi-numerical approach is more efficient than traditional solvers.

Abstract

The transport of energetic particles in a spatially varying magnetic field is described by the focused transport equation. In the past two versions of this equation were investigated. The more commonly used standard form described a pitch-angle isotropization process but does not conserve the norm. In the current paper we consider the focused transport equation in conservative form also called modified focused transport equation. This equation conserves the norm but does not describe pitch-angle isotropization. We use the previously developed subspace method to solve the focused transport equation analytically and numerically. For a pure analytical treatment we employ the two-dimensional subspace approximation. Furthermore, we consider a higher dimensionality for which one needs to evaluate occurring matrix exponentials numerically. This type of semi-numerical approach is much faster than traditional solvers and, therefore, it is very useful.