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

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.