标题： 子空间近似到聚焦传输方程。 II。 修改形式 显示英文标题

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

摘要： 在空间变化的磁场中，高能粒子的输运由聚焦输运方程描述。 在过去，对该方程的两个版本进行了研究。 更常用的标准形式描述了磁矩角各向同化过程，但不保持范数的守恒。 在本文中，我们考虑保守形式的聚焦输运方程，也称为修改的聚焦输运方程。 该方程保持范数的守恒，但不描述磁矩角各向同化。 我们使用之前开发的子空间方法对聚焦输运方程进行解析和数值求解。 对于纯解析处理，我们采用二维子空间近似。 此外，我们考虑更高维度的情况，这需要数值计算出现的矩阵指数。 这种半数值方法比传统求解器快得多，因此非常有用。 显示英文摘要

摘要： 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.