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Analytical description for energetic particle pitch angle and momentum evolution in an expanding magnetic flux rope

机译：膨胀磁通绳中的能量粒子桨距角和动量演化的分析描述

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We have investigated the energetic particle transport in an interplanetary space, especially, in an expanding magnetic flux rope. The energetic particle transport in the interplanetary space is usually described by the Fokker- Planck equation including effects of pitch angle diffusion, adiabatic focusing, and adiabatic deceleration. However, for the particle transport in expanding magnetic flux rope, we have no explicit expression for pitch angle and momentum evolution such as adiabatic focusing and deceleration. In this study, we derive analytical descriptions for pitch angle evolution and momentum loss rate of energetic particles in the expanding magnetic flux rope and compare the analytical solution with numerical simulation results. The analytical solutions with ignoring particle gyration do not reproduce the results of numerical simulation even when the particle Larmor radius is several orders of magnitude smaller than the flux rope radius. Taking an effect of particle gyration into consideration, our analytical solutions correspond to the results of numerical simulations. Our analytical expression for the pitch angle evolution and momentum loss rate can be used as a pitch angle and momentum evolution term in the Fokker-Planck equation for energetic particle transport in an expanding magnetic flux rope.
机译：我们研究了行星际空间中的能量粒子运输，特别是在膨胀磁通绳中。穿线空间中的能量粒子传输通常由Fokker-Planck方程描述，包括俯仰角扩散，绝热聚焦和绝热减速的效果。然而，对于膨胀磁通绳的颗粒输送，我们对俯仰角和动量演化没有明确的表达，例如绝热聚焦和减速。在这项研究中，我们在膨胀磁通绳绳索中获得了对高能粒子的俯仰角演变和动量损失率的分析描述，并将分析液与数值模拟结果进行比较。即使粒子拉马力半径是小于磁通绳半径的几个数量级，也不会再现数值模拟的分析溶液。考虑到粒子循环的效果，我们的分析解决方案对应于数值模拟的结果。我们在膨胀磁通绳中的高能量颗粒输送中的俯仰角演变和动量损失率的分析表达可以用作桨级方程中的俯仰角和动量演化术语。

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