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On the bounce-averaging of scattering rates and the calculation of bounce period

机译：散射速率的弹跳平均和弹跳周期的计算

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摘要

For many applications to planetary magnetospheres and elsewhere in the Universe, it is desirable to average physical quantities such as particle and plasma transport coefficients over a charged particle's bounce motion between magnetic mirror points along field lines. In this paper, we perform such bounce-averaging in a way that avoids singularities in the integrands of expressions that arise in calculations of this sort. Our method applies in principle to an almost arbitrary magnetic field model. We illustrate the advantage of using our method for removing the integrand's singularity through a change of variables (rather than by truncating the integral over latitude at points progressively nearer to the mirror point) by computing the D_(pp) component of the bounce-averaged momentum-space diffusion tensor in a dipolar magnetic field both ways for resonance interaction of geomagnetically trapped relativistic (1 MeV) electrons with field-aligned whistler-mode plasma waves at L 6 (a field line that passes near synchronous altitude). Moreover, we develop improved analytical approximations for particle bounce periods in a dipolar magnetic field by minimizing mean square errors with respect to expansion coefficients in algebraic representations of the bounce period.
机译：对于行星磁层和宇宙中其他地方的许多应用，希望在沿着磁力线的磁力镜点之间的带电粒子反弹运动中，平均物理量，例如粒子和等离子体的传输系数。在本文中，我们执行这种反弹平均的方法是避免此类计算中出现的表达式的被积数中的奇数。我们的方法原则上适用于几乎任意的磁场模型。我们通过计算变量平均反弹量的D_（pp）分量，说明了使用我们的方法通过改变变量（而不是在逐渐接近镜像点的点处将纬度上的整数截断）来去除被积奇异点的优势偶极磁场中的空间扩散张量，用于地磁俘获的相对论（1 MeV）电子与场对准的哨声模式等离子波在L 6（通过接近同步高度的场线）的共振相互作用。此外，我们通过最小化关于弹跳周期的代数表示中的膨胀系数的均方误差，开发了一种改进的偶极磁场中粒子弹跳周期的解析近似。

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