有限厚度斜激波的电子注入理论
Theory of Electron Injection at Oblique Shock of Finite Thickness
摘要：
本文提出了一种在无碰撞激波中产生宇宙线电子的电子注入扩散激波加速（DSA）理论。我们考虑最近提出的粒子加速机制称为随机冲击漂移加速（SSDA）。我们发现，SSDA可以理解为一个扩散粒子加速机制在斜激波的有限厚度。更具体地说，它是由一个解决方案的扩散-对流方程的粒子与特征扩散长度可比的冲击厚度。另一方面，如果扩散长度比厚度长得多，则相同的方程产生标准DSA。虽然SSDA预测，在一般情况下，光谱指数比DSA陡峭，它是更有效的低能电子加速，有利于注入。注入阈值能量对应于两个不同区域之间的跃迁能量。在典型的星际和行星际条件下，如果激波周围湍流的耗散尺度由离子惯性长度决定，则其量级为$0.1\text{-}1$ MeV。电子注入在高$M_\textrm{A} / \cos θ_{Bn}$时效率更高，其中$M_\textrm{A}$和$θ_{Bn}$是阿尔文马赫数和激波速度。该理论表明，电子有效加速到超相对论能量将更容易实现高马赫数年轻超新星遗迹冲击，但不是在弱或中等冲击在日光层，除非上游的磁场几乎垂直于冲击法线。
英文摘要：
A theory of electron injection into diffusive shock acceleration (DSA) for the generation of cosmic-ray electrons at collisionless shocks is presented. We consider a recently proposed particle acceleration mechanism called stochastic shock drift acceleration (SSDA). We find that SSDA may be understood as a diffusive particle acceleration mechanism at an oblique shock of finite thickness. More specifically, it is described by a solution to the diffusion-convection equation for particles with the characteristic diffusion length comparable to the shock thickness. On the other hand, the same equation yields the standard DSA if the diffusion length is much longer than the thickness. Although SSDA predicts, in general, a spectral index steeper than DSA, it is much more efficient for low-energy electron acceleration and is favorable for injection. The injection threshold energy corresponds to the transition energy between the two different regimes. It is of the order of $0.1\text{-}1$ MeV in typical interstellar and interplanetary conditions if the dissipation scale of turbulence around the shock is determined by the ion inertial length. The electron injection is more efficient at high $M_\textrm{A} / \cos θ_{Bn}$ where $M_\textrm{A}$ and $θ_{Bn}$ are the Alfvén Mach number and the shock obliquity. The theory suggests that efficient acceleration of electrons to ultra-relativistic energies will be more easily realized at high-Mach-number young supernova remnant shocks, but not at weak or moderate shocks in the heliosphere unless the upstream magnetic field is nearly perpendicular to the shock normal.
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