相对论对等离子体中韦伯模和撕裂模不稳定性的增长率
Growth rates of the Weibel and tearing mode instabilities in a relativistic pair plasma
摘要：
本文提出了一种求解非均匀磁化相对论等离子体线性色散关系的算法。该方法是以前报道的算法，仅限于同质的情况下的概括。扩展涉及到投影的扰动的空间依赖性到一组基函数，满足边界条件（谱伽辽金法）。为了测试这种算法在均匀的情况下，我们推导出一个相对论性麦克斯韦分布的韦伯不稳定性的增长率的解析表达式，并将其与数值结果进行比较。在非均匀的情况下，我们提出的相对论撕裂模式的色散关系的解决方案，使没有假设的电流片的厚度，并检查数值方法对解析表达式。
英文摘要：
We present an algorithm for solving the linear dispersion relation in an inhomogeneous, magnetised, relativistic plasma. The method is a generalisation of a previously reported algorithm that was limited to the homogeneous case. The extension involves projecting the spatial dependence of the perturbations onto a set of basis functions that satisfy the boundary conditions (spectral Galerkin method). To test this algorithm in the homogeneous case, we derive an analytical expression for the growth rate of the Weibel instability for a relativistic Maxwellian distribution and compare it with the numerical results. In the inhomogeneous case, we present solutions of the dispersion relation for the relativistic tearing mode, making no assumption about the thickness of the current sheet, and check the numerical method against the analytical expression.
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