用曲率修正的等离子体色散函数研究离子温度梯度驱动模的稳定和不稳定根
Stable and unstable roots of ion temperature gradient driven mode using curvature modified plasma dispersion functions
摘要：
本文重新考虑了具有绝热电子的离子温度梯度驱动（ITG）模的基本局域动力学理论。标准的不稳定，纯振荡以及阻尼的本地色散关系的解决方案，使用括号技术，使用的参数原则。该方法需要计算等离子体介电函数及其导数，其在这里使用具有曲率的修改的等离子体色散函数及其导数来实现，并且允许包围/跟随对应于ITG色散关系的不同根的等离子体介电函数的零点。我们提供了一个开放源代码的实现修改后的等离子体色散函数的曲率，这是在这个配方中使用的衍生物。研究局部ITG色散，我们发现，在不稳定的阈值附近的不稳定分支是相当不对称的振荡的解决方案对较低的波数（即漂移波），和阻尼的解决方案对较高的波数。这表明一个类似于逆级联的过程，通过耦合到振荡分支朝向较低的波数，可能在ITG的非线性演化中发挥作用，在不稳定阈值附近。此外，使用该算法，线性波扩散的边缘稳定ITG模式估计。
英文摘要：
Basic, local kinetic theory of ion temperature gradient driven (ITG) mode, with adiabatic electrons is reconsidered. Standard unstable, purely oscillating as well as damped solutions of the local dispersion relation are obtained using a bracketing technique that uses the argument principle. This method requires computing the plasma dielectric function and its derivatives, which are implemented here using modified plasma dispersion functions with curvature and their derivatives, and allows bracketing/following the zeros of the plasma dielectric function which corresponds to different roots of the ITG dispersion relation. We provide an open source implementation of the derivatives of modified plasma dispersion functions with curvature, which are used in this formulation. Studying the local ITG dispersion, we find that near the threshold of instability the unstable branch is rather asymmetric with oscillating solutions towards lower wave numbers (i.e. drift waves), and damped solutions toward higher wave numbers. This suggests a process akin to inverse cascade by coupling to the oscillating branch towards lower wave numbers may play a role in the nonlinear evolution of the ITG, near the instability threshold. Also, using the algorithm, the linear wave diffusion is estimated for the marginally stable ITG mode.
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