Stability of general plasma equilibria - I formal theory
Stability of general plasma equilibria - I formal theory
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DOI：
10.1088/0032-1028/10/5/301
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发表时间：
1968
期刊：
影响因子：
--
通讯作者：
J. Taylor;R. Hastie
中科院分区：
文献类型：
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作者：
J. Taylor;R. Hastie
本文介绍了一种详细研究真实的实验几何中静电不稳定性的方法。这些经常在平板模型中讨论，以及对它的修改，但目前的工作从一开始就包括了所有的几何效应。起点是无碰撞波尔兹曼方程，其近似值是平衡的标度长度与离子陀螺半径相比很长。主要的兴趣是在扰动的低频，但任意波长，这可能是可比的离子拉莫尔半径。因此，几种不稳定性，如漂移波，凹槽或捕获粒子，在理论的范围内。表达式首先获得的贡献所产生的电荷密度的任意静电扰动影响粒子的未扰动轨道是（i）之间的磁镜捕获;（ii）围绕封闭的磁力线循环;（iii）跟踪出的磁性表面。再加上泊松方程，这些表达式导致，通过适当的奈奎斯特轮廓，稳定性标准有效的任意平衡。最后，它示出了这种方法如何导致一个微分方程，其解决方案将确定稳定的实验配置，如多极。
A method is described for the detailed investigation of electrostatic instabilities in real experimental geometries. These have frequently been discussed in the plane slab model, and modifications of it, but the present work includes all geometrical effects from the outset. The starting point is the collisionless Boltzmann equation with the approximation that the scale length of the equilibrium is long compared to the ion gyro radius. The main interest is in perturbations of low frequency but of arbitrary wavelength, which may be comparable to the ion Larmor radius. Thus several instabilities such as drift wave, flute or trapped particle, come within the scope of the theory. Expressions are first obtained for the contribution to the charge density produced by an arbitrary electrostatic perturbation affecting particles whose unperturbed orbits are (i) trapped between magnetic mirrors; (ii) circulating around closed field lines; (iii) tracing out a magnetic surface. Together with Poisson's equation these expressions lead, via the appropriate Nyquist contours, to stability criteria valid for arbitrary equilibria. Finally it is shown how this method leads to a differential equation whose solution will determine the stability of an experimental configuration such as the multipole.