Variational Formulation of the Linear Mhd Stability of 3d-Plasmas with Noninteracting Hot-Electrons
Variational Formulation of the Linear Mhd Stability of 3d-Plasmas with Noninteracting Hot-Electrons
复制标题
非相互作用热电子 3d 等离子体线性 Mhd 稳定性的变分公式
DOI：
10.1088/0741-3335/34/6/009
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发表时间：
1992
影响因子：
2.2
通讯作者：
A. Cooper
中科院分区：
文献类型：
--
作者：
A. Cooper
在不考虑耗散机制的情况下，用变分形式给出了具有非相互作用热电子层和嵌套磁通面的三维等离子体的线性MHD稳定性问题。为此目的，将布泽尔磁坐标扩展到具有嵌套磁通表面的各向异性压力等离子体。考虑了一种修正的能量原理，其中热电子种电流是不可扰动的。施加等离子体不可压缩性，因此采用简化的动能来确定边缘稳定的条件。等离子体周围的真空区域被视为无剪切、无压力和无质量的假等离子体。对磁坐标周期角变量中的扰动进行傅里叶分解，采用有限元离散化方法将稳定性问题简化为一个特殊的块五对角矩阵特征值方程，该方程可以用逆向量迭代技术求解。所描述的公式有助于评估具有刚性热电子的三维等离子体组态对全局内外模式的线性MHD稳定性。将气胀模表示应用于等离子体内部势能，确定了MHD对局部模线性稳定的条件，推导出相应的气胀模方程。该方程的渐近分析得到Mercier判据。
The linear MHD stability problem for 3D plasmas with noninteracting hot electron layers and nested magnetic flux surfaces in the absence of dissipation mechanisms is formulated in variational form. Boozer magnetic coordinates are extended to anisotropic pressure plasmas with nested magnetic flux surfaces for this purpose. A modified energy principle in which the hot electron species current is imperturbable is considered. Plasma incompressibility is imposed and thus a simplified kinetic energy is employed to determine the conditions of marginal stability. The vacuum region surrounding the plasma is treated as a shearless, pressureless and massless pseudoplasma. Fourier decomposition of the perturbations in the periodic angular variables of the magnetic coordinates is applied and a finite element discretization scheme reduces the stability problem to a special block pentadiagonal matrix eigenvalue equation which is amenable to solution with an inverse vector iteration technique. The formulation described is useful to evaluate the linear MHD stability properties of 3D plasma configurations with rigid hot electrons to global internal and external modes. The conditions for linear MHD stability to local modes are determined with the application of the ballooning mode representation to the internal plasma potential energy to derive the corresponding ballooning mode equation. The asymptotic analysis of this equation yields the Mercier criterion.