Non-ideal stability: variational method for the determination of the outer-region matching data
Non-ideal stability: variational method for the determination of the outer-region matching data
复制标题
非理想稳定性：确定外区匹配数据的变分法
DOI：
10.1017/s0022377800015828
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发表时间：
1991
影响因子：
2.5
通讯作者：
R. Dewar
中科院分区：
文献类型：
--
作者：
A. Pletzer;R. Dewar
在研究磁等离子体对非理想模(如阻性模)的稳定性的框架内，考虑了由外(理想)区产生的渐近匹配数据的确定问题。在有限压等离子体中考虑同时具有撕裂宇称和交换(气球)宇称的模。匹配的数据形成了一个矩阵，其元素代表了小解对大解的强迫响应，显示了来自变分(能量)原理。所提出的变分原理既适用于柱面几何，也适用于二维(环形)几何。考虑到多个有理曲面的存在，得到了匹配数据矩阵的非对角线元素之间的互易关系。变分原理适用于数值逼近，特别适用于估计其收敛速度的有限元方法。通过在有理曲面附近填充节点，实现了与帐篷函数的网格节点数的平方成反比的最大收敛。
Within the framework of studies of the stability of magneto-plasmas to non-ideal modes, such as resistive modes, the problem of determining the asymptotic matching data arising from the outer (ideal) region is considered. Modes possessing both tearing and interchange (ballooning) parity are considered in finite-pressure plasmas. The matching data, which form a matrix whose elements represent the small solution response to forcing by a big solution, are shown to derive from a variational (energy) principle. The variational principle, as presented, applies to both cylindrical and two-dimensional (toroidal) geometries. Allowing for the presence of multiple rational surfaces, a reciprocity relation between off-diagonal elements of the matching data matrix is obtained. The variational principle is suitable for numerical approximation, and, in particular, for the finite-element method, for which convergence rates are estimated. By packing nodes near the rational surface, maximum convergence, proportional to the inverse square of the number of mesh nodes for tent functions, is achieved.