A new eigenvalue problem associated with the two-dimensional Newcomb equation without continuous spectra
A new eigenvalue problem associated with the two-dimensional Newcomb equation without continuous spectra
复制标题
与无连续谱的二维纽科姆方程相关的新特征值问题
DOI：
10.1063/1.873588
复制
发表时间：
1999
影响因子：
2.2
通讯作者：
Tomoko Watanabe
中科院分区：
文献类型：
--
作者：
S. Tokuda;Tomoko Watanabe
本文提出了轴对称环形等离子体（如托卡马克）中二维Newcomb方程的一个新的特征值问题，并用有限元方法进行了数值求解。在特征值问题的表述中，选择了权函数（动能积分）和有理曲面上的边界条件，使得特征值问题的谱只由实数特征值（点谱）组成，而不包含连续谱。对理想m=1模态的应用验证了该公式能够识别稳定状态和不稳定状态，并且数值得到的特征函数在有理曲面上表现出理论预测的奇异行为。
A new eigenvalue problem associated with the two-dimensional Newcomb equation in an axisymmetric toroidal plasma, such as a tokamak, has been posed and solved numerically by using a finite element method. In the formulation of the eigenvalue problem, the weight functions (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen such that the spectra of the eigenvalue problem are comprised of only the real and denumerable eigenvalues (point spectra) without continuous spectra. Applications to the ideal m=1 mode have verified that this formulation is able to identify stable states as well as unstable states, and that the numerically obtained eigenfunctions show the singular behavior predicted by the theory at rational surfaces.