Two‐dimensional analysis of trapped‐ion eigenmodes
Two‐dimensional analysis of trapped‐ion eigenmodes
复制标题
俘获离子本征模的二维分析
DOI：
10.1063/1.863118
复制
发表时间：
1980
影响因子：
4.6
通讯作者：
G. Rewoldt
中科院分区：
文献类型：
--
作者：
R. Marchand;W. Tang;G. Rewoldt
提出了轴对称环形几何形状中捕获离子不稳定性的第一个全二维本征模分析。通过对扰动静电势 φ（以 ϑ 为单位）进行傅里叶展开来考虑极向结构。假设扰动在典型的离子香蕉宽度 ρbi 上略有变化，每个极向谐波都表示为小半径中的截断泰勒级数，以解释径向结构。由此产生的一组耦合常二阶微分方程通过有限元方法进行数值求解。该形式也适用于径向局部和一维径向近似。给出了在这些限制下获得的结果，并发现与之前的计算相当一致。在低剪切等离子体中，完整的二维计算与一维径向近似在定性上一致。然而，对于更高的剪切力，二维计算会产生略有不同的图像......
The first fully two‐dimensional eigenmode analysis of the trapped‐ion instability in an axisymmetric toroidal geometry is presented. The poloidal structure is taken into account by Fourier‐expanding the perturbed electrostatic potential, φ, in ϑ. Assuming that the perturbation varies mildly over a typical ion‐banana‐width, ρbi, each poloidal harmonic is expressed as a truncated Taylor series in the minor radius to account for the radial structure. The resulting set of coupled ordinary second‐order differential equations is solved numerically by the method of finite elements. The formalism is also applicable to the radially local and one‐dimensional radial approximations. Results obtained in these limits are presented and found to be in reasonable agreement with previous calculations. In low shear plasmas, the full two‐dimensional calculation is in qualitative agreement with the one‐dimensional radial approximation. However, for higher shear the two‐dimensional calculation yields a somewhat different pictu...