The shear Alfvén continuum spectrum is studied for a tokamak with a single island chain using the ideal magnetohydrodynamics theory. We have taken into account the toroidal geometry and toroidal mode coupling with the island considered as a highly-shaped stellarator. Various new frequency gaps open up inside the island due to its asymmetry both poloidally and toroidally, such as the mirror-induced Alfvén eigenmode (MAE) gap and the helicity-induced Alfvén eigenmode (HAE) gap. We have shown that the MAE gap acts as the continuation of the outside toroidal Alfvén eigenmode (TAE) gap into the island. However, the combined TAE/MAE gap is getting narrower as the island grows, leaving only half of its original width with a moderate island size as much as 3.2% of the minor radius. In addition, the two-dimensional eigenfunction of the continuum mode on the lower tip of the MAE gap now has highly localised structures around the island's long axis, contrary to the usual oscillatory global solutions found with no or a low level of toroidal asymmetry—an indication of the continuous spectrum becoming discrete and dense. These results have implications for the frequency, mode structure and continuum damping of global TAEs residing in the gap.
剪切阿尔芬连续谱在具有单一岛链的托卡马克中，利用理想磁流体力学理论进行了研究。我们考虑了环向几何以及环向模耦合，并将该岛视为高形变仿星器。由于其在极向和环向的不对称性，岛内打开了多种新的频率间隙，例如镜像诱导阿尔芬本征模（MAE）间隙和螺旋性诱导阿尔芬本征模（HAE）间隙。我们已证明，MAE间隙是外部环向阿尔芬本征模（TAE）间隙向岛内的延续。然而，随着岛的增大，组合的TAE/MAE间隙逐渐变窄，当岛的大小达到小半径的3.2%时，其宽度仅剩原始宽度的一半。此外，在MAE间隙下尖端的连续谱本征函数，现在在岛的长轴附近具有高度局域化的结构，这与在无或低水平环向不对称性下通常观察到的全局振荡解形成对比——这表明连续谱变得离散且密集。这些结果对位于该间隙中的全局TAE的频率、模结构和连续阻尼具有启示意义。