发表机构
Institute for Fusion Studies and Physics Department, University of Texas at Austin（德克萨斯大学奥斯汀分校聚变研究所与物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究平面电流 - 涡旋片中不稳定性和阿尔文共振，扩展卢瑟福模型考虑剪切平衡流对磁岛大小的影响，发现极化电流影响撕裂模非线性增长，不同\(r\)值下磁岛饱和情况不同，且等\(\psi\)不能完全表征有阿尔文共振时磁岛的非线性增长。
AI 中文摘要
本文给出了平面电流 - 涡旋片中不稳定性和阿尔文共振的线性及非线性发展情况，其剪切平衡分布为\(\boldsymbol{B_{y0}} = \tanh(z)\boldsymbol{\hat{y}}\)和\(\boldsymbol{V_{y0}} = M_0\tanh(z/r)\boldsymbol{\hat{y}}\)。我们扩展了卢瑟福关于等\(\psi\)磁岛的非线性模型，以考虑剪切平衡流，并确定该流对磁岛大小的影响。发现平衡流引起的极化电流减缓了撕裂模的非线性增长。对于\(r > 1\)，磁岛饱和稍有加速；\(r < 1\)时减缓；\(r = 1\)时不变。最后发现，存在阿尔文共振时，等\(\psi\)不再能充分表征非线性区域磁岛的增长，该模型无法捕捉此类磁岛的动力学。
英文摘要
The linear and nonlinear development of instabilities and Alfvén resonances in a plane current-vortex sheet is presented here for sheared equilibrium profiles $\boldsymbol{B_{y0}} = \tanh(z)\boldsymbol{\hat{y}}$ and $\boldsymbol{V_{y0}} = M_0\tanh(z/r)\boldsymbol{\hat{y}}$. We extend Rutherford's nonlinear model for constant-psi magnetic islands to account for a sheared equilibrium flow and determine the flow's impact on the magnetic island's nonlinear evolution for $M_0<1$. In this regime, the flow introduces two nonlinear contributions: a polarization current term and a modification of the saturation term derived by Militello and Porcelli (2004). We find that the polarization current generated by the equilibrium flow consistently reduces the nonlinear growth rate of the tearing mode. The flow-induced modification of the saturation term, however, depends on the magnetic-to-velocity shear width ratio, $r$. For $r=1$, the saturation term is unchanged from the case without flow. For $r>1$, it increases in magnitude with $M_0$, strengthening its stabilizing effect and further reducing the island growth rate. In contrast, for $r<1$, the saturation term decreases in magnitude with increasing $M_0$ and can become positive, leading to a transition from a stabilizing to a destabilizing contribution. Nevertheless, throughout the parameter range considered, the combined effect of the polarization current and modified saturation term is to slow the growth of the magnetic island. Finally, we find that, in the presence of Alfvén resonances, the magnetic island's growth in the nonlinear regime is no longer adequately characterized by constant-psi, and the dynamics of such islands are not captured by the model.
