δ函数电流片由共振磁扰动引起的数值研究
Numerical study of $δ$-function current sheets arising from resonant magnetic perturbations
AI总结：
本研究通过GS求解器和SPEC代码数值求解HKT问题，验证了共振磁扰动下奇异电流片形成，并证明两代码结果高度一致。
摘要：
具有连续嵌套磁通面的一般三维环形理想磁流体动力学平衡，在施加共振扰动时容易形成奇异电流片。奇异电流片的存在表明，在非零电阻率的情况下，将发生磁重联，导致磁岛的形成，并且当磁岛重叠时可能产生随机磁力线区域。在理想磁流体动力学极限下，数值解析奇异电流片一直是一个重大挑战。本工作给出了Hahm-Kulsrud-Taylor（HKT）问题的数值解，该问题是共振奇异电流片形成的原型。HKT问题通过两个代码求解：一个Grad-Shafranov（GS）求解器和SPEC代码。GS求解器具有内置的嵌套磁通面，并具有预设的磁通量。SPEC代码实现了多区域松弛磁流体动力学（MRxMHD），其中解在每个区域内松弛到Taylor态，同时保持区域间界面上的力平衡。随着区域数量的增加，MRxMHD解趋近于假设连续嵌套磁通面的理想磁流体动力学解。我们通过彻底的收敛性研究，证明了两个代码获得的数值解之间具有极好的一致性。
英文摘要：
General three-dimensional toroidal ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces are susceptible to forming singular current sheets when resonant perturbations are applied. The presence of singular current sheets indicates that, in the presence of non-zero resistivity, magnetic reconnection will ensue, leading to the formation of magnetic islands and potentially regions of stochastic field lines when islands overlap. Numerically resolving singular current sheets in the ideal MHD limit has been a significant challenge. This work presents numerical solutions of the Hahm-Kulsrud-Taylor (HKT) problem, which is a prototype for resonant singular current sheet formation. The HKT problem is solved by two codes: a Grad-Shafranov (GS) solver and the SPEC code. The GS solver has built-in nested flux surfaces with prescribed magnetic fluxes. The SPEC code implements multi-region relaxed magnetohydrodynamics (MRxMHD), where the solution relaxes to a Taylor state in each region while maintaining force balance across the interfaces between regions. As the number of regions increases, the MRxMHD solution approaches the ideal MHD solution assuming a continuum of nested flux surfaces. We demonstrate excellent agreement between the numerical solutions obtained from the two codes through a thorough convergence study.
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