具有不变曲面的解析环形三维磁流体动力学平衡与稳态欧拉流
Analytic toroidal 3D MHD equilibria and steady Euler flows with invariant surfaces
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中文总结 AI 辅助
本文提出非轴对称环形磁流体动力学平衡的显式解析解族，具有嵌套磁通面，作为Grad猜想的反例，可用于验证数值代码。
中文摘要 AI 辅助
本文给出了磁流体动力学平衡方程的一系列显式解析解族，这些解等价于稳态不可压缩欧拉流。解是非轴对称的，并具有精确的嵌套环形磁通面。在求解过程中，未对逆纵横比或偏离轴对称性进行展开。磁场和磁通面在笛卡尔坐标下用初等函数显式给出。磁场、电流密度和标量压力在环形域内光滑。压力梯度仅在磁轴上消失。一个解族具有均匀的旋转变换$\iota=2$，而另一个解族具有剪切的$\iota$剖面。这些对Grad猜想的反例对于理解三维平衡的存在性和正则性以及测试数值代码具有重要价值。
英文摘要
Families of explicit analytic solutions of the magnetohydrodynamic equilibrium equations are presented, equivalent to steady incompressible Euler flow. The solutions are non-axisymmetric and possess exact nested toroidal flux surfaces. No expansion is made in inverse aspect ratio or in the deviation from axisymmetry. The magnetic field and flux surfaces are given explicitly in Cartesian coordinates using elementary functions. The field, current density, and scalar pressure are smooth over the toroidal domain. The pressure gradient vanishes only on the magnetic axis. One family of solutions has uniform rotational transform $ι=2$, while another family has a sheared $ι$ profile. These counterexamples to Grad's conjecture are valuable for understanding the existence and regularity of 3D equilibria and for testing numerical codes.
发表机构
- University of Maryland, College Park（马里兰大学帕克分校）
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