论文标题
在不对称限制容器中，对称理想的磁静脉平衡，具有非呈现压力梯度
Symmetric Ideal Magnetofluidostatic Equilibria with Non-Vanishing Pressure Gradients in Asymmetric Confinement Vessels
论文作者
论文摘要
我们研究了满足不对称限制容器中与切向边界条件的理想磁流失动力学的力平衡方程的稳定磁场的可能性，即在连续欧几里得异构体下不变的有界区域（翻译，旋转或组合）。下一代融合反应堆的设计通常会遇到这个问题。我们表明，如果一个人放宽了容器边界对应于压力等音表面的标准假设，则可以使用这种配置。我们展示了具有欧几里得对称性的平滑溶液，但在不对称的椭圆形结构域中解决了边界值问题，同时维持了非呈现压力梯度。该结果为不对称界面域中常规理想磁静脉平衡的存在提供了明确的答案。是否存在边界价值问题的规则不对称解决方案，问题保持开放。
We study the possibility of constructing steady magnetic fields satisfying the force balance equation of ideal magnetohydrodynamics with tangential boundary conditions in asymmetric confinement vessels, i.e. bounded regions that are not invariant under continuous Euclidean isometries (translations, rotations, or their combination). This problem is often encountered in the design of next-generation fusion reactors. We show that such configurations are possible if one relaxes the standard assumption that the vessel boundary corresponds to a pressure isosurface. We exhibit a smooth solution that possesses an Euclidean symmetry and yet solves the boundary value problem in an asymmetric ellipsoidal domain while sustaining a non-vanishing pressure gradient. This result provides a definitive answer to the problem of existence of regular ideal magnetofluidostatic equilibria in asymmetric bounded domains. The question remains open whether regular asymmetric solutions of the boundary value problem exist.
