论文标题
非轴对称MHD平衡的广义毕业生方程
Generalized Grad-Shafranov equation for non-axisymmetric MHD equilibria
论文作者
论文摘要
众所周知，接受欧几里得对称性连续家庭的静态MHD平衡的结构已得到充分了解。这样的场合配置受经典的毕业生shafranov方程的控制，该方程是两个空间维度的单个椭圆形PDE。通过揭示隐藏的对称性，我们表明，实际上所有平衡方程的平滑溶液都远离磁轴，可以满足Grad-Shafranov方程的概括。与经典毕业生级方程的解决方案相反，HE广义方程的解不是自动平衡，而是仅满足一个参数隐藏对称性的力平衡。然后，我们解释了如何使用广义的毕业生级方程来重新制定找到平衡方程的精确三维平滑溶液的问题，因为找到了最佳的量化体积具有相对的对称性。
The structure of static MHD equilibria that admit continuous families of Euclidean symmetries is well understood. Such field configurations are governed by the classical Grad-Shafranov equation, which is a single elliptic PDE in two space dimensions. By revealing a hidden symmetry, we show that in fact all smooth solutions of the equilibrium equations with non-vanishing pressure gradients away from the magnetic axis satisfy a generalization of the Grad-Shafranov equation. In contrast to solutions of the classical Grad-Shafranov equation, solutions of he generalized equation are not automatically equilibria, but instead only satisfy force balance averaged over the one-parameter hidden symmetry. We then explain how the generalized Grad-Shafranov equation can be used to reformulate the problem of finding exact three-dimensional smooth solutions of the equilibrium equations as finding an optimal volume-preserving symmetry.
