论文标题
真空磁场在通量表面附近具有精确的准对称性。第1部分：轴对称表面附近的解决方案
Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1: Solutions near an axisymmetric surface
论文作者
论文摘要
尽管有几个结果表明表面上存在准确的准对称场（Garren＆Boozer 1991a，B; Plunk＆Helander 2018），但我们使用真空表面扩张形式主义获得了第一个此类溶液。我们获得了一个函数$η$的单个非线性抛物线PDE，因此场强满足$ b = b（η）$。封闭式溶液是在圆柱，平板和同性动力学几何形状中获得的。获得了整个非线性方程的数值溶液在一般轴对称环形几何形状中，从而在轴对称表面附近产生了一类准螺旋局部真空平衡。分析模型提供了对非线性溶液的一般特征的更多见解，例如在板侧的表面扰动定位。
While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer 1991a,b; Plunk & Helander 2018), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic PDE for a function $η$ such the field strength satisfies $B = B(η)$. Closed-form solutions are obtained in cylindrical, slab, and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasi-helical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side.
