Existence and Stability of a Model for Three-Dimensional Toroidal Plasma Equilibria

对强非轴对称环形等离子体的模拟有很大的物理意义，但基本的存在问题使严格的数值分析到目前为止是不可能的。我们试图通过研究一类理想化的，但物理激励的，具有阶跃压力分布的磁流体动平衡来克服这一点，已经证明了它存在于轴对称附近。我们将(I)开发数值技术来将这些分段Beltrami态扩展到远离轴对称的地方(Ii)开发实际测试来确定存在何时破裂(Iii)分析关于这种平衡的小振荡的频谱(Iv)将模型扩展到双流体MHD。

There is great physical interest in modelling strongly non-axisymmetric toroidal plasmas, but fundamental existence problems have made rigorous numerical analysis so far impossible. We seek to overcome this by investigating a class of idealized, but physically motivated, magnetohydrodynamic equilibria with stepped pressure profiles for which existence in the neighbourhood of axisymmetry has been proven. We will (i) develop numerical techniques to extend these piece-wise Beltrami states far away from axisymmetry (ii) develop practical tests to determine when existence breaks down (iii) analyze the frequency spectrum of small oscillations about such equilibria (iv) extend the model to two-fluid MHD.