论文标题
关于多区域松弛的变分原理与电阻内层理论之间的关系
On the relationship between the multi-region relaxed variational principle and resistive inner layer theory
论文作者
论文摘要
我们表明，多区域松弛的磁性水力动力学（MRXMHD）模型的变异能原理可用于预测有限压力的线性撕裂不稳定性。在此模型中，等离子体体积切成被“理想界面”隔开的子体积，并且在每个体积中，磁场放松到泰勒状态，其中压力梯度$ \ nabla p = 0 $。 MRXMHD模型是在规格代码中实现的，以便计算每个区域中的平衡解决方案，同时跨接口的保留力平衡。按照规格计算的Hessian矩阵（离散的稳定性矩阵），也可以使用SPEC计算MRXMHD平衡的稳定性。在本文中，使用规格，我们研究了局部压力梯度和$ \ nabla p = 0 $在撕裂模式的谐振表面附近的效果。对于低β血浆，我们能够说明电阻性奇异层理论之间的关系[Coppi等。 （1966）nucl。 Fusion 6 101，Glasser等。流体物理学18，875-888（1975）]和MRXMHD模型。在奇异层中，体积平均磁性螺旋性和通量平均的环形通量被证明是规格模拟中线性撕裂模式的不变性。我们的计算MRXMHD稳定性的技术首先在圆柱形Tokamak中进行数值测试，并证明了其在环形几何形状中的应用。我们证明了通过规格模拟获得的稳定边界与电阻性内层理论之间的一致性。
We show that the variational energy principle of multi-region relaxed magnetohydrodynamic (MRxMHD) model can be used to predict finite-pressure linear tearing instabilities. In this model, the plasma volume is sliced into sub-volumes separated by "ideal interfaces", and in each volume the magnetic field relaxes to a Taylor state where the pressure gradient $\nabla p = 0$. The MRxMHD model is implemented in the SPEC code so that the equilibrium solution in each region is computed while the preserving force balance across the interfaces. As SPEC computes the Hessian matrix (a discretized stability matrix), the stability of an MRxMHD equilibrium can also be computed with SPEC. In this article, using SPEC, we investigate the effect of local pressure gradients and the $\nabla p = 0$ in the vicinity of the resonant surface of a tearing mode. For low beta plasma, we have been able to illustrate a relationship between the resistive singular layer theory [Coppi et al. (1966) Nucl. Fusion 6 101, Glasser et al. The Physics of Fluids 18, 875-888 (1975)], and the MRxMHD model. Within the singular layer, the volume-averaged magnetic helicity and the flux-averaged toroidal flux are shown to be the invariants for the linear tearing modes in SPEC simulations. Our technique to compute MRxMHD stability is first tested numerically in cylindrical tokamak and its application in toroidal geometry is demonstrated. We demonstrate an agreement between the stability boundary obtained with SPEC simulation and the resistive inner layer theories.
