It is shown that the variational principle of multi-region relaxed magnetohydrodynamics (MRxMHD) can be used to predict the stability and nonlinear saturation of tearing modes in strong guide field configurations without resolving the dynamics and without explicit dependence on the plasma resistivity. While the magnetic helicity is not a good invariant for tearing modes, we show that the saturated tearing mode can be obtained as an MRxMHD state of a priori unknown helicity by appropriately constraining the current profile. The predicted saturated island width in a tearing-unstable force-free slab equilibrium is shown to reproduce the theoretical scaling at small values of Δ ′ and the scaling obtained from resistive magnetohydrodynamics simulations at large Δ ′.

中文翻译：

---

使用变分原理直接预测非线性撕裂模式饱和

结果表明，多区域弛豫磁流体动力学（MRxMHD）的变分原理可用于预测强导场配置中撕裂模式的稳定性和非线性饱和，而无需解析动力学，也无需明确依赖等离子体电阻率。虽然磁螺旋度不是撕裂模式的良好不变性，但我们表明，通过适当约束电流分布，可以将饱和撕裂模式作为先验未知螺旋度的 MRxMHD 状态获得。显示在撕裂不稳定的无力平板平衡中预测的饱和岛宽度再现了小值 Δ ' 的理论比例和从大 Δ ' 的电阻磁流体动力学模拟获得的比例。