We derive a sufficient condition for the linear stability of plasma equilibria with incompressible flow parallel to the magnetic field, $\boldsymbol{B}$ , constant mass density and anisotropic pressure such that the quantity $\unicode[STIX]{x1D70E}_{d}=\unicode[STIX]{x1D707}_{0}(P_{\Vert }-P_{\bot })/B^{2}$ , where $P_{\Vert }$ ( $P_{\bot }$ ) is the pressure tensor element parallel (perpendicular) to $\boldsymbol{B}$ , remains constant. This condition is applicable to any steady state without geometrical restriction. The condition, generalising the respective condition for magnetohydrodynamic equilibria with isotropic pressure and constant density derived in Throumoulopoulos & Tasso (Phys. Plasmas, vol. 14, 2007, 122104), involves physically interpretable terms related to the magnetic shear, the flow shear and the variation of total pressure perpendicular to the magnetic surfaces. On the basis of this condition we prove that, if a given equilibrium is linearly stable, then the ones resulting from the application of Bogoyavlenskij symmetry transformations are linearly stable too, provided that a parameter involved in those transformations is positive. In addition, we examine the impact of pressure anisotropy, flow and torsion of a helical magnetic axis, for a specific class of analytic equilibria. In this case, we find that the pressure anisotropy and the flow may have either stabilising or destabilising effects. Also, helical configurations with small torsion and large pitch seem to have more favourable stability properties.

中文翻译：

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场定向不可压缩流各向异性压力平衡的线性稳定性

我们推导出具有平行于磁场的不可压缩流动的等离子体平衡的线性稳定性的充分条件， $\boldsymbol{B}$ , 恒定质量密度和各向异性压力使得量 $\unicode[STIX]{x1D70E}_{d}=\unicode[STIX]{x1D707}_{0}(P_{\Vert }-P_{\bot })/B^{2}$ ， 在哪里 $P_{\垂直}$ ( $P_{\bot }$ ) 是平行（垂直）的压力张量元素 $\boldsymbol{B}$ ， 保持不变。此条件适用于任何没有几何限制的稳态。该条件概括了在 Throumoulopoulos 和 Tasso (物理。等离子, 卷。14, 2007, 122104)，涉及与磁剪切、流动剪切和垂直于磁表面的总压力变化相关的物理可解释术语。在这个条件的基础上，我们证明，如果给定的平衡是线性稳定的，那么应用 Bogoyavlenskij 对称变换得到的平衡也是线性稳定的，前提是这些变换中涉及的参数是正的。此外，我们研究了压力各向异性、螺旋磁轴的流动和扭转对特定类型的解析平衡的影响。在这种情况下，我们发现压力各向异性和流动可能具有稳定或不稳定的效果。此外，具有小扭转和大螺距的螺旋结构似乎具有更有利的稳定性特性。