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首页> 外文期刊>Physics of plasmas >The eigenfrequency spectrum of linear magnetohydrodynamic perturbations in stationary equilibria: A variational principle
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The eigenfrequency spectrum of linear magnetohydrodynamic perturbations in stationary equilibria: A variational principle

机译：平稳平衡中线性磁流体动力扰动的本征谱：变分原理

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摘要

The frequencies of the normal modes of oscillation of linear magnetohydrodynamic perturbations of a stationary equilibrium are related to the stationary points of a quadratic functional over the Hilbert space of Lagrangian displacement vectors, which is subject to a constraint. In the absence of a background flow (or of a uniform flow), the relation reduces to the well-known Rayleigh-Ritz variational principle. In contrast to the existing variational principles for perturbations of stationary equilibria, the present treatment does neither impose additional symmetry restrictions on the equilibrium, nor does it involve the generalization to bilinear functionals instead of quadratic forms. This allows a more natural interpretation of the quadratic forms as energy functionals.
机译：平稳平衡的线性磁流体动力扰动的正常振动模态的频率与拉格朗日位移矢量的希尔伯特空间上二次函数的平稳点有关，这受到一个约束。在没有背景流（或均匀流）的情况下，该关系式简化为众所周知的瑞利-里兹变分原理。与现有的平稳平衡摄动变分原理相反，本处理既不对平衡施加其他对称限制，也没有涉及对双线性泛函而不是二次形式的泛化。这样可以更自然地将二次形式解释为能量泛函。

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