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arXiv 2104.01387physics.plasm-ph
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周期非对称域中的稳态等离子体流

Steady plasma flows in a periodic non-symmetric domain

Harold Weitzner, Wrick Sengupta

AI总结:

本研究将扰动方法扩展到带流动的MHD平衡,在非对称环形域中构造近平行流的稳态解,并推导广义Grad-Shafranov方程和Hamada条件,以抑制奇异电流。

摘要:

稳态等离子体流几乎只在具有连续对称性或开放域系统中被研究。在没有连续对称性的情况下,守恒量的缺失使得流动研究本质上具有挑战性。在环形域中,物理量的双周期性要求增加了复杂性。特别是,当磁场旋转变换为有理数时,非对称环形域中带流动的磁流体动力学(MHD)稳态模型允许奇点的产生,这与平衡MHD模型类似。在这项工作中,我们表明只要旋转变换接近有理数且磁剪切较弱,稳态流仍然可以维持。我们将Weitzner(Physics of Plasmas 21, 022515 (2014))为静态MHD平衡开发的全阶扰动方法技术扩展到带流动的MHD平衡。我们在双周期域中通过逐阶系统地消除磁共振,构造了具有近平行流的扰动MHD平衡。然后,我们利用流动问题的附加对称性(首次由E. Hameiri在(J. Math. Phys. 22, 2080 (1981) Sec. III)中讨论),获得了一类非对称三维MHD平衡的广义Grad-Shafranov方程,其中流动既平行于又垂直于磁场。对于这类流动,我们能够获得运动积分(如伯努利函数和角动量)的非对称推广。最后,我们获得了广义Hamada条件,这些条件是在磁场线闭合时抑制此类系统中奇异电流所必需的一致性条件。我们不试图解决流动的新经典阻尼问题。

英文摘要:

Steady plasma flows have been studied almost exclusively in systems with continuous symmetry or in open domains. In the absence of continuous symmetry, the lack of a conserved quantity makes the study of flows intrinsically challenging. In a toroidal domain, the requirement of double-periodicity for physical quantities adds to the complications. In particular, the magnetohydrodynamics (MHD) model of plasma steady-state with the flow in a non-symmetric toroidal domain allows the development of singularities when the rotational transform of the magnetic field is rational, much like the equilibrium MHD model. In this work, we show that steady flows can still be maintained provided the rotational transform is close to rational and the magnetic shear is weak. We extend the techniques developed in carrying out perturbation methods to all orders for static MHD equilibrium by Weitzner (Physics of Plasmas 21, 022515 (2014)) to MHD equilibrium with flows. We construct perturbative MHD equilibrium in a doubly-periodic domain with nearly parallel flows by systematically eliminating magnetic resonances order by order. We then utilize an additional symmetry of the flow problem, first discussed by E. Hameiri in (J. Math. Phys. \textbf{22}, 2080 (1981) Sec. III), to obtain a generalized Grad-Shafranov equation for a class of non-symmetric three-dimensional MHD equilibrium with flows both parallel and perpendicular to the magnetic field. For this class of flows, we are able to obtain non-symmetric generalizations of integrals of motion, such as Bernoulli's function and angular momentum. Finally, we obtain the generalized Hamada conditions, which are consistency conditions necessary to suppress singular currents in such a system when the magnetic field lines are closed. We do not attempt to address the question of neoclassical damping of flows.

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