具有近似磁通量面的等离子体中非线性磁场湍流的简化理想 MHD 系统

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL Journal of Mathematical Physics Pub Date : 2024-09-10 DOI:10.1063/5.0186445
Naoki Sato, Michio Yamada
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引用次数: 0

摘要

本文研究了稳定理想磁流体力学(MHD)构型附近磁场湍流的非线性演变,该构型以小电流、小等离子体流和近似通量面为特征,这种物理环境与恒星器中的等离子体约束有关。研究的目的是深入了解磁场动力学,阐明三维 MHD 平衡的可达性和稳定性,以及制定计算它们的实用方法。从理想的 MHD 方程出发,我们得到了磁通量函数和角度变量的两个耦合非线性偏微分方程的简化动力学系统,该系统与磁场的 Clebsch 表示相关。结果表明,在合适的边界和量规条件下,这种简化系统能保持磁能、磁螺旋度和总磁通量。确定了还原系统的非规范哈密顿结构,并用它来证明稳定解在只涉及一个克莱布什势的扰动下的非线性稳定性。哈密顿结构还被用于通过双括号方法构建耗散动力系统。这个耗散系统可以通过最小化能量来计算 MHD 平衡态,直到达到哈密顿的临界点。最后,提出了一种基于简化系统中两个稳定方程交替求解的迭代方案,作为计算 MHD 平衡的进一步方法。定理表明,只要在迭代的每一步都存在解,迭代方案就会收敛到非微观的 MHD 平衡点。
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A reduced ideal MHD system for nonlinear magnetic field turbulence in plasmas with approximate flux surfaces
This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal Magnetohydrodynamics (MHD) configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that is relevant for plasma confinement in stellarators. The aim is to gather insight on magnetic field dynamics, to elucidate accessibility and stability of three-dimensional MHD equilibria, as well as to formulate practical methods to compute them. Starting from the ideal MHD equations, a reduced dynamical system of two coupled nonlinear partial differential equations for the flux function and the angle variable associated with the Clebsch representation of the magnetic field is obtained. It is shown that under suitable boundary and gauge conditions such reduced system preserves magnetic energy, magnetic helicity, and total magnetic flux. The noncanonical Hamiltonian structure of the reduced system is identified, and used to show the nonlinear stability of steady solutions against perturbations involving only one Clebsch potential. The Hamiltonian structure is also applied to construct a dissipative dynamical system through the method of double brackets. This dissipative system enables the computation of MHD equilibria by minimizing energy until a critical point of the Hamiltonian is reached. Finally, an iterative scheme based on the alternate solution of the two steady equations in the reduced system is proposed as a further method to compute MHD equilibria. A theorem is proven which states that the iterative scheme converges to a nontrivial MHD equilbrium as long as solutions exist at each step of the iteration.
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来源期刊
Journal of Mathematical Physics
Journal of Mathematical Physics 物理-物理:数学物理
CiteScore
2.20
自引率
15.40%
发文量
396
审稿时长
4.3 months
期刊介绍: Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.
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