磁流体力学中的拓扑孤子

Constructing a class of topological solitons in magnetohydrodynamics

We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, $n_t$ and $n_p$ respectively. The special case of $n_t=1$ and $n_p=1$ corresponds to the Kamchatnov-Hopf soliton, a magnetic field configuration everywhere tangent to the fibers of a Hopf fibration so that the field lines are circular, linked exactly once, and form the surfaces of nested tori. We show that for $n_t \in \mathbb{Z}^+$ and $n_p=1$ these configurations represent stable, localized solutions to the magnetohydrodynamic equations for an ideal incompressible fluid with …

Topological Implications of the Total Generalized Electron-Flow Magnetic Helicity Invariant in Electron Magnetohydrodynamics

Topological implications of the total generalized electron-flow magnetic helicity He in electron magnetohydrodynamics(EMHD) are explored. The invariance of He is shown to imply the invariance of the sum of the linkage of the magnetic field lines, the linkage of electron-flow vorticity field lines and the mutual linkage among these two sets of field lines. This result appears to support a change in the magnetic field topology and hence pave the way for magnetic reconnection in EMHD via a change in the concomitant electron-flow vorticity topology.

Plasma Relaxation and Topological Aspects in Hall Magnetohydrodynamics

Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential vorticity." The Hall MHD Beltrami condition becomes equivalent to the "potential vorticity" conservation equation in two-dimensional (2D) hydrodynamics if the Hall MHD Lagrange multiplier beta is taken to be proportional to the "potential vorticity" as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as "po…

Shafranov维里定理与磁等离子体约束

Shafranov's virial theorem and magnetic plasma confinement

Shafranov的维里定理意味着非平凡的磁流体动力学平衡配置必须由外部提供的电流支持。在这里，我们将维里定理推广到场论，它与Derrick关于孤子稳定性的标度论证有关。然后，我们采用维里参数调查一个现实的场论模型的两个组成部分的等离子体，并得出结论，稳定的局域孤子可以存在于有限密度的等离子体的体积。这些孤子需要一个非平凡的电场，这意味着纯粹的磁流体力学参数是不足以描述稳定的，非平凡的结构内的大部分等离子体。

Noether Currents for Eulerian Variational Principles in Non Barotropic Magnetohydrodynamics and Topological Conservations Laws

We derive a Noether current for the Eulerian variational principle of ideal non-barotropic magnetohydrodynamics (MHD). It was shown previously that ideal non-barotropic MHD is mathematically equivalent to a five function field theory with an induced geometrical structure in the case that field lines cover surfaces and this theory can be described using a variational principle. Here we use various symmetries of the flow to derive topological constants of motion through the derived Noether current and discuss their implication for non-barotropic MHD.

Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics

The paper describes the unique geometric properties of ideal magnetohydrodynamics (MHD), and demonstrates how such features are inherited by extended MHD, viz. models that incorporate two-fluid effects (the Hall term and electron inertia). The generalized helicities, and other geometric expressions for these models are presented in a topological context, emphasizing their universal facets. Some of the results presented include: the generalized Kelvin circulation theorems; the existence of two Lie-dragged 2-forms; and two concomitant helicities that can be studied via the Jones polynomial, whic…