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arXiv physics/0102001physics.plasm-phphysics.space-ph
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等离子体中的拓扑扭转和拓扑自旋相干结构

Topological-Torsion and Topological-Spin as coherent structures in plasmas

R. M. Kiehn

摘要:

经典电磁学的偏微分方程可以由两个外部微分系统产生,这两个外部微分系统在拓扑上将场强和电势F-dA= 0与场激发和电荷电流密度J-dG = 0区分开来。势A的存在导致独立的3-形式的T-Torsion = A^F和T-Spin = A^G。这些3-形式的外导数(发散)产生定义两个经典庞加莱不变量的异常。这些形式的封闭积分,当冻结场的变形不变量时,定义等离子体中的拓扑相干结构。当T-Torsion(T-Spin)为零时的解定义了拓扑基础上的横向磁(电)模。当T-Torsion的发散不为零时,存在一个经典的机制,电荷沿磁场线加速产生辛等离子体电流;沿B场线的大温度梯度可以作为中子星中恒星等离子体喷流的来源。在这种情况下,扭转矢量由动作电位的共形不变性唯一定义。在挠率矢量方向上的等离子体电流使A^F和A^G保持共形不变,因此这些场被冻结,即使过程是不可逆的。与这种冻结场相关的衰减相干和可变形拓扑结构是持久和可观察的伪像,类似于尾流,可以出现在任何等离子体域中,例如围绕恒星的区域。

英文摘要:

The PDE's of classical electromagnetism can be generated from two exterior differential systems that distinguish topologically the field intensities and potentials, F-dA= 0, from the field excitations and the charge current densities, J-dG = 0. The existence of potentials, A, leads to the independent 3-forms of T-Torsion = A^F and T-Spin = A^G. The exterior derivatives (divergences) of these 3-forms produce anomalies that define the two classic Poincare invariants. The closed integrals of these forms, when deformation invariants of frozen-in fields, define topological coherent structures in the plasma. Solutions when T-Torsion (T-Spin) is zero define transverse magnetic (electric) modes on topological grounds. When the divergence of T-Torsion is not zero there exists a classical mechanism for charge acceleration along the magnetic field lines producing symplectic plasma currents; large temperature gradients along the B field lines can act as a source of stellar plasma jets in neutron stars. In such circumstances, the Torsion vector is uniquely defined by conformal invariance of the Action potentials. Plasma currents in the direction of the Torsion vector leave both A^F and A^G conformally invariant, hence these fields are frozen-in even though the processes are thermodynamically irreversible. The decaying coherent and deformable topological structures associated with such frozen-in fields are persistent and observable artifacts, similar to wakes, that can appear in any plasma domain, such as that which surrounds stars.

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