Hall等离子体中扭曲细丝的磁螺旋度拓扑
Topology of magnetic helicity of torsioned filaments in Hall plasmas
摘要：
在非完整系中，得到了库仑规范下等离子体细丝磁霍尔方程的一个解。该解的一些物理特征包括磁螺旋度的不守恒和丝中磁场的衰减。从数学的角度来看，弗伦内扭转的存在下，实际上被证明是根本的破坏的情况下，螺旋形的灯丝的磁螺旋守恒。由于即使在库仑规范中磁螺旋度也不守恒，而且磁场会衰减，我们可以说发电机作用失效了。实际上挠率的存在加强了磁场螺旋度守恒的破缺。在不考虑霍尔效应的情况下，Moffatt和Ricca（PRSA-1992）在完整细丝的情况下得到了与这里得到的公式类似的公式。结果表明，未打结的磁丝可能会对磁能的下限。讨论了扭数问题。
英文摘要：
A solution of magnetic Hall equations for plasma filaments in the Coulomb gauge is obtained in the non-holonomic frame. Some physical features of the solution include, the non-conservation of the magnetic helicity and the decay of the magnetic field in the filaments. From the mathematical point of view,the presence of Frenet torsion in the filament is actually shown to be fundamental for the breaking of conservation of magnetic helicity in the case of helicoidal filaments. Since the magnetic helicity is not conserved even in the Coulomb gauge, and the magnetic field decays, one can say that the dynamo action fails. Actually the presence of torsion enhances the breaking of magnetic field helicity conservation. A similar formula of the one obtained here without considering the Hall effect has been obtained by Moffatt and Ricca (PRSA-1992) in the case of holonomic filaments. It is shown that unknotted magnetic filaments may place a lower bound on the magnetic energy. Discussions on the writhe number are also discussed.
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