Abstract

We consider the magnetic collapse as a possible process of the magnetic field singularity formation in a finite time in the framework of ideal magnetohydrodynamics for incompressible fluids, which is important for various astrophysical applications (in particular, as the mechanism of formation of magnetic filaments in the convective zone of the Sun). The possibility of collapse is associated with the compressibility of the continuously distributed magnetic field lines. The well-known example of magnetic filament formation in the kinematic dynamo approximation with a given velocity field, which was considered for the first time by Parker in 1963, rather indicates that the magnetic field increases with time exponentially. In the case of the kinematic approximation for the induction equation, the filaments are formed in regions with a hyperbolic velocity profile.

中文翻译：

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关于电磁流体动力学崩溃的注意事项

摘要

在不可压缩流体的理想磁流体动力学的框架内，我们认为磁塌陷是在有限时间内形成磁场奇异性的可能过程，这对于各种天体物理应用（尤其是作为磁流体在磁流体中形成的机理）至关重要。太阳的对流区）。坍塌的可能性与连续分布的磁力线的可压缩性有关。在给定的速度场中，运动学发电机近似中磁丝形成的著名例子（Parker在1963年首次考虑）表明磁场随时间呈指数增长。对于归纳方程的运动学近似，