论文标题
平均电场发电机方程不适合用线性电动力
Ill-posedness of the mean-field dynamo equations with a linear electromotive force
论文作者
论文摘要
我们表明，当电动力线性地依赖于磁场时，非相关磁力发电机方程的初始值问题被证明不足。该结果意味着，磁能的增加不一定来自物理扩增机制，因为尽管有任何类似动力的过程，但某些磁模式可以随着波浪频率的增加而任意生长。因此，直到该顺序，该理论不适用于天体物理模拟。然后，我们研究了当电磁场衍生物中电动力线性的情况下，表明所得系统存在良好的问题。最后，我们将良好的理论应用于无力度制度，为此，我们找到了分析磁性螺旋性演变的相应磁能的边界。
We show that the initial-value problem for the non-relativistic magnetic dynamo equation turns out to be ill-posed when the electromotive force depends linearly on the magnetic field. This result implies that the increasing of magnetic energy does not necessarily come from physical amplification mechanisms, since certain magnetic modes could arbitrarily grow as wave-frequency increases, despite any dynamo-like process. Thus, up to this order, the theory is not suitable for astrophysical simulations. We then study the case when electromotive forces are linear in magnetic field derivatives, showing that the resulting system has a well-posed problem. Finally, we apply the well-posed theory to the force-free regime, for which we find bounds for the corresponding magnetic energy analyzing the evolution of the magnetic helicity.
