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.
Understanding large-scale dynamos in unstratified rotating shear flows
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（理论科学国际中心，塔塔基础研究所）；Princeton Plasma Physics Laboratory, Princeton University（普林斯顿等离子体物理实验室，普林斯顿大学）；Department of Astrophysical Sciences, Princeton University（天体物理学系，普林斯顿大学）；Department of Physics and Astronomy, University of Rochester（物理与天文系，罗切斯特大学）
Wave interference as the origin of the cyclic magnetorotational dynamo in accretion disks: insights from weakly nonlinear theory and local shearing box simulations
Institute for Advanced Study（高等研究院）；Princeton University（普林斯顿大学）；Perimeter Institute for Theoretical Physics（基础物理研究所）
Detecting deep axisymmetric toroidal magnetic fields in stars. The traditional approximation of rotation for differentially rotating deep spherical shells with a general azimuthal magnetic field
The PICO-Cluster Project: presenting the galaxy cluster sample and studying magnetic field growth, Faraday rotation and Braginskii heating
Niels Bohr Institute, University of Copenhagen（尼尔斯·玻尔学院，哥本哈根大学）；Leibniz-Institut für Astrophysik Potsdam (AIP)（波茨坦莱布尼茨天体物理研究所）；Max-Planck Institute for Astrophysics（马克斯·普朗克天体物理研究所）
