At the heart of today's solar magnetic field evolution models lies the alpha dynamo description. In this work, we investigate the fate of alpha-dynamos as the magnetic Reynolds number $Rm$ is increased. Using Floquet theory, we are able to precisely quantify mean field effects like the alpha and beta effect (i) by rigorously distinguishing dynamo modes that involve large scale components from the ones that only involve small scales, and by (ii) providing a way to investigate arbitrary large scale separations with minimal computational cost. We apply this framework to helical and non-helical flows as well as to random flows with short correlation time. Our results determine that the alpha-description is valid for $Rm$ smaller than a critical value $Rm_c$ at which small scale dynamo instability starts. When $Rm$ is above $Rm_c$ the dynamo ceases to follow the mean field description and the growth rate of the large scale modes becomes independent of the scale separation while the energy in the large scale modes is inversely proportional to the square of the scale separation. The results in this second regime do not depend on the presence of helicity. Thus alpha-type modeling for solar and stellar models needs to be reevaluated and new directions for mean field modeling are proposed.
Laminar and turbulent dynamos in chiral magnetohydrodynamics-I: Theory
具有相对论性粒子的等离子体的磁流体动力学（MHD）描述必然包括额外的新领域，与轴向电荷相关联的手性化学势（即，右手和左手相对论费米子之间的数量差异）。该手性化学势对等离子体的电流密度（\emph{chiral magnetic effect}）产生贡献。我们提出了一个自洽处理的\emph{chiral MHD equations}，其中包括反反应的磁场上的手征化学势和它的相互作用与等离子体速度场。一些新的现象被展出。首先，我们表明，手征磁效应的不可压缩流的Alfvén波的频率降低，可压缩流的Alfvén波和快磁声波的频率增加，并降低慢磁声波的频率。其次，我们表明，除了众所周知的层流手征发电机效应，这是不相关的流体运动，有一个发电机所造成的共同作用的速度剪切和手征磁效应。在湍流的平均动力学螺旋度消失的存在下，推导的平均场手征MHD方程描述了由手征α效应引起的湍流大尺度发电机，这对于大的流体和磁雷诺数是占主导地位的。手征α效应是由于手征磁效应和由缠结磁波动（其由剪切速度波动引起的大尺度磁场的缠结产生）产生的小尺度电流的波动的相互作用。这些发电机效应可能对早期宇宙、中子星和夸克-胶子等离子体的动力学产生有趣的影响。
