What is a large-scale dynamo?

We consider kinematic dynamo action in a sheared helical flow at moderate to high values of the magnetic Reynolds number Rm. We find exponentially growing solutions which, for large enough shear, take the form of a coherent part embedded in incoherent fluctuations. We argue that at large Rm large-scale dynamo action should be identified by the presence of structures coherent in time, rather than those at large spatial scales. We further argue that although the growth-rate is determined by small-scale processes, the period of the coherent structures is set by mean-field considerations

A model of plasma heating by large-scale flow

PublishedIn this work, we study the process of energy dissipation triggered by a slow large-scale motion of a magnetized conducting fluid. Our consideration is motivated by the problem of heating the solar corona, which is believed to be governed by fast reconnection events set off by the slow motion of magnetic field lines anchored in the photospheric plasma. To elucidate the physics governing the disruption of the imposed laminar motion and the energy transfer to small scales, we propose a simplified model where the large-scale motion of magnetic field lines is prescribed not at the footpoints but rather imposed volumetrically. As a result, the problem can be treated numerically with an efficient, highly accurate spectral method, allowing us to use a resolution and statistical ensemble exceeding those of the previous work. We find that, even though the large-scale deformations are slow, they eventually lead to reconnection events that drive a turbulent state at smaller scales. The small-scale turbulence displays many of the universal features of field-guided magnetohydrodynamic turbulence like a well-developed inertial range spectrum. Based on these observations, we construct a phenomenological model that gives the scalings of the amplitude of the fluctuations and the energy-dissipation rate as functions of the input parameters. We find good agreement between the numerical results and the predictions of the model.This research was supported by the NSF Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas at the University of Chicago, by the US DOE award no. DE-SC0003888, by the NASA grant no. NNX11AE12G, and by the National Science Foundation under grant no. NSF PHY11-25915 and no. AGS-1261659. SB and JM appreciate the hospitality and support of the Kavli Institute for Theoretical Physics, University of California, Santa Barbara, where part of this work was conducted. Simulations were performed at the Texas Advanced Computing Center (TACC) at the University of Texas at Austin under the NSF-Teragrid Projects TG-AST140015 & TG-PHY120042 and by the National Institute for Computational Sciences

Shear-Driven Dynamo Waves in the Fully Nonlinear Regime

Large-scale dynamo action is well understood when the magnetic Reynolds number (Rm) is small, but becomes problematic in the astrophysically relevant large Rm limit since the fluctuations may control the operation of the dynamo, obscuring the large-scale behavior. Recent works by Tobias & Cattaneo demonstrated numerically the existence of large-scale dynamo action in the form of dynamo waves driven by strongly helical turbulence and shear. Their calculations were carried out in the kinematic regime in which the back-reaction of the Lorentz force on the flow is neglected. Here, we have undertaken a systematic extension of their work to the fully nonlinear regime. Helical turbulence and large-scale shear are produced self-consistently by prescribing body forces that, in the kinematic regime, drive flows that resemble the original velocity used by Tobias & Cattaneo. We have found four different solution types in the nonlinear regime for various ratios of the fluctuating velocity to the shear and Reynolds numbers. Some of the solutions are in the form of propagating waves. Some solutions show large-scale helical magnetic structure. Both waves and structures are permanent only when the kinetic helicity is non-zero on average