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We study the inverse cascade of magnetic helicity in conducting fluids, as pertinent to the generation and dynamics of magnetic fields as observed, e.g., in the solar corona, by investigating the detailed transfer of helicity between different spherical shells in Fourier space in direct numerical simulations of three-dimensional magnetohydrodynamics (MHD). Two different numerical simulations are used, one in which the system is forced with an electromotive force in the induction equation and one in which the system is forced mechanically with an ABC flow and the magnetic field is solely sustained by a dynamo action. The magnetic helicity cascade at the initial stages of both simulations is observed to be inverse and local (in scale space) at large scales and direct and local at small scales. When saturation is approached, most of the helicity is concentrated at large scales and the cascade is nonlocal. Helicity is transferred directly from the forced scales to the largest scales. At the same time, a smaller in amplitude direct cascade is observed from the largest scale to small scales.

A three-dimensional numerical computation of magnetohydrodynamic dynamo behavior is described. The dynamo is mechanically forced with a driving term of the Taylor-Green type. The magnetic field development is followed from negligibly small levels to saturated values that occur at magnetic energies comparable to the kinetic energies. Although there is locally a nonzero helicity density, there is no overall integrated helicity in the system. Persistent oscillations are observed in the saturated state for not-too-large mechanical Reynolds numbers, oscillations in which the kinetic and magnetic energies vary out of phase but with no reversal of the magnetic field. The flow pattern exhibits considerable geometrical structure in this regime. As the Reynolds number is increased, the oscillations disappear and the energies become more nearly stationary, but retain some unsystematically fluctuating turbulent time dependence. The regular geometrical structure of the fields gives way to a more spatially disordered distribution. The injection and dissipation scales are identified, and the different components of energy transfer in Fourier space are analyzed, particularly in the context of clarifying the role played by different flow scales in the amplification of the magnetic field. We observe that small and large scales interact and contribute to the dynamo process.

Dynamo activity caused by waves in a rotating magnetoplasma is investigated. In astrophysical environments such as accretion disks and at sufficiently small spatial scales, the Hall effect is likely to play an important role. It is shown that a combination of the Coriolis force and Hall effect can produce a finite a-effect by generating net helicity at small scales. The shear/ion-cyclotron normal mode of the Hall plasma is the dominant contributor to the dynamo action for short-scale motions.

Direct numerical simulations of turbulent Hall dynamos are presented. The evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary turbulent regime by a stirring force at a macroscopic scale is studied to explore the conditions for exponential growth of the magnetic energy. Scaling of the dynamo efficiency with Reynolds numbers is studied, and the resulting total energy spectra are found to be compatible with a Kolmogorov-type law. A faster growth of large-scale magnetic fields is observed at intermediate intensities of the Hall effect.

The first direct numerical simulations of turbulent Hall dynamos are presented. The evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary regime of hydrodynamic turbulence (by a stirring force at a macroscopic scale) is studied to explore the conditions for exponential growth of the magnetic energy. The Hall current is shown to have a profound effect on turbulent dynamo action; it can strongly enhance or suppress the generation of the large-scale magnetic energy depending on the relative values of the length scales of the system.

A theoretical mean field closure for Hall magnetohydrodynamics (Hall-MHD) is developed to investigate magnetic field generation through dynamo processes in low electron density astrophysical systems. We show that by modifying the dynamics of microscopic flows, the Hall currents could have a profound impact on the generation of macroscopic magnetic fields. As an illustrative example, we show how dynamo waves are modified by the inclusion of Hall currents. By dropping the usual assumption of a correlation time t for the microscopic dynamics in the mean field dynamos, we find qualitative changes in the growth rate of dynamo modes.

We present a one-dimensional ao-dynamo model to study the role of stochastic fluctuations in nonlinear kinematic dynamos. We introduce nonlinearities in the form of a-quenching and consider the effect of a meridional flow. Solutions are seen to settle down to a nonlinear periodic mode with a given amplitude. We show that the system displays relaxation oscillations that are in good agreement with the oscillations observed in the sunspot number time series. Irregularities are generated by adding a random forcing term to the a-coefficient to simulate the spatial and temporal complexity of the turbulent motions in the dynamo region. These fluctuations induce amplitude and cycle period variability, fluctuations in the dividing line between polarities around the equator, emergence of regions of reverse polarity, and north-south asymmetries. These results are in good agreement with observations and can be explained as the interaction of the deterministic solution with overtones excited by noise.