Dynamo Action in Magnetohydrodynamics and Hall‐Magnetohydrodynamics

Abstract

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.

Wave turbulence in magnetized plasmas

“…It provides a multiscale description of magnetized plasmas from which both the standard and the electron MHD approximation may be recovered. Hall MHD is often used to understand, for example, the magnetic field evolution in neutron star crusts (Goldreich and Reisenegger, 1992), the turbulent dynamo (Mininni et al, 2003), the formation of filaments (Laveder, Passot and Sulem, 2002), the multiscale solar wind turbulence Krishan and Mahajan, 2004;Galtier, 2006a,b), or the dynamics of the magnetosheath (Belmont and Rezeau, 2001). Anisotropy in Hall MHD is clearly less understood than in MHD or electron MHD mainly because the numerical treatment is more limited since a wide range of scales are necessary to detect any multiscale effects.…”

Direct numerical simulations of helical dynamo action: MHD and beyond

“…The vector potential A is defined by B=∇×A. The simulations discussed in the following sections were made using a parallel pseudospectral code (Mininni et al, 2003. Equations (1) and (2) are integrated in a cubic box with periodic boundary conditions.…”

“…To help scale separation, the energy injection band is often restricted to a few wave numbers around the wavenumber k f orce . In our simulations we use an ABC force F with A=B=C (Childress, 1970), acting at k f orce (see Mininni et al (2003) for details). The amount of helicity in the flow is measured by the kinetic helicity (Moffatt, 1978) …”

“…Note that c/ω pi has dimensions of length (the ion skin depth), and corresponds to the lenghtscale where the Hall effect becomes non-negligible. General expressions for ε, as well as characteristic values for astrophysical objects can be found in Mininni et al (2003).…”

“…Later, several turbulent simulations were carried using mechanic helical forces (e.g. ABC type force), most of them with idealized conditions (Galanti et al, 1991;Brandenburg, 2001;Archontis et al, 2003;Mininni et al, 2003).…”