Turbulence and Magnetic Fields in Astrophysical Plasmas

Magnetic fields permeate the Universe. They are found in planets, stars, accretion discs, galaxies, clusters of galaxies, and the intergalactic medium. While there is often a component of the field that is spatially coherent at the scale of the astrophysical object, the field lines are tangled chaotically and there are magnetic fluctuations at scales that range over orders of magnitude. The cause of this disorder is the turbulent state of the plasma in these systems. This plasma is, as a rule, highly conducting, so the magnetic field lines are entrained by (frozen into) the fluid motion. As the fields are stretched and bent by the turbulence, they can resist deformation by exerting the Lorentz force on the plasma. The turbulent advection of the magnetic field and the field’s back reaction together give rise to the statistically steady state of fully developed MHD turbulence. In this state, energy and momentum injected at large (object-size) scales are transfered to smaller scales and eventually dissipated. Despite over fifty years of research and manymajor advances, a satisfactory theory of MHD turbulence remains elusive. Indeed, even the simplest (most idealised) cases are still not fully understood. One would hope that there are universal properties of MHD turbulence that hold in all applications — or at least in a class of applications. Among the most important questions for astrophysics that a successful theory of turbulence must answer are: