Scaling of magnetic turbulence with Lundquist number in relaxed state devices

Abstract

The scaling of magnetic turbulence with Lundquist number, B̃(S), as generated by the dynamo in reversed-field pinches and spheromaks, is addressed. A theoretical framework is described, showing how the fluctuations arise from the dynamo and what dynamics determine the B̃(S) scaling. There are two limits of the dynamo. For a discrete (sawtoothing) dynamo, the time average of the magnetic fluctuations is given by B̃∝S0, but it is argued that the averaged flux surface destroying magnetic field fluctuations scale as B̃br∝S−1/2. For a continuous dynamo, with a steady-state saturated turbulent spectrum, the magnetic field perturbations scale as B̃∝S−1/4. Previous theories of S scaling are reviewed.