arXiv2009
We develop a new model of the fluctuation dynamo in which the magnetic field is confined to thin flux ropes advected by a multi-scale flow which models turbulence. Magnetic dissipation occurs only via reconnections of flux ropes. The model is particularly suitable for rarefied plasma, such as the Solar corona or galactic halos. We investigate the kinetic energy release into heat, mediated by dynamo action, both in our model and by solving the induction equation with the same flow. We find that the flux rope dynamo is more than an order of magnitude more efficient at converting mechanical energy into heat. The probability density of the magnetic energy released during reconnections has a power-law form with the slope -3, consistent with the Solar corona heating by nanoflares. We also present a nonlinear extension of the model. This shows that a plausible saturation mechanism of the fluctuation dynamo is the suppression of turbulent magnetic diffusivity, due to suppression of random stretching at the location of the flux ropes. We confirm that the probability distribution function of the magnetic line curvature has a power-law form suggested by (Schekochihin et al., 2002). We argue, however, using our results that this does not imply a persistent folded structure of magnetic field, at least in the nonlinear stage.