The Dynamics of Flux Tubes in a High Beta Plasma

Abstract

We suggest a new model for the structure of a magnetic field embedded high $β$ turbulent plasma, based on the popular notion that the magnetic field will tend to separate into individual flux tubes. We point out that interactions between the flux tubes will be dominated by coherent effects stemming from the turbulent wakes created as the fluid streams by the flux tubes. Balancing the attraction caused by shielding effects with turbulent diffusion we find that flux tubes have typical radii comparable to the local Mach number squared times the large scale eddy length, are arranged in a one dimensional fractal pattern, have a radius of curvature comparable to the largest scale eddies in the turbulence, and have an internal magnetic pressure comparable to the ambient pressure. When the average magnetic energy density is much less than the turbulent energy density the radius, internal magnetic field and curvature scale of the flux tubes will be smaller than these estimates. Realistic resistivity does not alter the macroscopic properties of the fluid or the large scale magnetic field. In either case we show that the Sweet-Parker reconnection rate is much faster than an eddy turnover time. Realistic stellar plasmas are expected to either be in the ideal limit (e.g. the solar photosphere) or the resistive limit (most of the solar convection zone). All current numerical simulations of three dimensional MHD turbulence are in the viscous regime and are inapplicable to stars or accretion disks.