THE DYNAMICS OF FLUX TUBES IN A HIGH-BETA PLASMA .1. A GENERAL DESCRIPTION

We suggest a new model for the structure of a magnetic held embedded i n a plasma whose average turbulent and magnetic energy densities are b oth much less than the gas pressure. This model is based on the popula r notion that the magnetic held 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 cr eated as the fluid streams by the flux tubes. Balancing the attraction caused by shielding effects with turbulent diffusion we find that flu x 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 and curvature scale of the flux tubes will be smaller than these estimate s. Allowing for resistivity changes these properties but does not alte r the macroscopic properties of the fluid or the large-scale magnetic field. In either case we show that the Sweet-Parker reconnection rate is at least as fast as an eddy turnover time. Realistic stellar plasma s are expected to either be in the ideal limit (e.g., the solar photos phere) or the resistive limit (the bulk of the solar convection zone). Allowing for significant viscosity drastically changes the macroscopi c properties of the magnetic field. We find that all current numerical simulations of three-dimensional MHD turbulence are in the viscous re gime and are inapplicable to stars or accretion disks. However, these simulations are in good quantitative agreement with our model in the v iscous limit.