The Dynamics of Flux Tubes in a High Beta Plasma
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abstract

We suggest a new model for the structure of a magnetic field embedded high
$\beta$ 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.