Thin, rotating plasma disks

Abstract

The MHD equilibrium of thin, rotating plasma disks is considered. An axisymmetric steady state is assumed. A corotation lag is included, as is a nonzero toroidal field with Bphi varies as rBr. Rigorous expressions are obtained for a characteristic Alfven Mach number and temperature, both of which involve vertical averages. If there is strict corotation, the temperature always diverges at large radii. If there is a corotation lag, the temperature need not diverge, and the magnetodisk solutions can extend to arbitrarily large radii. With weak additional assumptions, it is shown that M sub A is less than 2 exp 1/2 for a mainly poloidal field and M sub A is less than unity for a mainly toroidal field. For the Jovian magnetodisk, M sub A = 0.8 from Voyager 1 inbound data, and the observation of a temperature nearly constant or slowly decreasing with r from 20 R sub J to 80 R sub J on the outbound pass implies a corotation lag there.