A Powerful Viscous Shear Instability in Weakly Magnetized, Dilute Plasmas

When the ion mean free path much exceeds the Larmor radius in a plasma, the viscous stress tensor is altered dramatically, and depends only upon quantities measured along the field lines. This regime corresponds to typical interstellar medium conditions in galaxies and protogalaxies, even if the magnetic field is extremely weak with negligible pressure and tension forces. Despite the fact that neither magneto-rotational modes nor dynamical stresses are associated with the field, whose only role is to channel angular momentum transport, we show that differential rotation in such a gas is highly unstable. The resulting nonlinear development is likely to be a turbulent process, important to the initial phases of the amplification of tiny magnetic fields in disk galaxies when magneto-rotational modes grow only very slowly. Subject headings: accretion, accretion disks; magnetic fields; MHD; instabilities; galaxies: magnetic fields.