Transsonic instabilities in tokamaks and astrophysical accretion flows

Waves and instabilities of transonically rotating toroidal plasmas present a very complex problem of interest for the two unrelated fields of magnetically-dominated laboratory plasmas and gravitationally-dominated astrophysical plasmas. The complexity originates from the transonic transitions of the poloidal flow which causes the character of the rotating equilibrium states to change dramatically, from elliptic to hyperbolic or vice versa, when the poloidal velocity surpasses certain critical speeds. Associated with these transitions the different types of magnetohydrodynamic (MHD) shocks may appear. Obviously, at such transitions the possible waves and instabilities of the system also change dramatically. We have investigated these changes for the two mentioned physical systems, starting from the point of view that the continuous spectrum of magnetohydrodynamics presents the best organizing principle for the structure of the complete spectrum since it is the most robust part of it. We found a new class of local MHD instabilities, that we called trans-slow Alfven continuum modes, which are due to poloidal flows exceeding the critical slow magnetosonic speed. They operate both in laboratory plasmas (tokamaks), in the absence of gravitational effects, and in astrophysical plasmas (accretion tori), when the gravitational field of a compact object dominates the flow. They become extremely violent when the mass of the central object is large, providing a new route to MHD turbulence in plasmas rotating about a massive central object.