MHD instabilities in astrophysical plasmas: very different from MHD instabilities in tokamaks!

The extensive studies of MHD instabilities in thermonuclear magnetic confinement experiments, in particular of the tokamak as the most promising candidate for a future energy producing machine, have led to an 'intuitive' description based on the energy principle that is very misleading for most astrophysical plasmas. The 'intuitive' picture almost directly singles out the dominant stabilizing field line bending energy of the Alfvén waves and, consequently, concentrates on expansion schemes that minimize that contribution. This happens when the wave vector of the perturbations, on average, is perpendicular to the magnetic field . Hence, all macroscopic instabilities of tokamaks (kinks, interchanges, ballooning modes, ELMs, neoclassical tearing modes, etc) are characterized by satisfying the condition , or nearly so. In contrast, some of the major macroscopic instabilities of astrophysical plasmas (the Parker instability and the magneto-rotational instability) occur when precisely the opposite condition is satisfied: . How do those instabilities escape from the dominance of the stabilizing Alfvén wave? The answer to that question involves, foremost, the recognition that MHD spectral theory of waves and instabilities of laboratory plasmas could be developed to such great depth since those plasmas are assumed to be in static equilibrium. This assumption is invalid for astrophysical plasmas where rotational and gravitational accelerations produce equilibria that are at best stationary, and the associated spectral theory is widely, and incorrectly, believed to be non-self adjoint. These complications are addressed, and cured, in the theory of the Spectral Web, recently developed by the author. Using this method, an extensive survey of instabilities of astrophysical plasmas demonstrates how the Alfvén wave is pushed into insignificance under these conditions to give rise to a host of instabilities that do not occur in laboratory plasmas.