The relevance of the ballooning approximation for magnetic, thermal, and coalesced magnetothermal instabilities

Approximate solutions of the linearized non-adiabatic MHD equations, obtained using the ballooning method, are compared with 'exact' numerical solutions of the full equations (including the effects of optically thin plasma radiation). It is shown that the standard ballooning method, developed within the framework of ideal linear MHD, can be generalized to non-ideal linear MHD. The localized (ballooning) spectrum has to be used with caution, but can give valuable (though limited) information on non-ideal stability. The numerical analysis also confirms and quantifies the interesting connection between magnetic and thermal instabilities. The existence of such a coupling is inherent in many qualitative discussions of magnetic disruptions. Finally, the hitherto unrecognized role of the thermal continuum in the unstable part of the 'magnetothermal' spectrum is investigated.