A fully toroidal fluid analysis of the magnetohydrodynamic ballooning mode branch in tokamaks

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Abstract
A comparatively complete two fluid description of collisionless electromagnetic ballooning modes has been derived. Using an unexpanded ion density response, it has been shown for the first time using a fluid theory that a necessary and sufficient condition for an instability of the magnetohydrodynamic (MHD) branch below the MHD beta limit is the presence of an ion temperature gradient exceeding a threshold. The cause of this instability has been identified and an analytical dispersion relation is given.