The stability of a stochastic plasma with respect to low frequency perturbations

Following the suggestion that substorm breakup might be caused by an interchange or ballooning instability, several magnetohydrodynamic (MHD) and gyrokinetic stability analysis have been performed for plasma sheet magnetic field geometries. However, the stochastic ion dynamics in the highly stressed, thin high-β near earth plasma sheet violate the locality requirements of MHD and the invariance of the magnetic moment, μ, required by gyrokinetic theories. In this paper, a proper quadratic form energy principle (for low frequency modes ω<ωb, ωb being the bounce frequency) which includes the dynamics of stochastic ions is developed, and it is demonstrated that the stochastic plasma is less stable than the corresponding adiabatic plasma.