Ballooning mode stability in the Hall-magnetohydrodynamics model

The governing equations of the ballooning modes are derived within the Hall-magneto-hydrodynamics (HMHD) model and given a standard Hamiltonian form, which is then used to derive sufficient conditions for stability. In most cases, ideal magnetohydrodynamics (MHD) stability implies HMHD stability, as is the case for tokamak configurations if the pressure is a monotone increasing function of density and the entropy is monotone decreasing. The same result holds for general MHD plasmas with constant entropy and for incompressible plasmas. However, in the case of (compressible) closed-line systems such as the field-reversed configuration, or in a typical magnetospheric magnetic field, MHD ballooning stability does not guarantee HMHD stability. For the explicitly solvable configuration of the Z pinch it is in fact shown that the plasma can be MHD stable but HMHD unstable.