Stability of a long field-reversed configuration: Complete two-fluid theory

The stability of a long field-reversed configuration is considered within the two-fluid model. A symmetric quadratic form is obtained with all Hall and finite Larmor radius (FLR) terms included. Assuming slow axial variation, this form is used to derive a leading-order stability formulation. As previously found for single fluid magnetohydrodynamics (MHD) analysis of this problem, the stability problem is posed as a field-line ordinary differential equation for the axial electron displacement alone. All stability results depend only on the ratio G=S*/E where E is the separatrix elongation and S* is the separatrix radius relative to the collisionless ion skin depth. Results are obtained for Hall MHD and also with FLR effects included (as large B gyroviscosity) and show stability for G<Gcrit. As previously concluded, it is found that Gcrit∼1 for Hall MHD. This result is now shown to be nearly independent of relative ion temperature and plasma compressibility. FLR is found to have a very strong stabilizing effect, with Gcrit a strong function of separatrix radius and ranging from 2 to 20 over a relevant experimental range. All modes are found to rotate in the electron diamagnetic direction