Effect of Ion Collisions and Other Terms on the Resistive-g Instability in Plasmas

The treatment is based on guiding center equations, which include collisional diffusion across the magnetic field lines. The eigenvalues of the resulting differential equation are found using phase integral methods. The localized resistive-g mode becomes stable at sufficiently low collision frequencies, the dominant stabilizing mechanism depending on the shear. For strong magnetic shear [shear length < radius of curvature of field lines × ¼(M/m)¼] ion collisional effects are found to first produce stability, whereas for weak magnetic shear the dominant effect comes from the electron acoustic term in Ohm's law. Analytic stability criteria are derived which show satisfactory agreement with a recent numerical solution of the same problem, but underline the danger of extrapolation based on the numerical solution.