Non-Linear Stability of a Weakly Ionized Plasma with a Nonuniform Magnetic Field

Using vector eignfunction expansion, an asymptotic nonlinear theory of a weakly ionized plasma in a strong magnetic field is presented. When the external field H is slightly larger than the critical magnetic field Hc, an instability exists. For slightly unstable plasma motions, a precise form on Landau's equation is obtained. The inclusion of nonlinearities gives rise to amplitude saturation. It is also shown that with the inclusion of small aperiodic disturbances, there exists, in the interval of possible plasma motions, a subinterval of stable plasma motions given by |ko - π| < (1/√3π) (H2/Hc2 - 1)1/2, where 2π//ko is the period.