Nonlinear Theory of the E x B Instability

A weakly ionized plasma will go unstable in the presence of a density gradient and parallel electric field, both at right angles to a magnetic field, if the electric field is of the right sign and sufficiently large. The nonlinear limit of the first mode to go unstable when E is increased is determined as a function of Δ [Δ ≡ (E - Ec)/Ec]. A general theory of this small amplitude behavior is used. The mode amplitude, frequency shift, density flattening, electric field change, and anomalous plasma transport are obtained as functions of Δ. It is shown that mode coupling corrections are small, and hence that the quasilinear result is sufficient.