Nonlinear saturation of the parallel velocity shear instability

The linear stability and eventual nonlinear saturation of electrostatic instabilities due to the shear in a plasma flow in the direction parallel to the magnetic field are described, analytically, via collisional fluid equations. Saturation is provided by coupling the linearly unstable eigenmode to a linearly damped nonlinear harmonic (double wave number). These modes are shown to saturate only when the linear instability driving term is below a critical value. The saturation amplitude is a function of the ratio of the ''ideal'' growth rate to the diamagnetic frequency and can easily reach levels of 25% or more. (C) 1996 American Institute of Physics.