Nonlinear structures of lower-hybrid waves driven by the ion beam

The lower-hybrid waves can be driven unstable by the transverse ion beam in a partially magnetized plasma of a finite length. This instability mechanism, which relies on the presence of fixed potential boundary conditions, is of particular relevance to axially propagating modes in a Hall effect thruster. The linear and nonlinear regimes of this instability are studied here with numerical simulations. In the linear regime, our results agree with analytical and numerical eigenvalue analysis conducted by Kapulkin and Behar [IEEE Trans. Plasma Sci. 43, 64 (2015)]. It is shown that in nonlinear regimes, the mode saturation results in coherent nonlinear structures. For the aperiodic instability [with $Re(ω)=0$—odd Pierce zones], the unstable eigen-function saturates into new stationary nonlinear equilibrium. In the case of oscillatory instability [$Re(ω)≠0$—even Pierce zones], the instability results in the nonlinear oscillating standing wave. It is also shown that finite Larmor radius effects stabilize instability for parameters corresponding to a large number of Pierce zones, and therefore, only few first zones remain relevant.