Nonlinear frequency shift induced by the lower-hybrid drift instability

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It is found that a finite perturbations of the ion orbits leads to a nonlinear frequency shift that reduces the mode frequency and has a weak stabilizing effect on the lower-hybrid drift instability. This result is obtained from a self-consistent solution of the Vlasov–Poisson equations using perturbation theory in which the nonlinear dielectric function and the nonlinear temporal evolution of a single unstable mode in the low drift velocity regime are calculated analytically. The nonlinear frequency shift does not seem to be a potent saturation mechanism in a collisionless plasma, but may be more relevant when there are ion-ion collisions.