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The linear properties and saturation mechanisms of the lower‐hybrid drift instability have been investigated using a one‐dimensional particle‐hybrid simulation. For low drift velocities (vd≪vti), ion trapping and current relaxation (vd→0) are competing processes for stabilization. If the relative electron–ion drift velocity is kept constant in time, ion trapping causes the end of instability growth; if this drift is allowed to decrease consistent with momentum balance, then saturation is due to current relaxation.

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.