Two strong counterpropagating waves in the cavity of a plasma-filled Čerenkov free electron maser modulate the density of the plasma electrons and ions. These density modulations induce periodic perturbations in the effective high-frequency dielectric constant of the plasma. When the intensity of the waves is high, and the ions can move to reduce the charge separation, the modulations are saturated. The two waves are then coupled by a self-induced distributed feedback. The distributed feedback is shown to resonantly enhance the gain of the Čerenkov amplifier. In the oscillator, the threshold gain is significantly reduced. Estimates of the oscillator efficiency show that the distributed feedback may enhance this efficiency to about eight times more than in a comparable vacuum Čerenkov oscillator.