The processes of plasma waves excitation under conditions of a double plasma resonance in a non-equilibrium plasma produced by high-power microwave radiation and confined in an open magnetic trap are studied. Two different dynamic regimes of kinetic instability have been experimentally observed: besides the generation of quasiperiodic series of short (∼50 ns) radiation pulses, a new scenario of instability in the form of generation of a single pulse of large (∼25 μs) duration with a slowly varying frequency near the second harmonic of the electron gyrofrequency in the center of the trap has been discovered. It is shown that the dynamic regimes of plasma wave generation observed in the experiment can arise when the processes of wave excitation and induced scattering compete, and the transition from quasi-continuous generation to pulse-periodic generation is determined by the ratio of the energy of non-equilibrium particles and the temperature of the background plasma. Hereinafter, the studied mechanisms will be used to explain similar phenomena in space, for example, sequences of pulses of different duration in the spectra of solar type-IV radio bursts.