When driven with an appropriately chirped pump, the amplitude of certain nonlinear oscillators and waves can grow without bound. As the pump frequency is chirped towards the resonant frequency of the wave, the pump and the wave will phase lock at very low wave amplitude. When the pump reaches the linear resonant frequency, significant amplitude growth begins. Thereafter the amplitude of the wave will be such that the nonlinear wave frequency matches the pump frequency. This phenomenon is called autoresonance, and is well known in accelerators, but has not been seen experimentally in a wave.
Experimental results are in remarkable agreement with theoretical predictions.
Autoresonance occurs in many systems. Here we will briefly describe the theory for a pendulum, but most of our experiments were done with the diocotron wave in a non-neutral plasma. The diocotron wave is a very high-Q oscillator which comes about because of the interaction of the plasma with the trap wall. Click on the movie of a diocotron at right to get an expanded view. If you drive the oscillator at its linear resonant frequency, it will grow for a while, but as its amplitude increases, its frequency will shift and the drive will slip out of resonance.