Second harmonic autoresonant control of the l=1 diocotron mode in pure-electron plasmas

An oscillator whose frequency is amplitude dependent can be controlled by a drive whose frequency sweeps through a resonance with the oscillator's fundamental frequency. This phenomenon is called autoresonance, and has been previously investigated for drives with frequencies near the oscillator's fundamental or subharmonic frequencies. This paper examines autoresonance for drives at twice the fundamental frequency, i.e, second harmonic autoresonance. The l=1 diocotron mode in pure-electron plasmas, a very high Q nonlinear oscillator, is the focus of the paper. The theory for this oscillator is derived, and compared to experimental results. The results can be generalized to any Duffing-like driven nonlinear oscillator in which the coupling between the drive and the oscillator depends at least weakly on the oscillator amplitude.