Fajans J, Gilson E, Friedland L
Department of Physics, University of California, Berkeley, Berkeley, California 94720-7300, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Sep;62(3 Pt B):4131-6. doi: 10.1103/physreve.62.4131.
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.
一个频率与振幅相关的振荡器可以由一个频率扫过与振荡器基频共振的驱动来控制。这种现象被称为自共振，此前已针对频率接近振荡器基频或次谐波频率的驱动进行过研究。本文研究了两倍基频驱动下的自共振，即二次谐波自共振。纯电子等离子体中的l = 1 diocotron模式是一种具有非常高Q值的非线性振荡器，是本文的重点。推导了该振荡器的理论，并与实验结果进行了比较。这些结果可以推广到任何类似杜芬振子的受驱动非线性振荡器，其中驱动与振荡器之间的耦合至少在一定程度上依赖于振荡器的振幅。
