Amplitude collapse of nonlinear double-layer oscillations

The negative differential resistance of a double layer can give rise to large amplitude oscillations in the potential drop over the double layer. Such oscillations are investigated in a triple-plasma machine for weak nonlinearity, implying approximately harmonic oscillations at low frequencies (omega much less than omega(pi)). The amplitude of the potential oscillations can approach the dc potential drop over the double layer. The oscillation exists within a certain interval of dc drops and vanishes outside this interval. An interesting nonlinear phenomenon that we call amplitude collapse is observed. The amplitude does not always decrease smoothly from its maximum value to zero when the dc drop is increased, but there is a sudden jump to vanishing amplitudes. For a decreasing dc voltage the corresponding sharp amplitude increase occurs at a lower voltage. This phenomenon, which is not predicted by the classical van der Pol equation, is shown to follow from the generalized van der Pol equation that describes the actual system, by using asymptotic solutions for weak nonlinearity.