Experimental observation of cnoidal waveform of nonlinear dust acoustic waves

Abstract

The experimentally measured waveform of nonlinear dust acoustic waves in a plasma is shown to be accurately described by a cnoidal function. This function, which is predicted by nonlinear theory, has broad minima and narrow peaks. Fitting the experimental waveforms to the cnoidal function also provides a measure of the wave's nonlinearity, namely, the elliptical parameter k. By characterizing experimental results at various wave amplitudes, we confirm that the parameter k increases and approaches a maximum value of unity, as the wave amplitude is increased. The underlying theory that predicts the cnoidal waveform as an exact solution of a Korteweg-de Vries model equation takes account of the streaming ions that are responsible for the spontaneous excitation of the dust acoustic waves. © 2018 Author(s).