Date of Graduation
Eberly College of Arts and Sciences
Physics and Astronomy
A program to implement a spectral analysis technique called the bispectrum was written and tested with computer generated time series data. The application of the algorithm to the study of nonlinear interactions was demonstrated by a comparison of computed quantities with results from model equations found in the literature. Specifically determined were: the amplitude and phase of coupling coefficients, the power transfer function, the fraction of power associated with nonlinear coupling, and the identification of waves involved in a quadratic coupling interaction. A method of distinguishing the two parent waves from the daughter wave in this three-wave interaction is proposed as a new application of the technique. These results, as well as the values computed from a Monte Carlo simulation of plasma turbulence were found to be consistent with expectations. Two experimental systems were investigated with the bispectrum. One was the periodically pulled time series data of a driven van der Pol oscillator (unijunction transistor circuit) which contained significant bispectral features but no real evidence of quadratic coupling. The other was plasma fluctuation data from the WVU-Q Machine, where the inhomogeneous energy-density driven mode exhibited a degree of coupling to lower frequencies that was absent in the case of the current driven mode.
Stauber, Renaud, "Applicability of Bispectral Analysis to Unstable Plasma Waves" (1995). Graduate Theses, Dissertations, and Problem Reports. 7489.