Bispectral analysis of nonlinear mixing in dusty plasma

We verified nonlinear mixing (NLM) in a dusty plasma medium using the forced Korteweg-de Vries (fKdV) model in a weakly nonlinear dynamical regime [1, 2]. The mixing modes are excited due to the nonlinear coherent three-wave interaction between the natural KdV mode and its harmonics with the external forcing. The power spectrum is the primary diagnostic tool used to capture the information of excited modes. However, the power spectral analysis doesn’t capture the phase information of the excited modes. Hence, it can’t distinguish between the coherent and incoherent modes of the fKdV model, i.e., we cant confirm the origin of modes due to mixing or some other spurious origin. To resolve this ambiguity, the phase information is captured by calculating the triple correlation of the time series of fKdV and the technique is known as bispectral analysis [3]. The bispectral analysis easily discriminates between the coherent and incoherent origin of modes obtained in the mixing profile.

In this work, we confirm using bispectral analysis that the modes that originated in the fKdV model are due to the three-wave mixing of a natural dust acoustic wave (DAW) mode and another forcing mode. Our results are in agreement with the dusty plasma experiment [4]. Furthermore, a kinetic model is also developed to study NLM in dusty plasma in which particles interact via Yukawa potential. We found that the results based on the classical molecular dynamics simulations agree with the fKdV model, where nonlinear and travelling form of force is used. Both the models can be extended to a nonlinear dispersive fluid-like medium.

References:

1. Liu, B. and Goree, J. and Flanagan, T. M. and Sen, A. and Tiwari, S. and Ganguli, G. and Crabtree, C.: Experimental observation of cnoidal waveform of nonlinear dust acoustic waves

2. Mir, A. A. and Tiwari, K. S. and Goree, J. and Sen, A. and Crabtree, C. and Ganguli, G.: A forced Korteweg-de Vries model for nonlinear mixing of oscillations in a dusty plasma

3. Mir, A. and Tiwari, S. and Sen, A.: Bispectral analysis of nonlinear mixing in a periodically driven Korteweg-de Vries system

4. Nosenko, V. and Avinash, K. and Goree, J. and Liu, B.: Nonlinear Interaction of Compressional Waves in a 2D Dusty Plasma Crystal