Nonlinear Mixing of Waves in a Yukawa One Component Plasma

TL;DR

This study investigates nonlinear wave mixing in a driven Yukawa one-component plasma (YOCP) using first-principles Langevin molecular dynamics (MD) in 2D and compares the results with the forced Korteweg-de Vries (fKdV) fluid model. By exciting two primary waves with frequencies f1 and f2, the authors analyze the resulting spectrum via power spectral density and bispectrum to identify a dominant three-wave mixing mechanism, validating the fKdV description for weakly nonlinear, dispersive dust-wave dynamics in Yukawa systems. The Langevin MD and fKdV models show striking agreement in both the mixing profiles and the set of dominant triadic interactions, despite fundamental differences such as dimensionality, viscosity, and driving schemes. The findings strengthen the case for using the fKdV as a predictive reduced model for NLM in dusty plasmas and highlight bispectral analysis as a powerful diagnostic for nonlinear coupling and energy transfer in complex plasma systems.

Abstract

The phenomenon of nonlinear wave mixing is investigated in a Yukawa one-component plasma using two-dimensional classical Langevin molecular dynamics simulations. The wave spectrum indicates that nonlinear interactions between the excited modes are primarily governed by a three-wave mixing mechanism, as confirmed by bispectral analysis. In particular, the mixing characteristics observed in the simulations closely resemble those reported in previous numerical studies of the forced Korteweg-de Vries (fKdV) model [ Phys. Plasmas 29, 032303 (2022)]. This similarity further validates the applicability of the fKdV fluid model in capturing the weakly nonlinear dynamics of dusty plasmas with reasonable accuracy.

Figures (5)

• Figure 1: A schematic to demonstrate the NLM using the Langevin simulation in LAMMPS. The system is bounded at $x=0$ and $x=L_x$ by a confining force $F_C$. Two waves are excited by laser forces $F_L$, each with a different frequency. Both the $F_C$ and $F_L$ are Gaussian in nature. Periodic boundary conditions are imposed along the y-direction. The region-of-interest (ROI) used to collect time series is the green-coloured region at the centre of the rectangular ($L_x = 10 L_y$) simulation box.
• Figure 2: A schematic to illustrate a typical three-wave interaction: (I) generic sum-interaction, (II) generic difference-interaction. If $f_1 = f_2$, (I) and (II) represent the harmonic generated by sum-self-interaction and deformation generated by difference-self-interaction, respectively.
• Figure 3: Time evolution of velocity perturbation excited by a single laser. Left column: velocity evolution in the xy domain. Right column: Fluidized velocity evolution in xy domain. Both show a clear indication of soliton trains. The inset in each subplot in the right column shows the evolution of the 2D energy spectrum $E(k_x, k_y)$.
• Figure 4: NLM observed in YOCP using the Langevin MD simulations. (a) PSD and (b) bicoherence of the time-series obtained from the time evolution of YOCP for $\Gamma = 100$, $\kappa = 0.1$ and damping rate $\nu = 100\ \omega_{pd}^{-1}$. The small insets show the PSD of individual waves with frequency $f_1 = 0.7$ Hz and $f_2 = 1.7$ Hz.
• Figure 5: Density fluctuations at three different times due to external forcing. Inset (a) shows a time series collected from a region near the 0.7 Hz driving, while inset (b) shows a time series collected from a region near the 1.7 Hz driving. The density fluctuations reach up to $10-20 \%$ of the equilibrium density.