Fractional Laplacian Spectral Approach to Turbulence in a Dusty Plasma Monolayer

TL;DR

This paper combines analytical fractional Laplacian spectral methods with large-scale simulations to explore how disorder and nonlocal interactions induce turbulence in dusty plasma monolayers, revealing key energy transfer mechanisms.

Contribution

It introduces a novel spectral approach using Fractional Laplacian Spectral techniques to analyze turbulence in dusty plasmas, validated by extensive many-body simulations.

Findings

Disorder and nonlocal interactions trigger dust turbulence.

Spectral analysis identifies active energy channels across scales.

Theoretical predictions align with simulation results.

Abstract

This work presents an analytical investigation of anomalous diffusion and turbulence in a dusty plasma monolayer, where energy transport across scales leads to the spontaneous formation of spatially disordered patterns. Many-body simulations of 10,000-particle dusty plasma monolayers are used to demonstrate how the global dynamics depend on the statistical properties of the dust assembly for realistic laboratory conditions. We find that disorder due to variations in the dust size distribution and charge-driven nonlocal interactions resulting in anomalous dust diffusion are key factors for the onset of instabilities. The resulting dynamics exhibit features of inertial turbulence over slightly more than half a decade of scales proportional or smaller than the Debye shielding length. These processes are examined analytically using a recently developed Fractional Laplacian Spectral (FLS) technique, which identifies the active energy channels as a function of scale, disorder concentration, and features of the nonlocal interactions. The predictions from the theoretical (spectral) analysis demonstrate agreement with the results from the many-body (kinetic) simulations, thus providing a powerful tool for the study of active turbulence.