Using Microgravity Dusty Plasma to Study Connections Between Non-Equilibrium Tsallis Statistics, Nonlinear Fokker Planck and Fractional Laplacian

Anomalous diffusion is characterized by particle mean squared displacement (MSD) which is not proportional to time t, but rather to some power of t. Another characteristic is the observation of non-Maxwellian velocity distributions functions. Here we analyze how Tsallis statistics and non-Maxwellian distributions model anomalous dust particle diffusion in microgravity dusty plasma. This study uses data from the Plasmakristall-4 (PK-4) facility on board the International Space Station (ISS) to create histograms of particle velocities which are then fitted against Kappa Distribution and Modified n-Kappa Distribution. Previous studies have shown that the particle velocity distributions in microgravity dusty plasmas exhibit ‘fat’ tails which can be described by a combination of Maxwellian and Kappa distributions. The present research aims to connect the observation of ‘fat’ tails with the occurrence of anomalous diffusion in dusty plasma. The distributions will be related to solutions of the non-linear Fokker-Planck equation, which describes the time evolution of the probability density function of the velocities for correlated diffusion. We also aim to find a phenomenological connection between these solutions and the predictions from a Fractional Laplacian Spectral (FLS) model. The FLS model calculates the probability for transport as a function of spatial scale and is informed from correlation lengths determined from the observed dust particle diffusion. These models will be used to develop a physical interpretation for the κ-parameter in the context of microgravity dusty plasma. We will also discuss a relation between the n-parameter in the modified n-Kappa distribution and the power of a nonlinear MSD and thus the power of the fractional Laplacian.