Analysis of Anomalous Diffusion and Velocity Distribution Anisotropy to Understand Structure Formation in Microgravity Dusty Plasma*

This study uses data from the Plasmakristall-4 facility on board the International Space Station to analyze dust particle diffusion in microgravity dusty plasma. Plotting the particle mean squared displacements (MSD) indicates a power-law dependence with time, which is a signature of anomalous diffusion. The histograms of particle velocities also display anomalous diffusion 'fat tails' best described by q-Gaussian distributions. Fitting techniques are used to extract both the exponent from the MSD plots and the q-exponent from the velocity histograms for all examined cases. A considerable anisotropy is observed when comparing the distributions obtained for particle velocities along versus across the direction of an externally applied electric field. Select cases also show signatures of diffusion regime changes, which are interpreted as emergence of structures with different scales within the dust cloud. The extracted exponents are rescaled into a Hamiltonian that consists of an anomalous diffusion term (a fractional Laplacian) and a stochastic disorder term. A fractional Laplacian Spectral code is used to assess the probability for nonlocal transport as a function of spatial scales to confirm the existance of multiple structure scales.