Correlations and Kappa Distributions: Numerical Experiment with 3D Collisions and Debye-like Shielding

Contrary to the common assumption of Maxwell–Boltzmann (MB) distributions, space plasmas are characterized by kappa distributions and reside in thermodynamic stationary states out of classical thermal equilibrium, owing to the correlations between the charged plasma particles. In this study, we extend prior work to include realistic 3D collisions and Debye-like shielding of the correlations to show how these two processes compete in the development of realistic plasma particle velocity distributions. We modify our prior numerical experiment to incorporate both 3D collisions and correlations that include realistic Debye-like shielding of plasma particles and run it over many collisions until it becomes stationary. While 3D collisions alone produce Maxwell–Boltzmann (MB) distributions of the particles (κ → ∞), introducing correlations drives the distributions to stationary states with finite thermodynamic kappa (κ), where stronger correlations produce lower values of κ, as observed in space plasmas. Further, development of correlation clusters around each collision rapidly produces thermodynamic systems where the Debye length is proportional to 1+1/κ0th, for invariant thermal kappa κ0th, just as predicted by theory. This simple numerical experiment explores much more realistic particle interactions to show how 3D collisions and properly shielded correlations compete to produce stationary states of plasma particle kappa distributions and illuminates how long-range interactions correlate particles over the scale of the Debye lengths.