A Simple Method for Modeling Collision Processes in Plasmas with a Kappa Energy Distribution

TL;DR

This paper introduces a straightforward method to model collision processes in plasmas with a kappa energy distribution by approximating it with a weighted sum of Maxwell-Boltzmann distributions, enabling accurate and easy-to-implement calculations.

Contribution

The authors present a novel approach to approximate kappa distributions using Maxwellian sums, improving accuracy and simplicity over existing reverse engineering methods.

Findings

Achieves better than 5% accuracy in reproducing kappa distribution rate coefficients.

Provides tabulated and polynomial fit parameters for kappa values from 1.7 to 100.

Demonstrates applications in plasma charge state distribution and solar flare modeling.

Abstract

We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in kappa-distribution plasmas, with a particular focus on atomic processes important for solar physics. The relevant collision process rate coefficients are generated by summing appropriately weighted Maxwellian rate coefficients. This method reproduces the rate coefficients for a kappa distribution to an estimated accuracy of better than 5%. This is equal to or better than the accuracy of rate coefficients generated using "reverse engineering" methods, which attempt to extract the needed cross sections from the published Maxwellian rate coefficient data and then reconvolve the extracted cross sections with the desired kappa distribution. Our approach of summing Maxwellian rate coefficients is easy to implement using existing spectral analysis software. Moreover, the weights in the sum of the Maxwell-Boltzmann distribution rate coefficients can be found for any value of the parameter kappa, thereby enabling one to model plasmas with a time-varying kappa. Tabulated Maxwellian fitting parameters are given for specific values of kappa from 1.7 to 100. We also provide polynomial fits to these parameters over this entire range. Several applications of our technique are presented, including the plasma equilibrium charge state distribution (CSD), predicting line ratios, modeling the influence of electron impact multiple ionization on the equilibrium CSD of kappa-distribution plasmas, and calculating the time-varying CSD of plasmas during a solar flare.