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

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 3%. 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 κ, thereby enabling one to model plasmas with a timevarying κ. Tabulated Maxwellian fitting parameters are given for specific values of κ 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.

Nonequilibrium Processes in the Solar Corona, Transition Region, Flares, and Solar Wind (Invited Review)

“…One solution is to express the non-Maxwellian as a superposition of Maxwellians, which was implemented in CHIANTI version 5 (Landi et al, 2006) and recently discussed in Hahn and Savin (2015), who provided an accurate way to decompose a κ-distribution into a linear series of Maxwellian distributions with different temperatures. Individual non-Maxwellian rates can then be calculated as a linear combination of the Maxwellian ones.…”

“…Since the non-Maxwellian distributions can be approximated by a sum of two or several Maxwellians (see Hahn and Savin, 2015, for the case of κ-distributions), the multi-Maxwellian interpretation of X-ray observations can also yield constraints on the number of high-energy particles. Such studies have been done by Ishikawa et al (2014) and Hannah et al (2016).…”

The collision frequency of electron‐neutral‐particle in the weakly ionized plasma with the power‐law velocity distribution

“…In the above expression (12), it is clear that, the nonextensive parameter q≠1, i.e. the power-law index, has a very significant effect on the average collision frequency of electrons-neutral-particles in the complex plasma with the velocity q-distribution, and when we take the limit q →1, the collision frequency (12) recovers the traditional form (8) in the plasma with a Maxwell velocity distribution.…”

Electron-impact Multiple-ionization Cross Sections for Atoms and Ions of Helium through Zinc

“…The total cross section is the sum of all the individual cross sections having the same set of Z, q i , and q f . Also, although we previously reported EIMI cross section estimates for Fe (Hahn & Savin 2015a), here we have made some minor revisions to those cross sections based on the current analysis of a wider range of ions.…”