# Ion parallel closures

## TL;DR

This paper derives ion parallel closures applicable to various atomic weights and charge numbers, expressing heat flow and viscosity as kernel-weighted integrals, with fitted kernels for practical use in ion fluid equations.

## Contribution

It introduces a general method for ion parallel closures valid for arbitrary collisionality and atomic parameters, with fitted kernels based on extensive moment solutions.

## Key findings

- Fitted kernel functions accurately represent heat flow and viscosity.
- Tabulated kernel parameters for different ion-electron temperature ratios.
- Closures enable simplified ion fluid modeling without solving kinetic equations.

## Abstract

Ion parallel closures are obtained for arbitrary atomic weights and charge numbers. For arbitrary collisionality, the heat flow and viscosity are expressed as kernel-weighted integrals of the temperature and flow-velocity gradients. Simple, fitted kernel functions are obtained from the 1600 parallel moment solution and the asymptotic behavior in the collisionless limit. The fitted kernel parameters are tabulated for various temperature ratios of ions to electrons. The closures can be used conveniently without solving the kinetic equation or higher order moment equations in closing ion fluid equations.