# Improved linearized model collision operator for the highly collisional regime

## TL;DR

This paper presents an improved linearized collision operator for multi-species plasmas that remains accurate in highly collisional regimes, preserving conservation laws and key relations, and is suitable for gyrokinetic turbulence simulations.

## Contribution

The authors develop a modified collision operator that extends applicability to highly collisional regimes while maintaining physical conservation laws and relations, suitable for advanced plasma simulations.

## Key findings

- Retains conservation of particles, momentum, and energy.
- Reproduces friction-flow relations of the Landau operator.
- Can be adapted for gyrokinetic turbulence modeling.

## Abstract

The linearized model collision operator for multiple species plasmas given by H. Sugama, T.-H. Watanabe, and M. Nunami [Phys.\ Plasmas {\bf 16}, 112503 (2009)] is improved to be properly applicable up to the highly collisional regime. The improved linearized model operator retains conservation laws of particles, momentum, and energy as well as it reproduces the same friction-flow relations as derived by the linearized Landau operator so that this model can be used to correctly evaluate neoclassical transport fluxes in all collisionality regimes. The adjointness relations and Boltzmann's H-theorem are exactly satisfied by the improved operator except in the case of collisions between unlike particle species with unequal temperatures where these relations and H-theorem still holds approximately because there is a large difference between the masses of the two species with significantly different temperatures. Even in the unequal-temperature case, the improved operator can also be modified so as to exactly satisfy the adjointness relations while it causes the values of the friction coefficients to deviate from those given by the Landau operator. In addition, for application to gyrokinetic simulations of turbulent transport, the improved operator is transformed into the gyrophase-averaged form with keeping the finite gyroradius effect.