# The collisional resonance function in discrete-resonance quasilinear plasma systems

## TL;DR

This paper develops an analytical method to determine the resonance broadening function in plasma systems with discrete resonances, improving the understanding of mode saturation and growth rates near thresholds.

## Contribution

It introduces a new analytical approach to calculate resonance broadening functions in discrete-resonance plasma systems, aligning quasilinear results with kinetic theory.

## Key findings

- Accurately determines the resonance width in plasma systems.
- Recovers nonlinear growth rates and saturation levels.
- Provides a distribution function for precise resonance analysis.

## Abstract

A method is developed to analytically determine the resonance broadening function in quasilinear theory, due to either Krook or Fokker-Planck scattering collisions of marginally unstable plasma systems where discrete resonance instabilities are excited without any mode overlap. It is demonstrated that a quasilinear system that employs the calculated broadening functions reported here systematically recovers the nonlinear growth rate and mode saturation levels for near-threshold plasmas previously calculated from kinetic theory. The distribution function is also calculated, which enables precise determination of the characteristic collisional resonance width.