# Cross-code gyrokinetic verification and benchmark on the linear collisionless dynamics of the geodesic acoustic mode

## TL;DR

This paper compares analytical theory with gyrokinetic simulations from three different codes to study the linear collisionless geodesic acoustic mode dynamics in tokamaks, considering various plasma parameters and regimes.

## Contribution

It provides a detailed benchmark and comparison of gyrokinetic codes against analytical theory for linear GAM behavior in tokamaks, clarifying code performance and validity regimes.

## Key findings

- Good agreement between codes and theory in certain regimes
- Identification of code-specific behaviors and limitations
- Insights into the linear GAM dynamics under various parameters

## Abstract

The linear properties of the geodesic acoustic modes (GAM) in tokamaks are investigated by means of the comparison of analytical theory and gyrokinetic numerical simulations. The dependence on the value of the safety factor, finite-orbit-width of the ions in relation to the radial mode width, magnetic-flux-surface shaping, and electron/ion mass ratio are considered. Nonuniformities in the plasma profiles (such as density, temperature, or safety factor), electro-magnetic effects, collisions and presence of minority species are neglected. Also, only linear simulations are considered, focusing on the local dynamics. We use three different gyrokinetic codes: the lagrangian (particle-in-cell) code ORB5, the eulerian code GENE and semi-lagrangian code GYSELA. One of the main aims of this paper is to provide a detailed comparison of the numerical results and analytical theory, in the regimes where this is possible. This helps understanding better the behavior of the linear GAM dynamics in these different regimes, the behavior of the codes, which is crucial in the view of a future work where more physics is present, and the regimes of validity of each specific analytical dispersion relation.