# Semianalytical calculation of the zonal-flow oscillation frequency in stellarators

## TL;DR

This paper introduces a semianalytical numerical method to efficiently and accurately calculate the zonal-flow oscillation frequency in stellarators, aiding the understanding of turbulence regulation in fusion devices.

## Contribution

A novel semianalytical approach for calculating zonal-flow oscillation frequency in stellarators, improving speed and accuracy over existing gyrokinetic simulation methods.

## Key findings

- The semianalytical method matches simulation results accurately.
- It is faster than traditional gyrokinetic simulation-based calculations.
- The approach provides physical insights into zonal-flow dynamics.

## Abstract

Due to their capability to reduce turbulent transport in magnetized plasmas, understanding the dynamics of zonal flows is an important problem in the fusion programme. Since the pioneering work by Rosenbluth and Hinton in axisymmetric tokamaks, it is known that studying the linear and collisionless relaxation of zonal flow perturbations gives valuable information and physical insight. Recently, the problem has been investigated in stellarators and it has been found that in these devices the relaxation process exhibits a characteristic feature: a damped oscillation. The frequency of this oscillation might be a relevant parameter in the regulation of turbulent transport, and therefore its efficient and accurate calculation is important. Although an analytical expression can be derived for the frequency, its numerical evaluation is not simple and has not been exploited systematically so far. Here, a numerical method for its evaluation is considered, and the results are compared with those obtained by calculating the frequency from gyrokinetic simulations. This "semianalytical" approach for the determination of the zonal-flow frequency reveals accurate and faster than the one based on gyrokinetic simulations.