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Due to their capability to reduce turbulent transport in magnetized plasmas,understanding the dynamics of zonal flows is an important problem in the fusionprogramme. Since the pioneering work by Rosenbluth and Hinton in axisymmetrictokamaks, it is known that studying the linear and collisionless relaxation ofzonal flow perturbations gives valuable information and physical insight.Recently, the problem has been investigated in stellarators and it has beenfound that in these devices the relaxation process exhibits a characteristicfeature: a damped oscillation. The frequency of this oscillation might be arelevant parameter in the regulation of turbulent transport, and therefore itsefficient and accurate calculation is important. Although an analyticalexpression can be derived for the frequency, its numerical evaluation is notsimple and has not been exploited systematically so far. Here, a numericalmethod for its evaluation is considered, and the results are compared withthose obtained by calculating the frequency from gyrokinetic simulations. This"semianalytical" approach for the determination of the zonal-flow frequencyreveals accurate and faster than the one based on gyrokinetic simulations.

Semianalytical calculation of the zonal-flow oscillation frequency in stellarators