Geodesic acoustic modes in a fluid model of tokamak plasma : the effects of finite beta and collisionality

TL;DR

This paper derives nonlinear equations for geodesic acoustic modes in tokamak plasmas, analyzing how collisionality and plasma beta influence GAM frequency, and compares theoretical predictions with experimental data revealing persistent discrepancies.

Contribution

It introduces a comprehensive fluid model for GAMs that includes collisionality, plasma beta, and external sources, and examines their effects on GAM frequency in tokamak edge plasmas.

Findings

GAM frequency increases with collisionality at low radial wave number

GAM frequency decreases with plasma beta

Discrepancies between theory and experiment suggest finite radial wave number effects are insufficient to resolve differences

Abstract

Starting from the Braginskii equations, relevant for the tokamak edge region, a complete set of nonlinear equations for the geodesic acoustic modes (GAM) has been derived which includes collisionality, plasma beta and external sources of particle, momentum and heat. Local linear analysis shows that the GAM frequency increases with collisionality at low radial wave number $k_{r}$ and decreases at high $k_{r}$. GAM frequency also decreases with plasma beta. Radial profiles of GAM frequency for two Tore Supra shots, which were part of a collisionality scan, are compared with these calculations. Discrepency between experiment and theory is observed, which seems to be explained by a finite $k_{r}$ for the GAM when flux surface averaged density $\langle n \rangle$ and temperature $\langle T \rangle$ are assumed to vanish. It is shown that this agreement is incidental and self-consistent inclusion of $\langle n \rangle$ and $\langle T \rangle$ responses enhances the disagreement more with $k_r$ at high $k_{r}$ . So the discrepancy between the linear GAM calculation, (which persist also for more "complete" linear models such as gyrokinetics) can probably not be resolved by simply adding a finite $k_{r}$.