Landau Damping of Geodesic Acoustic Mode in Toroidally Rotating Tokamaks

TL;DR

This paper derives an analytical dispersion relation for the geodesic acoustic mode (GAM) in rotating tokamaks, showing how toroidal rotation affects GAM frequency and damping, and compares modified and classical gyro-kinetic models.

Contribution

It provides a new analytical dispersion relation for GAM in rotating plasmas and examines the validity of classical gyro-kinetic equations under different electron temperature conditions.

Findings

Toroidal rotation increases GAM frequency.

Toroidal Mach number decreases Landau damping rate.

Classical gyro-kinetic matches modified results at zero electron temperature.

Abstract

Geodesic acoustic mode (GAM) is analyzed by using modified gyro-kinetic (MGK) equation applicable to low-frequency microinstabilities in a rotating axisymmetric plasma. Dispersion relation of GAM in the presence of arbitrary Mach number is analytically derived. Toroidal rotation plays the same effects on the GAM regardless of the orientation of equilibrium flow. It is shown that the toroidal Mach number $M$ increases the GAM frequency and dramatically decreases the Landau damping rate. The valid of classical gyro-kinetic (CGK) equation is also examined. For zero electron temperature, CGK is identical with MGK. For non-zero electron temperature, CGK gives the same real frequency of GAM as MGK but induces an instability with a growth rate proportional to $M^3/q$, where $q$ is the safety factor.