Collisional damping of the geodesic acoustic mode

The frequency and damping rate of the geodesic acoustic mode (GAM) is revisited by using a gyrokinetic model with a number-conserving Krook collision operator. It is found that the damping rate of the GAM is non-monotonic as the collision rate increases. At low ion collision rate, the damping rate increases linearly with the collision rate; while as the ion collision rate is higher than vti/R, where vti and R are the ion thermal velocity and major radius, the damping rate decays with an increasing collision rate. At the same time, as the collision rate increases, the GAM frequency decreases from the (7/4+τ)vti/R to (1+τ)vti/R, where τ is the ratio of electron temperature to ion temperature.