Numerical Investigation of Finite k Effect on Damping Rate of Geodesic Acoustic Mode in Collisionless Plasmas

Numerical method is applied to the investigation of the GAM damping rate with the finite k effects included. It is found that generally the damping rate given by the analytical method is smaller than that given by the numerical method, and the analytical damping rate has good approximation in the high q region (q>4). The difference between the analytical and numerical damping rates increases with the increasing k\ρ_i. However, for the short-wavelength case (k\ρ_i =0.2), the analytical methods are only good enough around q=4 because of the slow convergence of Bessel function with the large variable.