Linear Gyro-Kinetic Response Function for Zonal Flows

A linear response function for zonal flows is obtained by solving the gyro-kinetic equation. This is an extension of the previous work which adopted the method of "integrating along particle orbit" to solve the drift kinetic equation. The formula derived in this paper is used to calculate the dispersion relation of geodesic acoustic mode, which is compared with that of the gyro-kinetic analytic formula.