  We numerically study a method to increase the photon return flux of
continuous-wave laser guide stars using one-dimensional atomic cooling
principles. The method relies on chirping the laser towards higher frequencies
following the change in velocity of sodium atoms due to recoil, which raises
atomic populations available for laser excitation within the Doppler
distribution. The efficiency of this effect grows with the average number of
atomic excitations between two atomic collisions in the mesosphere. We find the
parameters for maximizing the return flux and evaluate the performance of
chirping for operation at La Palma. According to our simulations, the optimal
chirp rate lies between 0.8-1.0 MHz/$\mu$s and an increase in the fluorescence
of the sodium guide star up to 60% can be achieved with current 20 W-class
guide star lasers.
