Continuous-wave Doppler-cooling of hydrogen atoms with two-photon transitions

11 pages, 4 figures in eps formatWe propose and analyze the possibility of performing two-photon continuous-wave Doppler-cooling of hydrogen atoms using the 1S-2S transition. \"Quenching\" of the 2S level (by coupling with the 2P state) is used to increase the cycling frequency, and to control the equilibrium temperature. Theoretical and numerical studies of the heating effect due to Doppler-free two-photon transitions evidence an increase of the temperature by a factor of two. The equilibrium temperature decreases with the effective (quenching dependent) width of the excited state and can thus be adjusted up to values close to the recoil temperature