We investigate a source of H atoms generated by a low-pressure surface wave discharge (2.45 GHz). We study the influence of microwave power both on the discharge characteristics on the H atom density, which has been measured by actinometry. Dissociation levels of H2 are much higher (75%) at low microwave power than at high power (10%). Unlike what has been found in oxygen surface wave plasmas, discharge characteristics depend strongly on microwave power, due to an important coupling between discharge equilibrium and kinetics of the atomic hydrogen. These results are explained taking into account the effect of discharge tube wall temperature on atomic recombination. The wall recombination probability gamma is estimated as a function of the microwave power: it ranges from 6*10-3 to 6*10-2, which is very high in comparison with values determined previously under post-discharge conditions.