We have developed and carried out a detailed characterization of a cryogenically cooled (80K) high-pressure (50×105Pa) solenoid driven pulsed valve that has been used to produce dense jets of deuterium atomic clusters for interaction studies with high intensity laser. Rayleigh scattering was employed to investigate the scaling law between cluster size and upstream gas pressure，which was shown to be of the form Nc∝P2.890. Cluster size gets to its peak Nc≈2630 at 80K，48×105Pa. We also studied the cluster formation process，portrayed a characteristic curve which revealed cluster size temporal evolution. Our results are important for analyzing the cluster interaction with intense laser， and are expected to provide guidelines to choose proper fire time.