The flow of hydrogen, helium, and nitrogen through a millimeter long and micrometer size annulus capillary from a high pressure chamber to a low pressure chamber is measured in a wide pressure range. The corresponding gas conductance is deduced. Molecular, transition, and viscous regimes are observed. The local supply of gas strongly increases with pressure in the viscous regime up to a regime controlled by capillary exit loss. Based on such a geometry, the gas supply to a field ion source with a coaxial structure is shown to be increased by more than three orders of magnitude compared to a conventional supply. (C) 2008 American Vacuum Society.