Optimum design of pumping system for maintaining vacuum in a chamber open to the atmosphere through an aperture

Abstract

If a vacuum region must have an aperture to the atmosphere, the total volume pumping requirement due to the leak can be enormously reduced by using a series of apertures with inter-stage pumping between the apertures. An analysis of this system is developed which yields (i) the optimal inter-stage pressures for minimum total volume flow; and (ii) the corresponding volume flows to the pumps. In the special case for which all the apertures have the same volume flow per unit of upstream pressure, the optimal condition is that the pressure ratio be the same for each aperture; the volume flows to the pumps are then nearly identical. An illustrative example, with a pressure of 10 −6 mmHg in the vacuum region, shows that by using two apertures in series rather than one, the total volume flow to the pumps is reduced by a factor of 10 −4; with four apertures, the reduction factor is 10 −6. The reduction from each successive aperture becomes less and less, and practical considerations will dictate a number in the range of about two to six.