  A nonlinear analytical model for the pressure dynamics in a vacuum chamber,
pumped with a sputter ion pump (SIP), is proposed, discussed and experimentally
evaluated. The model describes the physics of the pumping mechanism of SIPs in
the context of a cold-atom experiment. By using this model, we fit pump-down
curves of our vacuum system to extract the relevant physical parameters
characterizing its pressure dynamics. The aim of this investigation is the
optimization of cold-atom experiments in terms of reducing the dead time for
quantum sensing using atom interferometry. We develop a calibration method to
improve the precision in pressure measurements via the ion current in SIPs. Our
method is based on a careful analysis of the gas conductance and pumping in
order to reliably link the pressure readings at the SIP with the actual
pressure in the vacuum (science) chamber. Our results are in agreement with the
existence of essentially two pumping regimes determined by the pressure level
in the system. In particular, we find our results in agreement with the
well-known fact that for a given applied voltage, at low pressures, the
discharge current efficiently sputters pumping material from the pump's
electrodes. This process sets the leading pumping mechanism in this limit. At
high pressures, the discharge current drops and the pumping is mainly performed
by the already sputtered material.
