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Flow of molecular gas into a complex vacuum system is investigated by alumped parameter model to estimate the time evolution of gas pressure $p_g$,which for the first time takes into account the realistic effect of time-delayarising due to multiple reasons such as valve response, pumping and transportof gas, conductance of the pipe network, etc. The net effect of all such delaystaken together into a single (constant) delay term gives rise to a scalar delaydifferential equation (DDE). Analytical solutions of a linear DDE in presenceof external forcing due to the (pulsed) injection of gas and outgassing from astainless steel (SS) wall are then derived using the Laplace transform method,where the transcendental characteristic equation is approximated by means ofrational transfer functions such as diagonal Pad{\'e} approximation. A goodagreement is obtained with the numerical results and it is shown from thesesolutions that a reasonably good match with experimental results is obtainedonly in the presence of a nonzero time-delay. An attempt is also made tosimplify the DDE into an ordinary differential equation (ODE) by using alow-order Taylor series expansion of the time-delay term. A singularperturbation method is used to solve the resultant initial value problem (IVP)type second-order ODE. It is found that unlike the Laplace transform method,the ODE closely approximates the DDE only if the delay is small. Emergence ofstable periodic oscillations in $p_g$, as a generic supercritical Hopfbifurcation, if time-delay exceeds a critical value is then established bynumerical and Poincar{\'e}-Lindstedt method.

A time-delay model for molecular gas flow into vacuum