Gas desorbed by electrons plays a key role in multipactor saturation and final plasma breakdown at the vacuum side of the window in high power microwave systems. A multipactor model involving electron-neutral collision and ionization is established. When desorption gas pressure reaches 1Torr, the electron impact energy apparently decreases, multipactor saturates at a lower surface charging field, and multipactor saturation meets easier, compared to vacuum. Experiments for different material windows of high power microwave, with the power of 1GW, frequency of 9.4GHz, and 20ns single and multiple pulses was conducted. It was discovered that gas pressure rose prominently in the horn, when breakdown occurred. The increase in local gas pressure during the 20ns pulse is estimated from the experiment to reach several Torr, a pressure that is consistent with the presented dynamic model.