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Using particle-in-cell/Monte Carlo simulation, the time-dependent physics of the multipactor electron discharge on a dielectric is studied within a transmission line model. It is discussed how RF magnetic field influences the initiation of multipactor and the multipactor behaviors at the upstream and downstream sides of the dielectric window. The effect of oblique incident high-power microwave (HPM) on the multipactor characteristic is also discussed. It is found that the interaction of electrons with the electromagnetic field can provide their return to the dielectric surface, which makes a multipactor possible even without any external static field. Multipactor discharge at the downstream side of the dielectric window is demonstrated to have a longer delay time, a smaller electron-surface interaction rate, and a much higher electron mean energy in comparison to those obtained at the upstream side. Thereby, the experimental observation that the threshold power is approximately 20% higher for the downstream side than it is for the upstream side is explained. Generally, the multipactor electron discharge is most likely to take place at the region where the RF electric field is parallel to the dielectric surface. The deposited power is greatest at normal incidence of HPM but is dramatically decreased for angles of obliqueness greater than approximately 5°- 10°. The oblique incident angle does not change the Lissajous behavior of the multipactor discharge on a dielectric but may affect the shape of the Lissajous curve greatly.