We report a detailed simulation of a bunched electron-beam accelerated in a TE[Formula: see text] cylindrical cavity immersed in a static inhomogeneous magnetic field using a relativistic full electromagnetic particle-in-cell (PIC). This type of acceleration concept is known as Spatial AutoResonance Acceleration (SARA) in which the magnetic field profile is such that it keeps the electron-beam in the acceleration regime along their trajectories. In this work, the numerical experiments are carried out including a bunched electron-beam with the concentrations in the range [Formula: see text]–[Formula: see text][Formula: see text]cm[Formula: see text] in a TE[Formula: see text] cylindrical microwave field, at a frequency of 2.45 GHz and an amplitude of 15 kV/cm. The electron energy reaches values up to 250 keV without significant unfocusing effect that can be used as a basis to produce hard X-ray. Additionally, a comparison between the data obtained from the full electromagnetic PIC simulations and the results derived from the relativistic Newton–Lorentz equation in a single particle approximation is carried out.