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A compact A6 relativistic magnetron is proposed which operates in the π-mode and whose radiation is extracted axially as a TE11 mode through a cylindrical waveguide with the same cross section as that of the anode block. This radiated mode is similar to a Gaussian microwave beam. The advantages of this magnetron include the minimal volume of the applied magnetic field and, as a consequence, the proximity of the electron dump to the anode block for the electrons leaking from the interaction space that minimizes both the diameter and the axial length of the magnetron. By using MAGIC particle-in-cell (PIC) simulations, we demonstrate the possibility of generating a Gaussian radiation pattern with power of about 0.5 GW when the applied voltage is 350 kV. This compact magnetron is easier to implement than the magnetron with diffraction output (MDO), although with reduced efficiency.