The authors study the virtual cathode oscillations with EM particle-in-cell computer simulations using the MAGIC code. The focus of the simulation is on the design of the cathode structure. The authors simulate the design of a new cathode structure which provides one solid and two annular electron beams whose positions are determined by the radial locations of the first three peaks of the Bessel function. Each electron beam is separated by a concentric anode structure and is guided to the cylindrical waveguide by a magnetic field. The thickness of each cathode piece and the gaps between the anode structure and cathode pieces and the widths of anode slits are chosen with the aid of the simulation such that the current density in the waveguide downstream of the anode slits is uniformly peaked at the peak locations of the Bessel function. Thus, TM05 mode microwave radiation can be generated in an open end waveguide with higher efficiency than that of a previous design.