In order to study the breakdown process of vacuum switch, we use a vacuum diode, which is composed of a cathode and an anode, to replace the vacuum switch. We find that there is wide band microwave radiation in the breakdown process of the vacuum diode. Because there is no structure of metallic bellow waveguide in the vacuum diode, the radiation mechanism of the vacuum diode is different from that of the plasma filled microwave device. It is hard to completely imitate the theory of the plasma filled microwave device. In order to clarify the mechanism of the microwave radiation from the vacuum diode, we analyze the breakdown process of the vacuum diode. When the anode plasma has been generated and the plasma closure has not occurred, the electrons emitted from the initial plasma will be incident on the anode plasma, and the vacuum diode will radiate microwave in this process. The self-generating magnetic field of the electron beam is a poloidal magnetic field. When the electron beam is incident on the plasma, the plasma will be magnetized by the poloidal magnetic field. The theory of magnetic fluid is used to analyze the problem in this paper, and the mathematical model of the vacuum diode radiation is obtained by using the simultaneous equations of the motion equations and Maxwell's equations. In this model, there is an interface between the electron beam and the magnetized plasma. The model is divided into two parts by the interface, i.e., inside of the electron beam and outside of the electron beam. The dispersion relation of the radiation generated by the vacuum diode is obtained by solving the mathematical model. Based on the dispersion relation and the experimental data, the dispersion curves are plotted for the different electron beam velocities. The dispersion curves show that the undulation of the dispersion curve becomes smaller and smaller with the decrease of the electron beam velocity, and the final dispersion curve will be approximated by a straight line. When the theoretical dispersion curves are compared with the actually measured time-frequency maps of the radiation, we find that they are well consistent with each other. Theoretical deduction and experiments indicate that the radiation generated by the vacuum diode originates from the interaction between the electron beam and the magnetized plasma.