Approximate analytic solution of coaxial intensive electron beam diode

According to the Maxwell equations, an analytic solution related with coaxial diode current, applied voltage and geometry parameters is obtained by introducing certain approximation. The relation among the coaxial diode impedance, the potential distribution in diode gap and the external voltage are also derived, and the relative error is analyzed comparing with the precision numerical evaluation of the 1D analytic model. Meanwhile, PIC simulations are carried out to test the accuracy of the analytic equations under practical parameters, which yield consistent results. The diode impedance obtained by the analytic solution is very close to the experimental data under relativistic voltage range of 300~700 kV.