Abstract: In this paper, electron motion in the adiabatic magnetron injection gun (AMIG) of Gyrotron is briefly described. A concept of equivalent diode operating with temperature limited emission in the cathode region is proposed. A formula calculating transverse beam energy determined by the electrode dimensions and electromagnetic parameters is derived from the adiabatic theory and the analysis of electron stream in this diode and the field between two concentric cylinders. With this formula, it is very convenient for us to rapidly and correctly determine the main parameters of the AMIG or judge the moving condition of the electron beam in Gyrotron according to practical parameters. The comparison between the calculations of the cathode field in this paper and the mumerical results of the AMIG given by computer shows that the difference is within five percent, and the former also coincide with the computed data from reference[1]. The calculations of transverse beam energy are in good agreement with experimental results.