Starting from the fundamental equations of motion of relativistic electrons

we have deduced the equations of the relativistic cyclotron electrons

in the velocity-phase space under TE mode. These equations are suitable for numerical computations in the interaction space of gyrotrons with standing wave field

such as the gyromonotron and gyroklystron

etc.In the case of gyrotrons operating at TE011 mode with the fundamental cyclotron frequency at X band （10 GHz）

the electronic efficiency of 57% and the orbital efficiency of 72% are obtained

while for gyrotrons operating at the TE021 mode with the second harmonic frequency at Ka band （35 GHz）

the electronic efficiency of 26% and the orbital efficiency of 40% are obtained.Effects of longitudinal distribution functions of RF fields in the opened resonators

the maximum amplitude of RF fields

the radius of the cyclotron beam and the longitudinal magnetic field on the parameters of the gyrotrons mentioned above are discussed in the paper

and the corresponding computed results are given as well.