Abstract: In this paper, the analytical solutions of equations of electron betatron motion are derived by W·K·B method for parameters of varyable B_wand γ. with the formula, the reasons that electrons run out of the waveguide are analyzed. Meanwhile, we have compared the analytical results with those which are simulated by WAGFEL code Under certain conditions, analytical results coincide with simulation results well.

Key words: rectangular waveguide, electron trajectories, betatron motion, W·K·B method