In this paper, the equations of FEL amplifier with aplanar wiggler are derived. FBC code based on equations is designed by H.P.Freund. WAGFEL code based on KMR theory are designed by us. Although there are obvious differences between WAGFEL and FBC code, in dealing with practical problems such as magnetic field and length of the entry wiggler, initial distribution of electron beam, fashon of the downstream tapered wiggler etc, a set of c-oupled nonlinear differential equations used in two codes is based on single-particle theory. Meanwhile, under the certain conditions, the computational results of both WAGFEL and FBC code coincide with those of the experiment well. Then the computional results used by WAGFEL and FBC code are compared.The results of TE₀₁ mode calculated with WAGFEL and FBC code are compared and analyzed under the condition of the constant and varyable amplitude of wiggler magnetic field B_w, respectively. The analyzed results show that regard the conditions and results of experiment as criterion, WAGFEL code is more useful in comparing similation results with experiment than FBC code. As a result, not only data of 4MeV amplifier which are computed by WAGFEL code are valuable, but WAGFEL code is feasible to design amplifier and study problems of FEL.

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.

From Single Particle theory, we derived Simulant equations with rectangular waveguide and obtained calculating formulas of TEmn and TMmn mode.Under the same conditions of calculation, it was shown that the results of the reduced one dimension is the same as those of one dimension.Our results are relatively near to LLNL's when only TE₀₁ mode is considered.With the two dimension code FEL-2-A on the basis of investigating its reliability,we analysed the effect on total output power by wtggler field of different linearly polarized,optical field and electron beam parameters under the conditions of constant wig-gler and different linearly polarized wiggler.These preliminary results will be of some reference value to design and experiment of low energy FEL amplifier.

In this paper, the internal electromagnetic pulses produced by the prompt-γ photons wore calculated by self-consistent and non-self-consistent mothod respectively in three dimension rectangle cavity of the matel. The computational results were analyzed. Under the condition that the electric field is weak and the cavity is small, the results obtained by self-consistent method coincide with the results by the non-self-consistent.