[en] A particle simulation code, TDA, which models the single-pass amplification process in a free-electron-laser (FEL) is developed and tested. The code allows for the treatment of the fully three-dimensional electron dynamics, thus taking into account the transverse betatron motion as well as the longitudinal bunching of the electrons. The paraxial wave equation that governs the growth and the diffraction of the selfconsistent radiation field (assumed to be axisymmetrtic), is discretized in the radial direction by the finite difference method. The benchmark study indicates that the single-pass gain, as well as the optical guiding phenomena can be well described by the code with a reasonable number of simulation particles (N ∼ 1000) and a radial mesh number not exceeding 64. A detailed discussion of the numerical method is presented. (author) 6 figs., 1 tab., 17 refs