  The equations of particle motion in the FELWI are derived using Hamiltonian
formalism. In small signal regime the uncoupled one dimensional phase equation
is derived in the form of pendulum equation. For the practical estimations the
same equation along with the equation of particle energy change are solved
using perturbation theory and the expressions for gain in FEL regime and
particle angle dependence of energy at the exit of first undulator are
obtained. Results for gain, particle phase and energy change depending on
device and beam parameters are presented.
