Undulator vs. optical klystron induced dynamics of a storage ring free electron laser

In storage ring free electron lasers an optical klystron is often used in order to optimize the gain in the straight section offered by the storage ring. We have modelled the dynamics of the coupled system, electron bunch—laser pulse, so far using an equivalent undulator to the optical klystron. We present here a one-dimensional model of the storage ring free electron laser taking into account the optical klystron effects, and we compare it to the same model using an equivalent undulator. We show that a proper evaluation of the gain at start up and the gain dependency on the energy spread for the equivalent undulator, leads to the same dynamics as that of the optical klystron.