Laser Heater and seeded Free Electron Laser

In this paper we consider the effect of laser heater on a seeded Free Electron Laser. We develop a model embedding the effect of the energy modulation induced by the heater with those due to the seeding. The present analysis is compatible with the experimental results obtained at FERMI displaying secondary maxima with increasing heater intensity. The treatment developed in the paper confirms and extends previous analyses and put in evidence further effects which can be tested in future experiments.