Effect of harmonic undulator optical klystron scheme on betatron oscillations in free electron laser

In this paper we discuss the harmonic undulator optical klystron free electron laser to enhance intensity and gain of free electron laser. Inclusion of betatron oscillation of electron while entering the undulator magnets gives extra perturbation which reduces its intensity and gain in free electron laser at several harmonics. In this we have enhanced our intensity and gain with the help of a harmonic undulator optical klystron scheme and compare the results with that of a standard optical klystron free electron laser.