Effects of space charge and multiple scattering on the gain of an X‐ray free electron laser using stimulated transition radiation

Abstract

For the X‐ray free electron laser using stimulated transition radiation in periodic stacks of metal foils or polymer films, the effects considered are those that are due to: (1) the space charge of the relativistic electron beam; (2) multiple scattering of the electron beam passing through the stacks; and (3) both the space charge and multiple scattering simultaneously. Taking these respective effects into account in a Boltzmann transport equation, dispersion relations are derived and gain coefficients of the laser are calculated and compared. As a result, it is found that the effect of multiple scattering is large and it depends also on the magnitude of the electron beam energy, e.g., for the case of 50 GeV, the gain coefficient is decreased by several dB. The effect of the space charge is relatively small. Also, the gain coefficient generally decreases with the beam energy.