Kinetic theory of free electron lasers

We have developed a comprehensive kinetic theory of the free-electron laser (FEL) interaction, including the effects of self-fields. To demonstrate its utility, three examples are selected for presentation. First, we discuss the role of emittance and axial velocity spread in order to define what constitutes beam quality in the context of FEL interaction. The longitudinal beam quality in an FEL may be quantified by the ratio of the thermal velocity to the difference between the beam and the ponderomotive wave velocity. Using this, we proceed to investigate the effect of longitudinal beam compression on the growth rate. In the last example, we consider the effect of self-fields. We find that self-fields can improve electron beam quality in certain regimes. The reason for this anti-intuitive result is a decrease in the axial velocity spread due to self-fields. That is, self-fields effectively cool the beam.