Initial electron distributions for free electron lasers generated by injector and accelerator simulations

Abstract

Early free electron laser (FEL) development was guided by simple performance criteria based on the number of undulator periods, electron beam quality, and current. The beam quality (emittance and energy spread) was used to characterize the initial distribution of axial electron velocities along the undulator axis. While the emittance and energy spread determine the overall width of the distribution, its detailed shape is also important. As new accelerators are designed specifically for FEL applications, it becomes important to obtain distribution shape information from simulations that include the electron gun, accelerator, and beam transport in addition to the usual electron/optical interaction in the undulator.The distribution at the entrance to the undulator can be calculated from numerical simulations of the cathode emission, acceleration, and transport of an electron beam. We have modeled the beam generation, from cathode emission up to the energy of the accelerator injector, using an axisymmetric, cylindrical geometry particle simulation (DPC). This code solves the relativistic force equation with fields obtained from Maxwell's equations in the Darwin model. The DPC calculation is run repeatedly varying parameters such as accelerating stress, electrode configuration, and axial magnetic field profile until a good match is obtained for the accelerator. The beam exiting from the injector can be accelerated and transported using the transfer matrix technique with a simple model for accelerating gaps and magnets. Alternatively, acceleration and transport can be simulated with a particle code that solves for the axisymmetric evolution of a slice of an electron beam including possible emittance growth.The phase space obtained from the accelerator can be evaluated for performance using either the simple FEL integral equation method or the more complete FRED simulation code.