Effect of solenoid lens field on electron beam emittance

In an injector system of an X-ray free electron laser (XFEL), solenoid lenses are typically used to confine low-emittance electron beams to low-energy region below a few MeV. Because non-thermionic emittance at such a low-energy region is easily deteriorated by nonlinear electromagnetic fields, it is important to determine the properties of a solenoid lens on electron beam emittance in the design of XFEL injectors. We derived an approximate solution to emittance growth due to lens aberration by a paraxial approximation. It was found that the derivative of the longitudinal magnetic field strongly affects beam emittance, and its growth is proportional to the fourth power of the beam radius. Various properties of the beam can be analyzed as long as the longitudinal magnetic field distribution is prepared using a simulation or measurement. In this study, a theoretical procedure to obtain the emittance growth in the solenoid lens is introduced and the design considerations of the solenoid lens of the SACLA injector are described.