Analytical and numerical investigations of the evolution of wake fields of accelerated electron beams encountering cavity discontinuities in laser-driven RF-free electron laser photoinjector

We report a rigorous derivation of an analytical expression for the wake fields of accelerated electron beams that takes into account the discontinuity of the accelerating cavities of linear accelerators. The approach employs Fourierʹs transforms, Greenʹs function techniques, and Laurent series in order to solve the full set of Maxwellʹs equations in the Lorentz gauge. This represents a significant step toward a realistic description of the evolution of wake fields in linear accelerators. The expression is applied to the “ELSA” photo injector to obtain relevant numerical results.