  A high peak current, flat longitudinal phase space electron beam is desirable
for efficient x-ray free electron laser (FEL) radiation in next generation
light sources. To attain such a beam requires the extensive design of the
linear accelerator (linac) including both linear and nonlinear effects. In this
paper, we propose a lumped longitudinal beam dynamics model for fast
optimization of the electron beam longitudinal phase space through the
accelerator. This model is much faster than available tracking programs and
also shows good agreement with the fully three-dimensional element-by-element
multi-particle simulations. We applied this model in a parallel multi-objective
differential evolution optimization program to an existing LCLS-II
superconducting linac design and obtained an optimal solution with
significantly higher core peak current than the original design.
