Comparison Between, and Validation Against an Experiment of, a Slowly-Varying Envelope Approximation Code and a Particle-in-Cell Simulation Code for Free-Electron Lasers.

Free-electron lasers (FELs) operate at wavelengths down to hard x-rays, and are either seeded or start from noise. There is increasing interest in x-ray FELs that rely on Self-Amplified Spontaneous Emission (SASE), and this involves increasing simulation activity in the design, optimization, and characterization of these x-ray FELs. Most of the simulation codes in use rely on the Slowly-Varying Envelope Approximation (SVEA) in which Maxwell's equations are averaged over the fast time scale resulting in relatively small computational requirements. While the SVEA codes are generally successful, the predictions of these codes sometimes differ in various aspects of the FEL interaction. In contrast, Particle-in-Cell (PiC) simulation codes do not average Maxwell's equations and are considered to be a more complete model of the underlying physics.Unfortunately, they require much longer run times than SVEA codes and have not been validated by comparison with experiment as often as the SVEA codes. In order to remedy this, and to resolve issues that arise due to different predictions between the SVEA codes, we present a comparison between one SVEA code (MINERVA) and a PiC simulation code (PUFFIN) with the experimental measurements obtained at the SPARC SASE FEL experiment at ENEA Frascati. The results show good agreement between the two codes and between the codes and the experiment. Since the formulations of the two codes share no common elements, this validates both formulations and demonstrates the capability to model the FEL interaction from the start of teh undulator through the undulator and into deep saturation.