Three-Dimensional, Time-Dependent Simulation of Free-Electron Lasers with Planar, Helical, and Elliptical Undulators

TL;DR

This paper introduces a comprehensive three-dimensional, time-dependent simulation framework for free-electron lasers that accommodates various undulator configurations and polarizations, validated against multiple experimental results.

Contribution

It develops a novel simulation model capable of handling arbitrary 3D undulator geometries and polarizations, including an analytic model for elliptical polarizations, linking with optical propagation codes.

Findings

Successfully modeled elliptically polarized FEL output using the APPLE-II undulator.

Validated simulation results against experimental data from multiple FEL facilities.

Demonstrated the model's capability to simulate different FEL configurations and polarizations.

Abstract

Free-electron lasers (FELs) have been built ranging in wavelength from long-wavelength oscillators using partial wave guiding through ultraviolet through hard x-ray that are either seeded or start from noise (SASE). In addition, FELs that produce different polarizations of the output radiation ranging from linear through elliptic to circular polarization are currently under study. In this paper, we develop a three-dimensional, time-dependent formulation that is capable of modeling this large variety of FEL configurations including different polarizations. We employ a modal expansion for the optical field, i.e., a Gaussian expansion with variable polarization for free-space propagation. This formulation uses the full Newton-Lorentz force equations to track the particles through the optical and magnetostatic fields. As a result, arbitrary three-dimensional representations for different undulator configurations are implemented, including planar, helical, and elliptical undulators. In particular, we present an analytic model of an APPLE-II undulator to treat arbitrary elliptical polarizations. To model oscillator configurations, and allow propagation of the optical field outside the undulator and interact with optical elements, we link the FEL simulation with the optical propagation code OPC. We present simulations using the APPLE-II undulator model to produce elliptically polarized output radiation, and present a detailed comparison with recent experiments using a tapered undulator configuration at the Linac Coherent Light Source. Validation of the nonlinear formation is also shown by comparison with experimental results obtained in the SPARC SASE FEL experiment at ENEA Frascati, a seeded tapered amplifier experiment at Brookhaven National Laboratory, and the 10-kW Upgrade Oscillator experiment at the Thomas Jefferson National Accelerator Facility.