Free-electron lasers (FELs) produce different optical polarizations including linear, elliptic and circular polarizations corresponding to the polarizations of the undulators used. X-ray FELs depend upon long undulator lines consisting of a sequence of short undulators. Linearly polarized undulators are most commonly used; hence the optical output is linearly polarized. Elliptic or circular polarizations are possible by varying the undulator orientation. Alternately, APPLE-II or Delta undulator designs produce undulating magnetic fields with arbitrary polarizations. We present a three-dimensional, time-dependent formulation that self-consistently includes two optical orientations and, therefore, treats any given sequence or combination of undulator including undulator imperfections and degradation.1 There are two principal characteristics of the formulation that underpin this capability. First, particles are tracked using the full Newton Lorentz force equations with analytic models of the undulators fields. This permits an accurate model of the interaction of the electrons with a large variety of undulator fields and orientations. Second, the electrons can couple simultaneously to two independent electromagnetic polarizations and, therefore, the optical polarization evolves self-consistently along the undulator line. We present the numerical model and give some examples using prevailing undulator configurations. 1. H.P. Freund and P.J.M. van der Slot, “Variable Polarization Control in Free-Electron Lasers,” J. Phys. Commun. 5, 085011 (2021). *This research used resources provided by the University of New Mexico Center for Advanced Research Computing, supported in part by the National Science Foundation.

Free-electron lasers (FELs) operate at wavelengths from millimeter waves through hard x-rays. At x-ray wavelengths, FELs typically rely on self-amplified spontaneous emission SASE emission which contains multiple temporal “spikes” that limit the longitudinal coherence of the optical output; hence, alternate methods that improve on the longitudinal coherence of the SASE emission are of interest. In this paper, we consider electron bunches that are shorter than the SASE spike separation.1 In such cases, the spontaneously generated radiation consists of a single optical pulse with improved longitudinal coherence than is found in typical SASE FELs. To investigate this regime, we use two FEL simulation codes. One (MINERVA) uses the slowly-varying envelope approximation (SVEA) which breaks down for extremely short pulses. The second (PUFFIN) is a particle-in-cell (PiC) simulation code that is considered to be a more complete model of the underlying physics and which is able to simulate very short pulses. We first anchor these codes by showing that there is substantial agreement between the codes in simulation of the SPARC SASE FEL experiment at ENEA Frascati. We then compare the two codes for simulations using electron bunch lengths that are shorter than the SASE spike separation. The comparisons between the two codes for short bunch simulations elucidate the limitations of the SVEA in this regime but indicate that the SVEA can treat short bunches that are comparable to the cooperation length. 1. L.T. Campbell, H.P. Freund, J.R. Henderson, B.W.J. McNeil, P. Traczykowski, and P.J.M. van der Slot, “Analysis of Ultra-Short Bunches in Free-Electron Lasers,” New. J. Phys. 22, 073031 (2020). *The research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under contract DE-AC02-06CH11357. We also thank the University of New Mexico Center for Advanced Research Computing, supported in part by the National Science Foundation, for providing high performance computing resources used for this work .Funding is also acknowledged via the following grants: Science and Technology Facilities Council (Agreement Number 4163192 Release #3); ARCHIE-WeSt HPC, EPSRC grant EP/K000586/1; John von Neumann Institute for Computing (NIC) on JUROPA at Jülich Supercomputing Centre (JSC), project HHH20. The authors acknowledge helpful discussions with L. Giannessi

MINERVA is a 3-D, time-dependent simulation code of FEL amplifiers, low-gain/high-Q and high-gain/low-Q oscillators, optical klystrons (including high-gain harmonic generation) and SASE configurations [1-7]. Oscillator simulations are done in conjunction with OPC [8]. MINERVA uses the Message Passing interface on Linux, Macintosh and Windows systems and has been successfully benchmarked against many experiments. Particle dynamics are treated using the full Lorentz force equations to track particles through the optical and magnetostatic fields. Hence, MINERVA treats both fundamental and (linear and nonlinear) harmonic generation from first principles. The optical field is a superposition of Gaussian modes using the slowly-varying envelope approximation in which the x- and y-components of the field are integrated independently, and tracks the particles and fields as they propagate along the undulator line from the start-up through linear growth and into the nonlinear regime using either 2nd or 4th order Runge-Kutta integrators. MINERVA includes 3-D descriptions of planar, helical, and elliptical undulators (including a model of an APPLE-II undulator) with the fringing fields in the entry/exit transition regions. Magnetostatic field models for quadrupoles and dipoles are also included. As such, MINERVA implicitly simulates the evolution of the polarization of the optical field through an arbitrary sequence of undulators. MINERVA and OPC can be downloaded from MINERVA: https://gitlab.utwente.nl/tnw/ap/lpno/public-projects/MINERVA/-/releases OPC: https://gitlab.utwente.nl/tnw/ap/lpno/public-projects/Physics-OPC/-/releases as well as user manuals, release notes and sample scripts showing to run MINERVA/OPC. 1. H.P. Freund, P.J.M. van der Slot, D.L.A.G. Grimminck, I.D. Setya and P. Falgari, “3-D, time-dependent simulation of FELs with planar, helical, and elliptical undulators,” New J. Phys. 19, 023020 (2017). 2. H.P. Freund and P.J.M. van der Slot, “Studies of a terawatt x-ray FEL,” New J. Phys. 20, 073017 (2018). 3. H.P. Freund, P.J.M. van der Slot, and Yu. Shvyd’ko, “An x-ray Regenerative Amplifier FEL using diamond pinhole mirrors,” New J. Phys. 21, 093028 (2019). 4. L.T. Campbell, H.P. Freund, J.R. Henderson, B.W.J. McNeil, P. Traczykowski, and P.J.M. van der Slot, “Analysis of ultra-short bunches in FELs,” New. J. Phys. 22, 073031 (2020). 5. H.P. Freund and P.J.M. van der Slot, “Variable polarization control in FELs,” J. Phys. Commun. 5, 085011 (2021). 6. P.J.M. van der Slot and H.P. Freund, “3-D, time-dependent analysis of high- and low-Q FEL oscillators,” Appl. Sci. 11, 4978 (2021). 7. H.P. Freund, D.C. Nguyen, P.A. Sprangle, and P.J.M. van der Slot, “3-D, time-dependent simulation of a Regenerative Amplifier FEL,” Phys. Rev. ST-AB 16, 010707 (2013). 8. J.G. Karssenberg, P.J.M. van der Slot, I.V. Volokhine, J.W.J. Verschuur and K.-J. Boller “Modeling paraxial wave propagation in FEL oscillators,” J. Appl. Phys. 100, 093106 (2006).

X-ray free-electron lasers (FELs) rely on SASE due to the lack of seed lasers and the difficulty in obtaining mirrors. Progress in diamond crystal Bragg mirrors enables the design of x-ray FEL oscillators. Regenerative amplifiers (RAFELs) are high gain/low-Q oscillators that out-couple most of the optical power. An x-ray RAFEL based on the LCLS-II at SLAC using a six-mirror resonator out-coupling 90% or more through a pinhole in the first downstream mirror is analyzed using the MINERVA and OPC to model the optical field within the undulator and the remainder of the resonator respectively.1 Results show substantial powers at the fundamental (3.05 keV) and 3rd harmonic (9.15 keV). 1. H.P. Freund, P.J.M. van der Slot, and Yu. Shvyd’ko, “An X-Ray Regenerative Amplifier Free-Electron Laser Using Diamond Pinhole Mirrors,” New J. Phys. 21, 093028 (2019). *This research was supported under DOE Contract DE-SC0018539. Work at Argonne National Laboratory was supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357. We also thank the University of New Mexico Center for Advanced Research Computing, supported in part by the National Science Foundation, for providing high performance computing resources used for this work.

The electron-beam properties needed for successful implementation of a free-electron-laser oscillator (FELO) on a superconducting TESLA-type linac at the Fermilab Accelerator Science and Technology (FAST) facility include the intrinsic normalized emittance and the submacropulse centroid stability. We have demonstrated that short-range wakefields (SRWs) and long-range wakefields including higher-order modes (HOMs) are generated for off-axis beams in the two, 9-cell capture cavities and eight, 9-cell cavities of a cryomodule in the FAST linac. The resulting degradation of the emittance and centroid stability would impact the FELO performance. At 300 MeV and with the 4.5-m long, 5-cm period undulator, the saturation of a vacuum ultraviolet (VUV) FELO operating at 120 nm has previously been simulated with GINGER and MEDUSA-OPC using the non-degraded beam parameters. The measured electron-beam dynamics due to the SRWs (submicropulse, 100-micron head-tail kicks) and HOMs (submacropulse centroid slew of up to 100s of microns) will be presented. These are mitigated by steering on axis as guided by the minimization of the HOM signals. Simulations using MINERVA:OPC of the effects of submacropulse centroid slew on FELO performance will also be reported.