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Register a new userThree-Dimensional, Time-Dependent Simulation of Free-Electron Lasers with Planar, Helical, and Elliptical Undulators
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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.
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The explicit expressions for the average number of twisted photons radiated by a charged particle in an elliptical undulator in the classical approximation as well as in the approach accounting for the quantum recoil are obtained. It is shown that radiation emitted by a particle moving along an elliptical helix which evolves around the axis specifying the angular momentum of twisted photons obeys the selection rule: $m+n$ is an even number, where $m$ is a projection of the total angular momentum of a twisted photon and $n$ is the harmonic number of the undulator radiation. This selection rule is a generalization of the previously known selection rules for radiation of twisted photons by circular and planar undulators and it holds for both classical and quantum approaches. The class of trajectories of charged particles that produce the twisted photon radiation obeying the aforementioned selection rule is described.
Existing FEL facilities often suffer from stability issues: so electron orbit, transverse electron optics, electron bunch compression and other parameters have to be readjusted often to account for drifts in performance of various components. The tuning procedures typically employed in operation are often manual and lengthy. We have been developing a combination of model-free and model-based automatic tuning methods to meet the needs of present and upcoming XFEL facilities. Our approach has been implemented at FLASH cite{flash} to achieve automatic SASE tuning using empirical control of orbit, electron optics and bunch compression. In this paper we describe our approach to empirical tuning, the software which implements it, and the results of using it at FLASH. We also discuss the potential of using machine learning and model-based techniques in tuning methods.
A model of a Free Electron Laser operating with an elliptically polarised undulator is presented. The equations describing the FEL interaction, including resonant harmonic radiation fields, are averaged over an undulator period and generate a generalised Bessel function scaling factor, similar to that of planar undulator FEL theory. Comparison between simulations of the averaged model with those of an unaveraged model show very good agreement in the linear regime. Two unexpected results were found. Firstly, an increased coupling to harmonics for elliptical rather than planar polarisarised undulators. Secondly, and thought to be unrelated to the undulator polarisation, a signficantly different evolution between the averaged and unaveraged simulations of the harmonic radiation evolution approaching FEL saturation.
The interaction between noncolinear laser and relativistic electron beams in static magnetic undulator has been studied within the framework of dispersion equations. For a free-electron laser without inversion (FELWI), the threshold parameters are found. The large-amplification regime should be used to bring an FELWI above the threshold laser power.
In this paper, we report results of simulations, in the framework of both EuPRAXIA cite{Walk2017} and EuPRAXIA@SPARC_LAB cite{Ferr2017} projects, aimed at delivering a high brightness electron bunch for driving a Free Electron Laser (FEL) by employing a plasma post acceleration scheme. The boosting plasma wave is driven by a tens of SI{}{terawatt} class laser and doubles the energy of an externally injected beam up to GeV{1}. The injected bunch is simulated starting from a photoinjector, matched to plasma, boosted and finally matched to an undulator, where its ability to produce FEL radiation is verified to yield $O( um{e11})$ photons per shot at m{2.7}.
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