Free-electron Laser Simulation Research Articles

Accelerating the convergence of free electron laser simulations by retrieving a spatially coherent component of microbunching

A simple method to reduce the numerical cost in free electron laser (FEL) simulations is presented, which is based on retrieving a spatially coherent component of microbunching to suppress artifact effects that can potentially overestimate the FEL gain; this significantly reduces the number of macroparticle to reach the numerical convergence and enables the computation of amplified radiation with semianalytical formulas. Examples of FEL simulations performed to demonstrate the proposed method show that the computation time to get a reliable result is reduced by 1–2 orders of magnitude depending on the simulation condition. Published by the American Physical Society 2024

Unaveraged simulations of a cavity based free electron laser

The computer simulation of a cavity-based (oscillator) Free-Electron Laser (FEL) requires the modelling of both the electron-light interaction in the FEL undulator and the radiation propagation within the optical cavity. The unaveraged 3D FEL simulation code Puffin has been coupled with the Optical Propagation Code (OPC) to allow a broadband, high temporal-resolution cavity FEL to be modelled for the first time. This requires the translation of the radiation field formats between the Puffin and OPC codes. This translation is described and the coupled codes are then used to model an example of a Regenerative Amplifier FEL operating in the VUV.

Effect of ion channel guiding on the saturation mechanism of single and two-stream free-electron lasers based upon a rectangular hybrid wiggler

The paper studies a simulation of a one-dimensional nonlinear free electron laser that includes a square hybrid wiggler, prebunched electron beam, and ion-channel guiding mechanism. The Lorentz equations of motion and the Maxwell equations were combined to derive a set of non-linear differential equations solved numerically within the framework of slowly varying amplitude and wavenumber. The relativistic electron beam is assumed to be cold, and self-fields of the electron beam and the slippage of the radiation wave are ignored. The appropriate parameters are chosen in such a way that the Raman regime is being considered, where there is high density and low energy. The effect of ion-channel densities on the saturation of the device is studied for both groups Ι and ΙΙ orbits. It is found that as the ion channel density increases, the range of saturation radiation for group Ι circuits increases, too. In contrast, the saturated radiation amplitude for group ΙΙ orbits is decreased with increasing the ion-channel density. Moreover, the results of the numerical calculations show that the saturation length for an FEL with a prebunched beam is considerably shorter than that of a uniform electron beam. A free electron laser (FEL) model called the two-stream FEL, which uses two relativistic electron beams of different energy, is also studied. Comparing the radiation amplitude between FEL and TSFEL shows that TSFEL is more efficient than FEL.

The Saturation Mechanism in a two-stream free-electron laser based upon a rectangular hybrid wiggler

This paper presents a one-dimensional nonlinear simulation of a square hybrid two-stream free electron laser (TSFEL) consisting of an axial magnetic field guide. It is supposed that the two cold relativistic electron beams differ in energy, while the electron beam’s self-fields, and radiation wave slippage relative to electron beams are neglected. A set of differential equations of the first order of coupled nonlinearity, obtained from the combination of Maxwell’s equations and Lorentz’s equations, can be numerically solved using a Runge–Kutta algorithm of fourth-order based on slowly varying amplitudes and wavenumbers approximation. According to the results of the calculations, the increase in the axial magnetic field will increase the efficiency in group I orbits while the saturation length decreases. The results for group II orbits are different from those of group I, so the efficiency decreases with the increasing axial magnetic field. There is, however, an increase in saturation length. Additionally, it is found that prebunching significantly reduces the length of saturation. A comparison of radiation saturation in an FEL and a TSFEL indicates that a TSFEL has a higher efficiency than an FEL. In contrast, the TSFEL has shorter saturation lengths.

Up-sampling of electron beam simulation particles with addition of shot-noise

An algorithm and numerical code for the up-sampling of a system of particles, from a smaller to a larger number, is described. The method introduces a Poissonian ‘shot-noise’ to the up-sampled distribution, typical of the noise statistics arising in a bunch of particles generated by a particle accelerator. The algorithm is applied to a 6-Dimensional phase-space distribution of relatively few simulation particles, representing an electron beam generated by particle accelerator modelling software, for subsequent injection into an Free Electron Laser (FEL) amplifier which is used here to describe the model. A much larger number of particles is usually required to model the FEL lasing process than is required to model the electron beam accelerators that drive it. A numerical code developed from the algorithm was then used to generate electron bunches for injection into to an unaveraged 3D FEL simulation code, Puffin. Results show good qualitative and quantitative agreement with analytical theory. The program and user manual is available for download.

A Super-Fast Free-Electron Laser Simulation Code for Online Optimization

The X-ray free-electron lasers (FELs) have stimulated the growing interest of researchers in different fields. This gives rise to an increasing simulation work of design and optimization of FEL facilities and demonstrations of novel FEL ideas. Most of the multi-dimensional simulation codes in use require large computational resources, while one-dimensional simulation codes can merely give an acceptable description of the FEL amplification process. This paper presents the development of a super-fast time-dependent FEL simulation code, which is mainly designed for seeded FEL and its application on a seed FEL facility. The diffraction factors have been introduced in order to model the effects of radiation field diffraction and drastically simplified the working equations. Meanwhile, a specially designed module for seeded FEL has been added in order to study the laser-electron beam interactions with arbitrarily parameters. The code can also provide a fairly accurate, quasi-real-time assistant tool for online optimization.

Intensity optimization of x-ray free-electron laser by using phase shifters

This paper presents a method that uses a gap scan of the phase shifter to optimize the intensity of a free-electron laser (FEL) by matching its phase with that of the electron beam. Phase shifters are essential instruments, especially for a long undulator line, which is segmented by drift sections. The phase-matched (in-phase) and the 180\ifmmode^\circ\else\textdegree\fi{} offset (out-of-phase) conditions are investigated using linear theory, FEL simulations, and experiments to understand how the phase shifter affects FEL amplification. We show that the FEL intensity is dominantly reduced by phase mismatch in the saturation region, where the microbunched electron beam is sufficiently developed, and that the difference of FEL intensity between the in-phase and out-of-phase conditions is an effect of evolution of the bunching factor. At the Pohang Accelerator Laboratory x-ray Free-Electron Laser (PAL-XFEL), the gap scan of the phase shifter at 9.7 keV increased FEL intensity by 4 times compared to the calculated gap of the phase shifter. This intensity increase was obtained dominantly in the saturation region.

Analysis of ultra-short bunches in free-electron lasers

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). Typical SASE emission contains multiple temporal ‘spikes’ which limit the longitudinal coherence of the optical output; hence, alternate schemes 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. In such cases, the spontaneously generated radiation consists of a single optical pulse with better 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 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 slice 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.

Fully 3D time-dependent simulation of free electron laser within an overmoded rectangular waveguide

Numerical simulation codes are basic tools for designing Free Electron Lasers (FELs). This paper describes a numerical approach for the time-dependent, three-dimensional simulation of the free electron laser (FEL) using a rectangular waveguide within overmoded configuration when the radiation wavelength is much shorter than the waveguide cut-off wavelength. Instead of developing a new code, the Genesis simulation code is modified for our purpose. This approach presented here can be used for extending the capacity of Genesis code to cover this special configuration. The major modification is to apply the boundary conditions on the waveguide walls to the steady-state radiation field equations in a limited rectangular region and the full Cartesian mesh using the Alternating Direction Implicit (ADI) integration scheme to solve the field equation remains adopted.

Modelling a laser plasma accelerator driven free electron laser

Free-electron lasers (FEL) are the brightest, coherent sources of short wavelength radiation from the VUV into the x-ray. There is much research interest in reducing the cost and the size of FELs by utilising new accelerator techniques. Laser-plasma accelerator (LPA) are a promising accelerator for next generation compact FEL light sources with many potential advantages due to the high acceleration gradient and large peak currents they offer. The electron beams of a LPA typically have a smaller transverse emittance, a large energy spread and tend to be of shorter duration and higher current than conventional Radio Frequency (RF) accelerators. In this paper, a FEL driven by an electron beam from a typical LPA was simulated using the 3D FEL simulation code Puffin. It is shown that lowering the homogenous electron beam energy spread increases the radiation energy output in a short undulator and , as become less than the FEL, or Pierce parameter (), then the peak radiation energy increases and the saturation length reduces significantly as expected.

Harmonic Generation in Planar Undulators in Single-Pass Free Electron Lasers

The paper presents a theoretical study of the harmonic power evolution in a single-pass free-electron laser (FEL) and a comparison with some of the experimental results. The phenomenological approach which considers the main FEL parameters (current density, the Lorentz factor, electron energy spread, and the beam geometry) provides a description of any undulator. With due regard to the real laser beam parameters, the effect from high-order harmonic radiation and the beam deviation from the undulator axis on the FEL irradiation is investigated. The Bessel coefficients are calculated for the undulator in the presence of the second periodic field. The phenomenological approach provides the free-electron laser simulation experiments at Sorgente Pulsata Auto-amplificata di Radiazione Coerente (SPARC), SPring-8 Angstrom Compact Free-Electron Laser (SACLA) and Linac Coherent Light Source (LCLS). These studies include the high-harmonic generation, a comparison of the emission power evolution with the experimentally obtained data on the harmonic generation including even and odd high-order harmonics, gain and saturation lengths and the respective power. A possible effect from the third harmonic of the planar undulator magnetic field is studied in relation to the FEL irradiation. It is shown that this effect is insignificant even at the magnetic-field harmonic amplitude equaling ~1/10 of the amplitude of the ideal magnetic field in the periodic undulator. It is found that the second-harmonic generation in FEL lasing is rather weak, that is in good agreement with the measurement results as well as the behavior of the high-order harmonics.

Advances in numerical methods under wiggler period averaging for free electron laser simulation

Advances in numerical methods for free-electron-laser (FEL) simulation under wiggler period averaging (WPA) are presented. First, WPA is generalized using the perturbative Lie map method. The conventional WPA is identified as the leading order contribution. Next, the shot-noise model under WPA is improved along with a particle migration scheme across the numerical mesh. The artificial shot noise arising from particle migration is suppressed. The improved model also allows using arbitrary mesh size, slippage resolution, and integration step size. These advances will improve modeling of longitudinal beam profile evolution for fast FEL simulation.

Nonlinear simulation of free electron laser in a rectangular waveguide and ion-channel guiding

In this study, the free electron laser (FEL) with a planar wiggler and an ion-channel in a rectangular waveguide is studied for TE waves with numerical simulation. The output power of FEL is obtained self-consistently from the equation of motion and Maxwell's equations. Numerical analysis shows that using the ion-channel, in spite of the magnetic field case [Sakamoto et al., J. Appl. Phys. 75, 36 (1994)], can improve output power in addition to guiding the electrons into the center and prevent dissipation of the beam.

Three-dimensional, time-dependent simulation of free-electron lasers with planar, helical, and elliptical undulators

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. 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, which is used to treat general 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 Sorgente Pulsata Auto-amplificata di Radiazione Coerente 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.

First observation of SASE radiation using the compact wide-spectral-range XUV spectrometer at FLASH2

The Free-electron LASer in Hamburg (FLASH) has been extended with a new undulator line FLASH2 in 2014. A compact grazing-incident wide-spectral-range spectrometer based on spherical-variable-line-spacing (SVLS) gratings in the extreme ultraviolet (XUV) region was constructed to optimize and characterize the free-electron laser (FEL) performance at FLASH2. The spectrometer is equipped with three different concave SVLS gratings covering a spectral range from 1 to 62nm to analyze the spectral characteristics of the XUV radiation. Wavelength calibration and evaluation of the spectral resolution were performed at the plane grating monochromator beamline PG2 at FLASH1 before the installation at FLASH2, and compared with analytical simulations. The first light using self-amplified spontaneous emission from FLASH2 was observed by the spectrometer during a simultaneous operation of both undulator lines—FLASH1 and FLASH2. In addition, the spectral resolution of the spectrometer was evaluated by comparing the measured spectrum from FLASH2 with FEL simulations.

Three-dimensional simulation of thermal harmonic lasing free electron laser with detuning of the fundamental

Detuning of the fundamental is a way to enhance harmonic generation. By this method, the wiggler is composed of two segments in such a way that the fundamental resonance of the second segment to coincide with the third harmonic of the first segment of the wiggler to generate extreme ultraviolet radiation and x-ray emission. A set of coupled, nonlinear, and first-order differential equations in three dimensions describing the evolution of the electron trajectories and the radiation field with warm beam is solved numerically by CYRUS 3D code in the steady-state for two models (1) seeded free electron laser (FEL) and (2) shot noise on the electron beam (self-amplified spontaneous emission FEL). Thermal effects in the form of longitudinal velocity spread are considered. Three-dimensional simulation describes self-consistently the longitudinal spatial dependence of radiation waists, curvatures, and amplitudes together with the evaluation of the electron beam. The evolutions of the transverse modes are investigated for the fundamental resonance and the third harmonic. Also, the effective modes of the third harmonic are studied. In this paper, we found that detuning of the fundamental with shot noise gives more optimistic result than the seeded FEL.

An application of laser–plasma acceleration: towards a free-electron laser amplification

The laser–plasma accelerator (LPA) presently provides electron beams with a typical current of a few kA, a bunch length of a few fs, energy in the few hundred MeV to several GeV range, a divergence of typically 1 mrad, an energy spread of the order of 1%, and a normalized emittance of the order of π.mm.mrad. One of the first applications could be to use these beams for the production of radiation: undulator emission has been observed but the rather large energy spread (1%) and divergence (1 mrad) prevent straightforward free-electron laser (FEL) amplification. An adequate beam manipulation through the transport to the undulator is then required. The key concept proposed here relies on an innovative electron beam longitudinal and transverse manipulation in the transport towards an undulator: a ‘demixing’ chicane sorts the electrons according to their energy and reduces the spread from 1% to one slice of a few ‰ and the effective transverse size is maintained constant along the undulator (supermatching) by a proper synchronization of the electron beam focusing with the progress of the optical wave. A test experiment for the demonstration of FEL amplification with an LPA is under preparation. Electron beam transport follows different steps with strong focusing with permanent magnet quadrupoles of variable strength, a demixing chicane with conventional dipoles, and a second set of quadrupoles for further focusing in the undulator. The FEL simulations and the progress of the preparation of the experiment are presented.

基于带状束的史密斯-帕塞尔自由电子激光模拟与分析

基于带状束的史密斯-帕塞尔自由电子激光模拟与分析

Nonlinear third harmonic radiation in thermal free electron laser with modified wiggler

Simulation of free electron laser (FEL) with modified wiggler consisting of a conventional planar wiggler with third harmonic field component is presented. A set of self consistent nonlinear differential equations is derived and solved numerically by Runge–Kutta method. The optimum amplitudes of fundamental and third harmonic wiggler filed are obtained to increase the third harmonic radiation in comparison with conventional wiggler and also to have lower electron beam energy compared to conventional wiggler with the same wavelength. For the thermal effect the axial energy spread of electron beam, without any spread in the transverse velocity, is assumed. A peculiar region is found in which there is a sharp increase of the radiation amplitude. Thermal effect of the electron beam was found to be irregular in this peculiar region.

Optimization of single-step tapering amplitude and energy detuning for high-gain FELs

We put forward a method to optimize the single-step tapering amplitude of undulator strength and initial energy tuning of electron beam to maximize the saturation power of high gain free-electron lasers (FELs), based on the physics of longitudinal electron beam phase space. Using the FEL simulation code GENESIS, we numerically demonstrate the accuracy of the estimations for parameters corresponding to the linac coherent light source and the Tesla test facility.