Electron Energy Spread Research Articles

Аналитический учет внеосевых эффектов в рентгеновском излучении гармоник лазеров на свободных электронах

We give analytical description of generation of harmonics of the undulator radiation (UR) with account for the finite electron beam size, emittance, off-axis beam deviation and electron energy spread, as well as for the constant magnetic components and field harmonics effects. We give exact analytical expressions for the generalized Bessel and Airy functions, which describe the spectrum line shape and intensities in the two-frequency bi-harmonic undulator with account for the above factors. The obtained analytical formulae distinguish contributions of each field component and every undulator and beam parameter on the harmonic radiation in free electron lasers (FEL). The effect of the field on the harmonic radiation is analyzed with account for the beam finite size and its off-axis deviation. The phenomenological model is employed for the FEL modeling; with its help we study the harmonic generation, including even ones, in the experiments LCLS and LEUTL. We demonstrate analytically that strong second FEL harmonic in X-ray FEL at the wavelengths λ = 0.75nm in the LCLS experiment is caused by the deviation of the electron trajectories off the axis in 15 μm on the gain length 1.6 m, which is comparable with the beam size; the strong second FEL harmonic in the LEUTL experiment at the wavelength λ = 192nm can be attributed to interaction of the electrons in wide, ~ 0.2 mm, beam with the photon radiation at the gain length 0.87 m. The modeling results fully agree with the measurements. The developed formalism allows the analysis of projected and built FELs and their radiation, helps minimizing losses and correcting magnetic fields; it also shows physical background and reasons for each harmonic radiated power in the FEL.

Investigation of electron energy spread effects on the intracavity MIR-FEL power at the PBP-CMU electron linac laboratory

At the PBP-CMU Electron Linac Laboratory, the existing linear accelerator system is under developing to produce electron beams with suitable properties for generation of oscillator mid-infrared free-electron laser (MIR-FEL) and super-radiant terahertz (THz) undulator radiation. This work focuses on the simulation of the oscillator MIR-FEL with expected electron beam energy of 20 – 25 MeV to evaluate the required electron beam parameters. To achieve FEL saturation, the single-pass FEL simulation using the code GENESIS 1.3 was performed to estimate the laser wavelength, FEL gain and electron macro-pulse duration. In the simulation, electron beams with energy spread of 0, 0.5 and 1.0 %, and the electron peak current of 25 and 50 A were considered. As a result, the electron beam with energy of 20 – 25 MeV can produce the FEL wavelengths of 13.5 – 21.2 µm using a 1.6-m undulator with maximum undulator parameter of 1.07. The largest FEL gain is 216% when using electron beam energy and peak current of 20 ± 0% MeV and 50 A, which requires the electron macro-pulse duration of 1.6 µs to saturate FEL. Due to the possible macro-pulse duration at our facility of 6 µs, the operation of electron beam with energy spread of 0.5% and peak current of higher than 25 A is required to saturate FEL. Results from this single-pass simulation can be used as a based information for further practical consideration with multi-pass simulation.

Генерация гармоник в экспериментах с лазерами на свободных электронах в рентгеновском диапазоне --- теоретический анализ

Analytical description of the generation of harmonics of the undulator radiation (UR) in free electron lasers (FELs) is given for various FEL experiments in the X-ray band. The expressions for the spectral line shape and intensity are written explicitly in terms of the generalized Bessel and Airy functions with account for the electron energy spread, beam sizes and emittances, spectral line split and non-periodic magnetic fields. The presented theory describes well the radiation spectral properties and harmonic intensities in all studied FEL experiments: SACLA, LCLS, PAL-XFEL, SwissFEL et al., in various conditions with the radiation in wide range of frequencies, covering hard X-rays.

Laser wakefield acceleration driven by a few-terawatt laser pulse in a sub-mm nitrogen gas jet

Quasi-monoenergetic electron bunches with energies peaked in 10–20 MeV are generated from laser wakefield acceleration (LWFA) by focusing few-TW laser pulses onto a sub-mm gas jet of dense nitrogen. A 152-μm diameter orifice is used to produce transient (≤20 ms), free-flow nitrogen jets, while the plasma electrons with a 860-μm wide Gaussian density profile and a density up to ∼2.8 × 1019 cm−3 enable self-focusing effect and self-modulation instability to develop on the pump pulse, resulting in a high intensity to drive the LWFA. Meanwhile, this Gaussian nitrogen plasma facilitates ionization-induced injection and density down-ramp injection throughout the acceleration process and consequently improves the energy and charge stabilities of output electrons. When 40-fs, 3.2-TW, 810-nm pump pulses are applied, output electrons with a peak energy ∼11 MeV and a charge ∼20 pC are routinely generated with ≤20% energy and charge stabilities, ∼20 mrad divergence, and ∼10 mrad pointing variation. A large electron energy spread is attributed to the dominant mechanisms of ionization and down-ramp injections. This scheme represents a viable approach for implementing a high-repetition-rate LWFA, from which stable tens-of-MeV electrons can be generated with less than 150 mJ of on-target laser energy.

Periodic self-injection of electrons in a few-cycle laser driven oscillating plasma wake

Millijoule-energy few-cycle laser pulses excite the plasma wakefield and accelerate electrons at kilohertz repetition rate, generating mega-electron volt (MeV) electron bunches with femtosecond temporal duration for ultrafast electron diffraction applications. By simulating few-cycle laser pulses interacting with the underdense nitrogen plasma, we have studied the mechanism of periodic electron self-injection, which manifests the laser carrier envelop phase (CEP) effect in few-cycle laser wakefield acceleration. A few-cycle laser pulse experiencing a significant wavelength redshift induces the transverse oscillation of the plasma bubble at the same frequency as the laser CEP changes by 2π. The oscillation of the plasma bubble periodically injects free electrons into the bubble at a doubled frequency, broadening the electron energy spread.

Ultracold Electrons via Near-Threshold Photoemission from Single-Crystal Cu(100).

Achieving a low mean transverse energy or temperature of electrons emitted from the photocathode-based electron sources is critical to the development of next-generation and compact x-ray free electron lasers and ultrafast electron diffraction, spectroscopy, and microscopy experiments. In this Letter, we demonstrate a record low mean transverse energy of 5meV from the cryo-cooled (100) surface of copper using near-threshold photoemission. Further, we also show that the electron energy spread obtained from such a surface is less than 11.5meV, making it the smallest energy spread electron source known to date: more than an order of magnitude smaller than any existing photoemission, field emission, or thermionic emission based electron source. Our measurements also shed light on the physics of electron emission and show how the energy spread at few meV scale energies is limited by both the temperature and the vacuum density of states.

Attosecond electron bunch measurement with coherent nonlinear Thomson scattering

We present a novel method for measurement of ultrashort electron-bunch duration, in principle, as short as zeptosecond (${10}^{\ensuremath{-}21}\text{ }\text{ }\mathrm{s}$). The method employs nonlinear Thomson scattering of relativistically intense laser light, and takes advantage of the nonlinear dependence and coherence of scattered light on electron bunch length. We validate the method and test its range of applicability via simulations by using realistic (nonideal) electron beams. Due to the wide flexibility in choice of interaction geometry and scattering laser pulse properties enabled by the method, it is shown to be applicable over a wide range of electron beam parameters, including energy, energy spread, and divergence angle.

Electron impact excitation of Ge-like to Cu-like xenon ions in the extreme ultraviolet

Electron impact excitation of Ge-like (Xe22+) to Cu-like (Xe25+) highly charged xenon ions are studied and dipole allowed fine-structure transitions in the wavelength range 9–25 nm are considered. We use relativistic distorted wave method to calculate the electron excitation cross sections for the different transitions of the four ions in the scattered electron energy range from excitation threshold to 1500 eV. The ionic bound state wavefunctions have been obtained using multi-configuration Dirac–Fock method. To ascertain the accuracy of the wavefunctions, the wavelengths and oscillator strengths of the considered transitions in these ions are calculated and compared with the previously reported measurements and other theoretical calculations, where available. For plasma diagnostic applications, the obtained cross sections are further used to calculate the rate coefficients of the transitions as well as fitted with an analytical expression which can be used in plasma model conveniently.

Undulator and free-electron laser radiation with field harmonics and off-axis effects taken into account analytically

We present an analytic description of the generation of undulator radiation (UR) harmonics in a generalized elliptic undulator with field harmonics. The obtained analytic expressions for generalized Bessel and Airy functions describe the UR spectral lines and radiation intensity in the general and particular cases of two-frequency planar and helical undulators and also for other elliptic and planar undulators. We analytically describe the effect of finite electron beam size, beam emittance, off-axis deflection of electrons, electron energy spread, and beam-bending permanent magnetic components. The obtained analytic expressions distinguish the contributions made by each field component and by the beam and undulator parameters to the generation of radiation harmonics. Using an analytic model of single-pass free-electron lasers (FELs), we analyze the power evolution of harmonics in the LCLS, LEUTL, and SACLA FEL experiments. We discuss the effect that the beam and undulator parameters have on the generation of harmonics. It is shown that the strong second harmonics of radiation observed in experiments are caused by the detected beam deviation from the axis by 15μm over one gain length of 1.5 m in the X-ray LCLS FEL and by the large beam cross section of ∼ 200;μm in the LEUTL FEL. The results of modeling are fully consistent with experiments, which confirms the validity of the presented theoretical description of FEL power and radiation spectral density.

Benchmarking of Monte Carlo model of Siemens Oncor® linear accelerator for 18MV photon beam: Determination of initial electron beam parameters.

This study aims to benchmark a Monte Carlo (MC) model of the 18 MV photon beam produced by the Siemens Oncor® linac using the BEAMnrc and DOSXYZnrc codes. By matching the percentage depth doses and beam profiles calculated by MC simulations with measurements, the initial electron beam parameters including electron energy, full width at half maximum (spatial FWHM), and mean angular spread were derived for the 10×10 cm2 and 20×20 cm2 field sizes. The MC model of the 18 MV photon beam was then validated against the measurements for different field sizes (5×5, 30×30 and 40×40 cm2) by gamma index analysis. The optimum values for electron energy, spatial FWHM and mean angular spread were 14.2 MeV, 0.08 cm and 0.8 degree, respectively. The MC simulations yielded the comparable measurement results of these optimum parameters. The gamma passing rates (with acceptance criteria of 1% /1 mm) for percentage depth doses were found to be 100% for all field sizes. For cross-line profiles, the gamma passing rates were 100%, 97%, 95%, 96% and 95% for 5×5, 10×10, 20×20, 30×30 and 40×40 cm2 field sizes, respectively. By validation of the MC model of Siemens Oncor® linac using various field sizes, it was found that both dose profiles of small and large field sizes were very sensitive to the changes in spatial FWHM and mean angular spread of the primary electron beam from the bending magnet. Hence, it is recommended that both small and large field sizes of the 18 MV photon beams should be considered in the Monte Carlo linac modeling.

Electrostatic Cumulation at Relativistic Energies

The electrostatic cumulation of current density in relativistic vacuum diodes with ring-type cathodes is described theoretically and confirmed experimentally. The distinctive feature of the suggested cumulation mechanism is a very low energy spread of electrons. As a result of electrostatic cumulation, a thin relativistic electron beam with a current density of 1 kA/mm2 can be formed.

Effects of waveguides on a free-electron laser with two electron beams

AbstractThe effects of the phase variation, the evolution of the electron beam, the evolution of the radiation intensity, and the higher-order modes due to waveguides on a free-electron laser (FEL) oscillator have been analyzed by using two electron beams of different energies based on the proposed FEL facility which is to be operated in the far-infrared and infrared regions. The three-dimensional (3D) effects on a FEL oscillator due to waveguides and higher-order modes were studied using an extended 3D FEL code with two electron beams that we have developed. The effects of the variation on the amplitude of radiation on the electron beam's emittance and energy spreads were also calculated in the case of waveguide for multi-particle and multi-pass numbers by using a new 3D code. The phase variation, the variation in the beam envelope, the evolution of the amplitude, and power were calculated for the fundamental mode. The results were compared with those of the higher-order modes of the wiggler for various TE and TM modes for determining the FEL's performance which is required for high-quality electron beams.

Proof-of-Principle Experiment for Nanoparticle-Assisted Laser Wakefield Electron Acceleration

In the present work, we demonstrate for the first time a proof-of-principle experiment for nanoparticle-assisted laser wakefield acceleration. The nanoparticles, generated through laser ablation of aluminium, were introduced into the plasma and used to trigger the injection of electrons into the nonlinear plasma wake excited by a high power femtosecond laser. In this experiment, a significant enhancement of the electron beam energy, energy spread and divergence is obtained compared with the case when electrons are self-injected. The best quality electron bunches presented peak energy up to 338 MeV with a relative energy spread of 4.7% and vertical divergence of 5.9 mrad. This method can be further improved by adding an aerodynamic lens system, for instance, which would control the nanoparticle size, density, material and injection position thus allowing accurate control of the laser wakefield accelerator.

Revisiting the Fe xvii Line Emission Problem: Laboratory Measurements of the 3s–2p and 3d–2p Line-formation Channels

Abstract We determined relative X-ray photon emission cross sections in Fe xvii ions that were mono-energetically excited in an electron beam ion trap. Line formation for the 3s (3s−2p) and 3d (3d−2p) transitions of interest proceeds through dielectronic recombination (DR), direct electron-impact excitation (DE), resonant excitation (RE), and radiative cascades. By reducing the electron-energy spread to a sixth of that of previous works and increasing counting statistics by three orders of magnitude, we account for hitherto unresolved contributions from DR and the little-studied RE process to the 3d transitions, and also for cascade population of the 3s line manifold through forbidden states. We found good agreement with state-of-the-art many-body perturbation theory (MBPT) and the distorted-wave (DW) method for the 3s transition, while in the 3d transitions known discrepancies were confirmed. Our results show that DW calculations overestimate the 3d line emission due to DE by ∼20%. Inclusion of electron-electron correlation effects through the MBPT method in the DE cross-section calculations reduces this disagreement by ∼11%. The remaining ∼9% in 3d and ∼11% in 3s/3d discrepancies are consistent with those found in previous laboratory measurements, solar, and astrophysical observations. Meanwhile, spectral models of opacity, temperature, and turbulence velocity should be adjusted to these experimental cross sections to optimize the accuracy of plasma diagnostics based on these bright soft X-ray lines of Fe xvii.

Energy levels, oscillator strengths, radiative transition probabilities, level lifetimes and electron-impact excitation rate coefficients for Ne-like Mo XXXIII

The energy levels, oscillator strengths, radiative decay rates, lifetimes, collision strengths, direct and resonance electron-impact excitation rate coefficients have been computed for the 257 fine-structure levels arising from 1s22s22p5nl and 1s22s2p6n′l′ configurations belonging to the Mo32+ ion with n≤7, l≤4 and n′≤5, l′≤4. The model-potential approach is used for the target ion structure calculations. Additionally, we employ the multiconfiguration Dirac–Hartree–Fock method to further assess the energy levels and transition probabilities. The collision strengths for the electron-impact direct excitation are computed within the relativistic distorted-wave approximation at 34, 135, 680, 1700, 5436, and 12,740 eV scattered electron energy values. We also perform collision calculations at 85, 175, and 450 keV electron energies using the plane-wave approximation and interpolate the reduced cross section within Fano plots, thus accounting for relativistic effects at asymptotic energies. This assures the convergence of Maxwellian integration for effective collision strengths calculation at electron temperatures up to 80 keV. The resonance contribution to the excitation rates is accounted for within the independent process isolated resonance approximation by including Na-like Mo31+ doubly excited autoionization states arising from the 1s227nln′l′ configurations with n≤7,l≤4,n′≤20,l′≤8. Contributions from high n′≥21 Rydberg states to the excitation rate coefficients are included by employing the n′−3 extrapolation law for radiative and autoionization decay rates. Radiative decay of resonances to lower autoionization states followed by autoionization cascade as well as radiative damping via core transitions are included in our model. The highest rate coefficients corresponding to ground state excitations are the 2p–3d allowed and 2p–3p electric monopole transitions, respectively. Intercombination and generally higher-order electric multipole transitions amount to lower excitation rate coefficients but are not to be neglected. Magnetic transitions are only relevant for low electron temperatures since both their direct and resonance contributions to excitation significantly decrease with increasing electron energy. Present results compare well with existing data from literature. The resonance contributions play an important role in the accuracy of rate coefficients, especially for weak forbidden transitions at low electron temperatures. These results may be useful in fusion related plasmas, astrophysics and fundamental physics.

Femtosecond phase control in high-field terahertz-driven ultrafast electron sources

Terahertz-based electron acceleration has recently emerged as a promising candidate for driving next-generation high-brightness electron sources. Although initial demonstrations have proven the feasibility of this technology for accelerating and manipulating the phase space of electrons, further demonstrations of exquisite timing control are required to make use of terahertz acceleration for demanding applications such as light sources and ultrafast electron diffraction. In this paper, we use a two-stage segmented-terahertz-electron-accelerator-and-manipulator (STEAM) setup to demonstrate control over the electron beam energy, energy spread, and emittance. The first rebunching stage is used to tune the duration of 55 keV electron bunches from a DC electron gun that enables femtosecond phase control at the second accelerating stage. For optimized parameters, energy spread and emittance are reduced by 4× and 6×, respectively, relative to operation with the first stage off. A record energy gain of ∼70 keV was achieved at a peak accelerating field of 200 MV/m, resulting in a >100% energy boost in a terahertz-powered accelerator for the first time. These results represent a critical step forward for the practical implementation of terahertz-powered devices in ultrafast electron sources.

Energy Enhancement and Energy Spread Compression of Electron Beams in a Hybrid Laser-Plasma Wakefield Accelerator

We experimentally demonstrated the generation of narrow energy-spread electron beams with enhanced energy levels using a hybrid laser-plasma wakefield accelerator. An experiment featuring two-color electron beams showed that after the laser pump reached the depletion length, the laser-wakefield acceleration (LWFA) gradually evolved into the plasma-driven wakefield acceleration (PWFA), and thereafter, the PWFA dominated the electron acceleration. The energy spread of the electron beams was further improved by energy chirp compensation. Particle-in-cell simulations were performed to verify the experimental results. The generated monoenergetic high-energy electron beams are promising to upscale future accelerator systems and realize monoenergetic γ -ray sources.

Optimal parameters for radiation reaction experiments

As new laser facilities are developed with intensities on the scale of , it becomes ever more important to understand the effect of strong field quantum electrodynamic processes, such as quantum radiation reaction, which will play a dominant role in laser-plasma interactions at these intensities. Recent all-optical experiments, where GeV electrons from a laser wakefield accelerator encountered a counter-propagating laser pulse with a0 > 10, have produced evidence of radiation reaction, but have not conclusively identified quantum effects nor their most suitable theoretical description. Here we show the number of collisions and the conditions required to accomplish this, based on a simulation campaign of radiation reaction experiments under realistic conditions. We conclude that while the critical energy of the photon spectrum distinguishes classical and quantum-corrected models, a better means of distinguishing the stochastic and deterministic quantum models is the change in the electron energy spread. This is robust against shot-to-shot fluctuations and the necessary laser intensity and electron beam energies are already available. For example, we show that so long as the electron energy spread is below 25%, collisions at a0 = 10 with electron energies of could differentiate between different quantum models in under 30 shots, even with shot-to-shot variations at the 50% level.

Comparative Analysis of Phenomenological and Numerical Modeling of Experimentswith Single-Pass Free-Electron Lasers

We model the evolution of radiation harmonics in a single-pass free-electron laser using a phenomenological model, in which the main losses are taken into account separately for each of the harmonics. The modeling results are compared with the corresponding FEL experiments and the simulations, which we performed using the PERSEO code. A wide wavelength range (0.15–500 nm) is considered. The phenomenological description based on the use of several basic FEL parameters, such as the electron beam current, average energy, energy spread, and emittance of electrons, yields the results that correspond well to the LEUTL, SPARC, and LCLS experiments in various conditions. The evolution of the radiation power, bunching, and electron energy spread in the Spring 8 FEL at the follow-up stage is also considered. The necessity to improve electron beam parameters for generation of harmonics in this FEL is shown. The phenomenological model allows assessing the operation of the available and future FELs fast. Using it, one can model FELs with nearly any undulator with allowance for higher harmonics of their magnetic fields. Moreover, this model makes it possible to describe easily various effects in designed FELs, e.g., those with dephasing of electrons and photons, filtering of harmonics, and other features.

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.