Conventional Free-electron Laser Research Articles

Single-electron nano-chip free-electron laser

A conventional free-electron laser is useful but large, driven by a beam with many relativistic electrons. Although, recently, keV electron beams have been used to excite broadband radiation from material chips, there remains a quest for a chip-size free-electron laser capable of emitting coherent radiation. Unfortunately, those keV emitters from electron microscopes or dielectric laser accelerators usually deliver a small current with discrete moving electrons separated by a distance of a few or tens of microns. To envisage a chip-size free-electron laser as a powerful research tool, we study in this paper achievable laser radiation from a single electron and an array of single electrons atop a nano-grating dielectric waveguide. In our study, thanks to the strong coupling between the electron and the guided wave in a structure with distributed feedback, a single 50-keV electron generates 1.5-µm laser-like radiation at the Bragg resonance of a 31-µm long silicon grating with a 400-nm thickness and 310-nm period. When driven by a train of single electrons repeating at 0.1 PHz, the nano-grating waveguide emits strong laser radiation at the second harmonic of the excitation frequency. A discrete spectrum of Smith–Purcell radiation mediated by the waveguide modes is also predicted in theory and observed from simulation in the vacuum space above the grating waveguide. This study opens up the opportunity for applications requiring combined advantages from compact high-brightness electron and photon sources.

Efficiency enhancement of free-electron laser oscillator by kicking the electron beam orbit in a transverse gradient undulator

The conversion efficiency of a conventional free-electron laser (FEL) is on the level of Pierce parameter, which means that only a small portion of electron beam energy is converted into the electric field. Undulator tapering is a common way to enhance the FEL efficiency, however, it has limited effect when applying in the FEL oscillator. Inspired by the fast kicker developed in the high-repetition-rate FELs and storage rings, in this paper we propose to kick the electron beam orbit transversely in a transverse gradient undulator (TGU) after the FEL is saturated in oscillator. The electron beam will experience a different undulator strength after the beam orbit is deflected to the off-axis position. It can be regarded as a dynamic tapering method within the macrobunch while the dynamic detuning on the undulator strength with the normal tapering method is almost impossible in oscillator. Though the TGU will reduce the initial small-signal gain, the FEL efficiency still can be greatly enhanced. Numerical simulations demonstrated that the maximum FEL power can be enhanced to more than 3 times of the normal FEL oscillator.

Generation of Coherent X-ray Harmonic Radiation in a Single-Pass Free-Electron Laser with Phase Shift of Electrons Relative to Photons

Evolution of bunching and harmonic power is theoretically studied for a single-pass free-electron laser (FEL) in which electrons are periodically phase-shifted relative to photons in intervals between undulators with harmonics of magnetic field. Analytical calculations are used to reveal the configuration of magnetic field of an asymmetric elliptical and planar undulators that make it possible to suppress the fundamental and amplify several higher harmonics. The evolution of power and bunching is analyzed using a phenomenological model of FEL that describes violation of bunching between the undulator stages and a relatively high sensitivity of electron–photon interaction at wavelengths of higher harmonics to energy spread, size, deflection of the beam from the axis, etc. Expressions for the Bessel coefficients of the planar and elliptical undulators with field harmonics are analytically studied. Such undulators can be used in phase-shifted FELs for an increase in the power of higher (X-ray) harmonics by a factor of up to 100 in comparison with conventional FELs.

The Single Particles, Clusters and Biomolecules and Serial Femtosecond Crystallography instrument of the European XFEL: initial installation.

The European X-ray Free-Electron Laser (FEL) became the first operational high-repetition-rate hard X-ray FEL with first lasing in May 2017. Biological structure determination has already benefitted from the unique properties and capabilities of X-ray FELs, predominantly through the development and application of serial crystallography. The possibility of now performing such experiments at data rates more than an order of magnitude greater than previous X-ray FELs enables not only a higher rate of discovery but also new classes of experiments previously not feasible at lower data rates. One example is time-resolved experiments requiring a higher number of time steps for interpretation, or structure determination from samples with low hit rates in conventional X-ray FEL serial crystallography. Following first lasing at the European XFEL, initial commissioning and operation occurred at two scientific instruments, one of which is the Single Particles, Clusters and Biomolecules and Serial Femtosecond Crystallography (SPB/SFX) instrument. This instrument provides a photon energy range, focal spot sizes and diagnostic tools necessary for structure determination of biological specimens. The instrumentation explicitly addresses serial crystallography and the developing single particle imaging method as well as other forward-scattering and diffraction techniques. This paper describes the major science cases of SPB/SFX and its initial instrumentation - in particular its optical systems, available sample delivery methods, 2D detectors, supporting optical laser systems and key diagnostic components. The present capabilities of the instrument will be reviewed and a brief outlook of its future capabilities is also described.

Interaction of a relativistic electron beam with a laser pulse in the presence of a magnetized plasma medium

Significant progress has been made using plasma channels to guide relativistic e-beams in magnetostatic wiggler free-electron lasers (FELs). In this regard, we study the interaction of an intense laser pulse (as a laser wiggler) with a relativistic electron beam embedded in a background of magnetized plasma. The short wavelength of the laser wiggler ( ∼ µm) allows a higher radiation frequency to be obtained than from conventional magnetostatic wigglers. Laser-plasma interaction in a magnetized plasma channel has been studied. Numerical results reveal that the laser self-focusing and self-compression can be enhanced with increasing the external axial magnetic field strength, which leads to a decrease in the spot size of the laser beam. Hence, we employ the laser beam as a suitable laser wiggler in a FEL-device. Injection of plasma in the interaction region of a laser-wiggler-FEL suggests the possibility of producing short wavelengths ( ∼ x-ray) using lower energy beams ( ∼ O(10) MeV). Furthermore, this configuration has a higher tunability by controlling the plasma density in addition to the e-beam energy tunability of the conventional FELs. Effects of the external axial guide magnetic field and plasma medium on the gain of the FEL have been studied. It is found that by increasing the plasma frequency the FEL-gain increases. The effects of e-beam self-electric and self-magnetic fields on the laser gain have also been investigated in the presence of various plasma frequencies. The results indicate that in the presence of beam self-fields, the sensitivity of the gain increases in the vicinity of resonance regions. Besides, the normalized wiggler-induced self-magnetic field has been obtained which reveals that it is a positive parameter, i.e., it can act as a paramagnetic correction to the wiggler magnetic field, therefore, the gain enhancement can be due to the paramagnetic effect of the self-magnetic field. This concept opens a path toward a new source of soft x-ray pulse based on table-top plasma loaded laser wigglers.

Wave–particle interactions in a resonant system of photons and ion-solvated water

We investigate a laser model for a resonant system of photons and ion cluster-solvated rotating water molecules in which ions in the cluster are identical and have very low, non-relativistic velocities and direction of motion parallel to a static electric field induced in a single direction. This model combines Dicke superradiation with wave–particle interaction. As the result, we find that the equations of motion of the system are expressed in terms of a conventional free electron laser system. This result leads to a mechanism for dynamical coherence, induced by collective instability in the wave–particle interaction.

Plasma and cyclotron frequency effects on output power of the plasma wave-pumped free-electron lasers

Significant progress has been made employing plasmas in the free-electron lasers (FELs) interaction region. In this regard, we study the output power and saturation length of the plasma whistler wave-pumped FEL in a magnetized plasma channel. The small wavelength of the whistler wave (in sub-μm range) in plasma allows obtaining higher radiation frequency than conventional wiggler FELs. This configuration has a higher tunability by adjusting the plasma density relative to the conventional ones. A set of coupled nonlinear differential equations is employed which governs on the self-consistent evolution of an electromagnetic wave. The electron bunching process of the whistler-pumped FEL has been investigated numerically. The result reveals that for a long wiggler length, the bunching factor can appreciably change as the electron beam propagates through the wiggler. The effects of plasma frequency (or plasma density) and cyclotron frequency on the output power and saturation length have been studied. Simulation results indicate that with increasing the plasma frequency, the power increases and the saturation length decreases. In addition, when density of background plasma is higher than the electron beam density (i.e., for a dense plasma channel), the plasma effects are more pronounced and the FEL-power is significantly high. It is also found that with increasing the strength of the external magnetic field frequency, the power decreases and the saturation length increases, noticeably.

Plasma effects on the free-electron laser gain with a plasma wave undulator

Employing a magnetized plasma medium in the interaction region of a free-electron laser (FEL) offers the possibility of generating short wavelengths using moderate energy beams. Plasma in the presence of static magnetic field supports right and left circularly polarized electromagnetic modes. By superposition of these two modes, a linearly polarized electromagnetic mode is generated which can be employed as a plasma undulator in a FEL. This configuration has a higher tunability by controlling the plasma density on top of the -tubability of the conventional FELs. The roles of the axial magnetic field and plasma on the laser gain and the electron trajectories of an e-beam propagating through the plasma medium have been studied and new orbits of group (I, II, and III) have been found. Moreover, the stability of these orbits for different values of plasma frequencies has been investigated. It is shown that by increasing the axial guide magnetic field strength, the gain for orbits of group I trivially increase, while a decrease in gain has been obtained for orbits of group II and group III. In addition, it is found that with increasing the plasma frequency (or plasma density) the gain for orbits of group I and group II trivially decreases and shift to the lower cyclotron frequencies, while an increase in gain has been obtained for orbits of group III.

Growth rate enhancement of free-electron laser by two consecutive wigglers with axial magnetic field

The operative mechanism for a free-electron laser (FEL) with two consecutive helical wigglers having opposite circular polarization in the presence of an axial magnetic field is proposed and analysed. With the help of fluid theory, a tenth-degree polynomial dispersion equation for electromagnetic and space–charge waves is derived. The results are used to illustrate and discuss the dependence of growth rate on different system parameters. Finally, it is shown that for the same system parameters the growth rate of the proposed structure is more than the growth rate of instability in a conventional FEL.

Investigation of the electron trajectories and gain regimes of the whistler pumped free-electron laser

A free-electron laser (FEL) scheme, which employs the whistler wave as a slow electromagnetic wave wiggler, was studied theoretically. Subjected to the transverse fields of whistler wave wiggler, the beam electrons are the source of the energy needed to produce electromagnetic radiation. The strength and the period of the wiggler field depend on the parameters of the magnetoplasma medium. This configuration has a higher tunability by controlling the plasma density, on top of the γ-tunability of the conventional FELs. The theory of linear gain and electron trajectories was presented and four groups (I, II, III, and IV) of electron orbits were found in the presence of an axial guide magnetic field. Using perturbation analysis, it is found that these groups of orbits were stable except small regions of group I and IV orbits. The function Φ which determines the rate of change of axial velocity with beam energy was also derived. In the case in which Φ<0 represents a negative-mass regime in which the axial velocity accelerates as the electrons lose energy. Numerical solutions showed that by increasing the cyclotron frequency, the gain for group I and III orbits increased, while a gain decrement was obtained for group II and IV orbits.

Start-to-end modelling of a mode-locked optical klystron free electron laser amplifier

A free electron laser (FEL) in a mode-locked optical klystron (MLOK) configuration is modelled using start-to-end simulations that simulate realistic electron beam acceleration and transport before input into a full three-dimensional FEL simulation code. These simulations demonstrate that the MLOK scheme is compatible with the present generation of radiofrequency accelerator designs. A train of few-optical cycle pulses is predicted with peak powers similar to those of the equivalent conventional FEL amplifier. The role of electron beam energy modulation in these results is explained and the limitations of some simulation codes discussed. It is shown how seeding the FEL interaction using a High Harmonic seed laser can improve the coherence properties of the output.

Simulation of free-electron lasers seeded with broadband radiation

The longitudinal coherence of free-electron laser (FEL) radiation can be enhanced by seeding the FEL with high harmonics of an optical laser pulse. The radiation produced by high-harmonic generation (HHG), however, has a fast-varying temporal profile that can violate the slowly varying envelope approximation and limited frequency window that is employed in conventional free-electron laser simulation codes. Here we investigate the implications of violating this approximation on the accuracy of simulations. On the basis of both analytical considerations and 1D numerical studies, it is concluded that, for most realistic scenarios, conventional FEL codes are capable of accurately simulating the FEL process even when the seed radiation violates the slowly varying envelope approximation. We additionally discuss the significance of filtering the harmonic content of broadband HHG seeds.

Gain enhancement in two-stream electromagnetically pumped free electron laser with ion-channel guiding

A theory of two-stream electromagnetic wave-wiggler free-electron lasers (TSEMWFEL) with an ion-channel guiding is proposed and investigated. An analysis of the two-stream steady-state electrons trajectories is obtained by solving the equation of motion in the electromagnetic wave wiggler and ion-channel guiding. The electron trajectories and the small signal gain are derived. Numerical calculations show that there are seven group trajectories rather than the two groups reported for conventional free-electron lasers. The characteristics of the linear-gain and the normalized maximum gain are studied numerically. It was also shown that the normalized gain of groups I and II is decreased and for groups (IV–VII) are increasing by growing [Formula: see text]. Furthermore, it was found that the two-stream with ion-channel field enhances the maximum gain in comparison with that for single beam.

Electron trajectory and growth rate in two-stream electromagnetically pumped free-electron lasers with ion-channel guiding

A theory of the two-stream electromagnetic wave wiggler free-electron lasers (TSEMWFEL) with ion-channel guiding is proposed and investigated. An analysis of the two-stream steady-state electron trajectories is done by solving the equation of motion in the electromagnetic wave wiggler and ion-channel guiding. Numerical calculations show that there are seven groups of trajectories rather than the two groups reported for the conventional free-electron laser (FEL). The dispersion relation is derived by employing linear fluid theory. The characteristics of the dispersion relation are analyzed numerically. The results show that employing two streams rather than a single stream in an FEL with ion-channel guiding gives rise to an enhancement in the growth rate, and using ion-channel guiding instead of an axial magnetic field in a two-stream FEL causes the growth rate to increase. Our numerical study of the normalized maximum growth rate and maximum wavenumber as a function of ion-channel frequency for different trajectories is presented.

Laser-pumped coherent x-ray free-electron laser

In a laser-pumped x-ray free-electron laser (FEL) an intense laser field replaces the magnetic wiggler field of a conventional FEL. Depending on the intensity and quality of both the electron beam and pump laser, the Thomson backscattered radiation can be coherently amplified. In a conventional FEL the generation of x rays requires electron beam energies in the multi-GeV range. In a laser-pumped x-ray FEL, electron beam energies in the multi-MeV range would be sufficient. To generate coherent x rays with this mechanism a number of physics and technology issues must be addressed. Foremost among these are the stringent requirements placed on the electron beam quality and brightness as well as on the pump laser. The seed radiation for the laser-pumped FEL is the laser-induced spontaneous radiation. The evolution of incoherent radiation into coherent radiation as well as the power gain lengths associated with the coherent x rays are analyzed and discussed. There is excellent agreement between our analytical results and GENESIS simulations for the radiated power, gain length, conversion efficiency, linewidth, and saturation length. These issues, as well as others, necessary to achieve coherent amplified x rays in a laser-pumped FEL are discussed. While a coherent x-ray source would have a number of attractive features, the requirements placed on both the electron beam and pump laser are extremely challenging.

Short Rayleigh length free electron lasers

Conventional free electron laser (FEL) oscillators minimize the optical mode volume around the electron beam in the undulator by making the resonator Rayleigh length about one third to one half of the undulator length. This maximizes gain and beam-mode coupling. In compact configurations of high-power infrared FELs or moderate power UV FELs, the resulting optical intensity can damage the resonator mirrors. To increase the spot size and thereby reduce the optical intensity at the mirrors below the damage threshold, a shorter Rayleigh length can be used, but the FEL interaction is significantly altered. We model this interaction using a coordinate system that expands with the rapidly diffracting optical mode from the ends of the undulator to the mirrors. Simulations show that the interaction of the strongly focused optical mode with a narrow electron beam inside the undulator distorts the optical wave front so it is no longer in the fundamental Gaussian mode. The simulations are used to study how mode distortion affects the single-pass gain in weak fields, and the steady-state extraction in strong fields.

X-ray generation in an ion channel

X-ray generation by relativistic electrons in an ion channel is studied. The emission process is analyzed in the regime of high harmonic generation when the plasma wiggler strength is large. Like for the conventional free electron laser, the synchrotron-like broadband spectrum is generated in this regime. An asymptotic expression for the radiation spectrum of the spontaneous emission is derived. The radiation spectrum emitted from an axisymmetric monoenergetic electron beam is analyzed. The stimulated emission in the ion channel is studied and the gain of the ion-channel synchrotron-radiation laser is calculated. It is shown that the use of laser-produced ion channels leads to a much higher power of x-ray radiation than the one in a self-generated channel. In addition, the mean photon energy, the number of emitted photons and the brilliance of the photon beam increase dramatically. Three-dimensional particle-in-cell simulations of a 25-GeV electron bunch propagating in a laser-produced ion channel are made. Several GeV γ-quants are produced in a good agreement with the analytical results.

The free electron laser interaction with a short-Rayleigh-length optical mode

High-power, short-wavelength free electron lasers (FELs) can make use of a short-Rayleigh-length (SRL) optical mode in order to reduce the intensity on resonator mirrors. The conventional FEL interaction attempts to optimize the coupling between the electron beam and optical mode by minimizing the optical mode volume around the electron beam. In contrast, the SRL FEL focuses optical power in a small region of the undulator, which accelerates the electron bunching process. As a result, the fundamental FEL interaction is significantly altered with a rapidly changing optical field and phase along the undulator. Advantages and disadvantages of FELs designed with an SRL optical mode are discussed.

A millimetre-wave second harmonic waveguide FEL

Second harmonic waveguide free electron lasers (FELs) have been shown to be capable of both effective electron energy reduction and large interaction gain in the X-band region. In this paper, we consider the extension of this unconventional waveguide FEL scheme into the millimetre-wave region. Through assessment of their resonant conditions, small-signal gain, energy spread effects, and amplification saturation, second harmonic waveguide FELs are studied for their operation around 300 GHz and compared to their operation in the X-band. Against the same set of system parameters, further comparisons are also made to comparable conventional waveguide FELs. These studies suggest that second harmonic waveguide FELs are as effective at 300 GHz as at 8 GHz as a generic technique to reduce the necessary electron energy for a strong FEL radiation at a given frequency.

Energy spread effects in second harmonic waveguide FELs

It has been recently established that second harmonic waveguide free electron lasers (FELs) can significantly reduce electron energy required for strong laser amplification at a given frequency. Compared to conventional waveguide FELs, their interaction gain has a stronger dependence upon the wiggler field and as such it is preferable to operate them with large wiggler field to achieve high interaction gain. Given that the energy dependence of the electron velocity and hence the phase of the ponderomotive potential is likely to be amplified at large wiggler field, it is possible that the high gain anticipated with large wiggler field may be compromised with more severe energy spread effects. To this end, we use a recently developed numerical code for waveguide FELs to study energy spread effects in second harmonic waveguide FELs. Numerical examples are used to assess both the small and large wiggler cases. It is shown that the energy spread induced gain degradation remains relatively unchanged as the wiggler field increases. Instead the bandwidth of positive interaction is found as a dominant factor to control the gain degradation. Comparison with conventional waveguide FELs is also presented to reinforce the above finding. Therefore the wiggler field strength can be treated as a free design parameter and used to achieve large interaction gain without contributing to the energy spread induced gain degradation.