A review of free‐electron lasers

Critical role of isopotential surfaces for magnetostatic ponderomotive forces

By producing localized wave regions at the ends of an open-field-line magnetic confinement system, ponderomotive walls can be used to differentially confine different species in the plasma. Furthermore, if the plasma is rotating, this wall can be magnetostatic in the laboratory frame, resulting in simpler engineering and better power flow. However, recent work on such magnetostatic walls has shown qualitatively different potentials than those found in the earlier, nonrotating theory. Here, using a simple slab model of a ponderomotive wall, we resolve this discrepancy. We show that the form of the ponderomotive potential in the comoving plasma frame depends on the assumption made about the electrostatic potential in the laboratory frame. If the laboratory-frame potential is unperturbed by the magnetic oscillation, one finds a parallel-polarized wave in the comoving frame, while if each field line remains equipotential throughout the perturbation region, one finds a perpendicularly polarized wave. This in turn dramatically changes the averaged ponderomotive force experienced by a charged particle along the field line, not only its scaling, but also its direction.

Generating Coherent Phonon Waves in Narrow-Band Materials: A Twisted Bilayer Graphene Phaser

Twisted bilayer graphene (TBG) exhibits extremely low Fermi velocities for electrons, with the speed of sound surpassing the Fermi velocity. This regime enables the use of TBG for amplifying vibrational waves of the lattice through stimulated emission, following the same principles of operation of free-electron lasers. Our Letter proposes a lasing mechanism relying on the slow-electron bands to produce a coherent beam of acoustic phonons. We propose a device based on undulated electrons in TBG, which we dub the phaser. The device generates phonon beams in a terahertz (THz) frequency range, which can then be used to produce THz electromagnetic radiation. The ability to generate coherent phonons in solids breaks new ground in controlling quantum memories, probing quantum states, realizing nonequilibrium phases of matter, and designing new types of THz optical devices.

Non-diffracting multi-electron vortex beams balancing their electron-electron interactions

The wave-like nature of electrons has been known for almost a century, but only in recent years has the ability to shape the wavefunction of EBeams (Electron-Beams) become experimentally accessible. Various EBeam wavefunctions have been demonstrated, such as vortex, self-accelerating, Bessel EBeams etc. However, none has attempted to manipulate multi-electron beams, because the repulsion between electrons rapidly alters the beam shape. Here, we show how interference effects of the quantum wavefunction describing multiple electrons can be used to exactly balance both the repulsion and diffraction-broadening. We propose non-diffracting wavepackets of multiple electrons, which can also carry orbital angular momentum. Such wavefunction shaping facilitates the use of multi-electron beams in electron microscopy with higher current without compromising on spatial resolution. Simulating the quantum evolution in three-dimensions and time, we show that imprinting such wavefunctions on electron pulses leads to shape-preserving multi-electrons ultrashort pulses. Our scheme applies to any beams of charged particles, such as protons and ion beams.Vortex electron beams are generated using single electrons but their low beam-density is a limitation in electron microscopy. Here the authors propose a scheme for the realization of non-diffracting electron beams by shaping wavepackets of multiple electrons and including electron-electron interactions.

A simplified description of X-ray free-electron lasers

It is shown that an elementary semi-quantitative approach explains essential features of the X-ray free-electron laser mechanism, in particular those of the gain and saturation lengths. Using mathematical methods and derivations simpler than complete theories, this treatment reveals the basic physics that dominates the mechanism and makes it difficult to realise free-electron lasers for short wavelengths. This approach can be specifically useful for teachers at different levels and for colleagues interested in presenting X-ray free-electron lasers to non-specialized audiences.

Three-dimensional theory of emittance in Compton scattering and x-ray protein crystallography

A complete, three-dimensional theory of Compton scattering is described, which fully takes into account the effects of the electron beam emittance and energy spread upon the scattered x-ray spectral brightness. The radiation scattered by an electron subjected to an arbitrary electromagnetic field distribution in vacuum is first derived in the linear regime, and in the absence of radiative corrections; it is found that each vacuum eigenmode gives rise to a single Doppler-shifted classical dipole excitation. This formalism is then applied to Compton scattering in a three-dimensional laser focus, and yields a complete description of the influence of the electron beam phase-space topology on the x-ray spectral brightness; analytical expressions including the effects of emittance and energy spread are also obtained in the one-dimensional limit. Within this framework, the x-ray brightness generated by a 25 MeV electron beam is modeled, fully taking into account the beam emittance and energy spread, as well as the three-dimensional nature of the laser focus; its application to x-ray protein crystallography is outlined. Finally, coherence, harmonics, and radiative corrections are also briefly discussed.

Ultrashort free-electron laser pulse

Three-dimensional characteristics of short free-electron laser pulses are analyzed. When the optical pulse length is short, the growth rate and optical guiding will vary among the Fourier components comprising the pulse. Matched beam solutions of the wave equation, including diffraction and nonparaxial effects, are discussed. In certain limits a front to back asymmetry develops along the pulse as well as a frequency spread across it. In these limits the asymmetry and the frequency spread are relatively small unless the number of optical cycles in the pulse approaches unity.

Stochastic electron gas theory of coherence in laser-driven synchrotron radiation

The transition from coherent to incoherent laser-driven synchrotron radiation is studied within the framework of a stochastic electron gas model. The fundamental difference between this approach and a relativistic fluid model resides in the fact that, for any number of incoherently phased point electrons, the 4-current contains Fourier components at arbitrarily short wavelengths, whereas the fluid model introduces an unphysical cutoff scale.