Virtual dielectric waveguide mode description of a high-gain free-electron laser I: Theory

A set of mode-coupled excitation equations for the slowly-growing amplitudes of dielectric waveguide eigenmodes is derived as a description of the electromagnetic signal field of a high-gain free-electron laser, or FEL, including the effects of longitudinal space-charge. This approach of describing the field basis set has notable advantages for FEL analysis in providing an efficient characterization of eigenmodes, and in allowing a clear connection to free-space propagation of the input (seeding) and output radiation. The formulation describes the entire evolution of the radiation wave through the linear gain regime, prior to the onset of saturation, with arbitrary initial conditions. By virtue of the flexibility in the expansion basis, this technique can be used to find the direct coupling and amplification of a particular mode. A simple transformation converts the derived coupled differential excitation equations into a set of coupled algebraic equations and yields a matrix determinant equation for the FEL eigenmodes. A quadratic index medium is used as a model dielectric waveguide to obtain an expression for the predicted spot size of the dominant system eigenmode, in the approximation that it is a single gaussian mode.Comment: 14 page

Minimum Spectral Bandwidth in Echo Seeded Free Electron Lasers

This paper examines the impact of non-linear longitudinal phase distortions on the spectral bandwidth in echo seeded free electron lasers (FELs). It extends the existing theory developed in Hemsing [1] for echo-enabled harmonic generation (EEHG) to include finite laser pulse durations. An analytic expression for the shape of the optimized longitudinal bunching envelope is derived, and is used to determine the laser and electron beam pulse durations that minimize the seeded bandwidth in the presence of arbitrary phase distortions. The time-bandwidth product (TBP) is also derived, and is shown that the TBP and the bandwidth increase by no more than 2 from their transform-limited values when the bandwidth is minimized

Longitudinal dispersion of orbital angular momentum modes in high-gain free-electron lasers

The physical effects of optical mode dispersion in the electron beam of a free-electron laser are investigated for modes that carry orbital angular momentum. The analysis is performed using a derived equivalence between two different formulations that describe the radiation fields in the linear regime

Free electron laser generation of X-ray Poincaré beams

An optics-free method is proposed to generate x-ray radiation with spatially variant states of polarization via an afterburner extension to a free electron laser. Control of the polarization in the transverse plane is obtained through the overlap of different coherent transverse light distributions radiated from a bunched electron beam in two consecutive orthogonally polarised undulators. Different transverse profiles are obtained by emitting at a higher harmonic in one or both of the undulators. This method enables the generation of beams structured in their intensity, phase, and polarization - so-called Poincaré beams - at high powers with tunable wavelengths. Simulations are used to demonstrate the generation of two different classes of light with spatially inhomogeneous polarization - cylindrical vector beams and full Poincaré beams

Active Q-switched X-Ray Regenerative Amplifier Free-Electron Laser

Despite tremendous progress in x-ray free-electron laser (FEL) science over the last decade, future applications still demand fully coherent, stable x-rays that have not been demonstrated in existing X-ray FEL facilities. In this Letter, we describe an active Q-switched x-ray regenerative amplifier FEL scheme to produce fully coherent, high-brightness, hard x rays at a high-repetition rate. By using simple electron-beam phase space manipulation, we show this scheme is flexible in controlling the x-ray cavity quality factor Q and hence the output radiation. We report both theoretical and numerical studies on this scheme with a wide range of accelerator, x-ray cavity, and undulator parameters

Breaking the Attosecond, Angstrom and TV/M Field Barriers with Ultra-Fast Electron Beams

Recent initiatives at UCLA concerning ultra-short, GeV electron beam generation have been aimed at achieving sub-fs pulses capable of driving X-ray free-electron lasers (FELs) in single-spike mode. This use of very low Q beams may allow existing FEL injectors to produce few-100 attosecond pulses, with very high brightness. Towards this end, recent experiments at the LCLS have produced {approx}2 fs, 20 pC electron pulses. We discuss here extensions of this work, in which we seek to exploit the beam brightness in FELs, in tandem with new developments in cryogenic undulator technology, to create compact accelerator-undulator systems that can lase below 0.15 {angstrom}, or be used to permit 1.5 {angstrom} operation at 4.5 GeV. In addition, we are now developing experiments which use the present LCLS fs pulses to excite plasma wakefields exceeding 1 TV/m, permitting a table-top TeV accelerator for frontier high energy physics applications