High-gain Free-electron Laser Research Articles

Development of coherence in the high-gain Compton free-electron laser

The start-up of the free-electron laser is treated by linear analysis in the high-gain Compton regime. The results are compared with computer simulation.

FELS, a 3-dimensional FEL simulation code including storage-ring operation of high-gain FELS

Abstract The free-electron-laser code FELS is a program to model a high-gain free-electron laser in the short-wavelength long pulse regime. The code can be run to describe the single-pass amplifier operation, and the oscillator configuration. Two different types of optical cavities are implemented, the nearly concentric and the ring resonator. Furthermore, the modelling not only of operation with linacs but also with storage ring devices is included. Two versions provide calculation with and without the harmonics of the spontaneous undulator spectrum included [1,2]. This paper will review the models of the FEL, the optical resonator, and the storage ring, and the implementation of the code, shortly. Furthermore, simulation results which point out the differences between ID, 2D and 3D calculations for the example of FELICITA II, the second FEL experiment at DELTA, are included [3,4].

Theory of the high-gain optical klystron.

We present an analytic expression of the harmonic bunching produced by the dispersive section of a free-electron laser (FEL) optical klystron operating in the high-gain exponential regime. This model allows the evaluation of the operating constraints and limits, the possible optimizations and advantages of such a device with respect to the conventional FEL configuration, i.e., shortening of the overall length and reduction of the induced energy spread, provided that the initial energy spread is smaller than the one required for the normal high-gain FEL operator. The analytical expressions derived here are confirmed by the numerical solution of the full nonlinear set of equations for the FEL.

Model studies on the ELFA wiggler

A wiggler for the ELFA high-gain single-pass Compton FEL (free-electron laser) is under study. The preliminary design of the wiggler ( lambda /sub w/=12 cm, B/sub w/=3.6 kG, total length L=6-7 m) has shown the need for model studies in order to optimize the pole and the coil geometry. The main characteristics of an electromagnet model and the high-precision apparatus for magnetic measurements are described. The results of the model field measurement are presented and discussed. The data are also compared with theoretical predictions, based on 2-D codes and simple analytical models. The first set of measurements made on the model has shown good agreement with the main design goals. Peak field level, field waveform in the midplane, and transverse field pattern seem to be satisfactory. >

Three-mode treatment of a high-gain steady-state free-electron laser.

A description of the steady-state nonlinear behavior of a Compton free-electron-laser (FEL) amplifier is presented, in which the radiation field is written in both linear and nonlinear regimes as the sum of three coupled ``normal modes.'' In the linear regime these modes reduce themselves to the noninteracting modes of the usual linear theory. The two linearly stable modes turn out to be nonlinearly unstable, because their amplitudes grow exponentially as the FEL enters into the nonlinear regime. We derive a self-contained system of three nonlinear dynamical equations for these modes in two different approaches. The system is then reduced to comparatively simple forms in which only cubic nonlinearities appear. In this way, we are able to describe the FEL saturation process and the first peak in the amplitude of the radiation field with a good degree of accuracy. The large-amplitude oscillations in the field intensity, which are the main feature of the FEL nonlinear dynamics, are also reproduced through the nonlinear coupling between the normal modes.

Superradiant evolution of radiation pulses in a free-electron laser.

We demonstrate analytically and numerically superradiant spiking behavior in the leading and trailing regions of a radiation pulse propagating within a long electron pulse in a single-pass, high-gain free-electron laser (FED). A single superradiant spike is observed when the radiation pulse is shorter than a cooperation length ${\mathit{L}}_{\mathit{c}}$. We show this work may be relevant to the understanding of the spiking behavior in the FEL oscillator, and to possible spiking mechanisms in a perturbed steady-state amplifier.

Microscopic gain mechanism in the high-gain free electron laser

In this article we present a detailed investigation of the microscopic electron/radiation evolution in a high-gain free electron laser (FEL). Both the steady-state and in particular the superradiant regimes are investigated. Solutions of the one-dimensional FEL evolution equations are represented dynamically by animated computer graphics to produce “movies” of the electrons/radiation evolution. We believe this form of representation of the FEL process provides a clearer, intuitive picture of the underlying mechanisms involved. This has been of particular importance in the understanding of more complex FEL mechanisms such as superradiant phenomena.

Resonator modes in high-gain free electron lasers

When the gain in a free electron laser is high enough to produce optical guiding, the resonator mode distorts and loses its forward-backward symmetry. We show that the resonator mode in a high-gain FEL can be easily constructed using the mode expansion technique taken separately in the interaction and the free-space regions. We propose design strategies to achieve maximal gain and optimal mode quality, and discuss the stability of the optimized mode.

Design of a high-field taperable helical wiggler

The advantages of a helical wiggler have long been recognized, but earlier concepts do not meet the taper and field-control requirements of a modern high-gain free electron laser. This work presents a design of an electromagnetic helical wiggler where the field and steering-free taper are completely adjustable. The unique coil and core geometry makes it possible to produce fields over 5 kG in a bore of 2.5 cm. The paper discusses the concept, magnetic-field analysis, electron-beam trajectories and practical considerations of the wiggler.

Linear theory of superradiance in a free-electron laser.

This study is motivated by the analytical solutions of superradiance in a high-gain free-electron laser obtained by Bonifacio, Maroli, and Piovella, using the technique of Laplace transforms (Opt. Commun. 68, 369 (1988)). An error in these analytical solutions is remedied by a correct treatment of the boundary conditions on the electron beam, and the earlier theory is extended to allow for both electron shot noise and an optical pulse in the initial state. It is shown that, when the optical pulse is shorter than the electron pulse, superradiant behavior can also occur at the leading edge of the optical pulse.

Large harmonic bunching in a high-gain free-electron laser

Properly taking into account the coupling between different harmonics in a high-gain free-electron laser (FEL), we demonstrate that the exponential gain of the fundamental radiation wavelength drives the third-harmonic bunching at a rate which is three times that of the fundamental. This leads to almost equal saturation bunching parameters on the fundamental and the harmonic wavelength. This is the underlying mechanism of the resonant-frequency tripling method in a two-wiggler FEL.

A landau-ginzburg equation for a high-gain free electron laser

We show that the steady-state regime of a high-gain single-pass FEL can be described by a Landau-Ginzburg equation with complex coefficients. This provides the simplest analytically solvable model of the approach to saturation for the field amplitude and phase and is formally identical to that of an atomic laser.

Development of Five Compact Storage Rings, TERAS, NIJI-I–IV, at ETL

At the Electrochemical Laboratory (ETL) four compact storage rings, TERAS, NIJI-I–III, have been already constructed and a compact storage ring, NIJI-IV, with long straight sections for FEL experiments will be constructed in 1990. TERAS is an 800-MeV storage ring. It has been operated since Oct. 1981 for research on atomic, molecular and solid state physics and ULSI lithography, generation of polarized SR and gamma-rays and for a free electron laser (FEL) experiment. NIJI-I (NIJI means rainbow) is a 270-MeV compact ring and has been operated from Feb. 1986 to March 1989 for machine studies of beam storage higher than 0.5 A at low energies below 150 MeV. NIJI-II is a 600-MeV conventional type compact ring and was operated in July 1989.NIJI-III is a 620-MeV superconducting type ring. NIJI-II and NIJI-III will be used for FEL and ULSI lithography experiments. Before the superconducting magnets are installed, NIJI-III with conventional type magnets has already been constructed and operated in June 1989. The conventional type magnets of NIJI-III will be replaced by superconducting type ones, starting in the fall of 1989 one by one. NIJI-IV is a 500-MeV conventional type compact ring with straight sections longer than 5 m where an optical klystron can be installed to achieve a high gain FEL experiment.

Superradiance in the high-gain free-electron laser.

In this paper we describe the effects of slippage on the single-pass high-gain free-electron laser (FEL) amplifier. We use a one-dimensional computational code to show the existence of two new dynamical regimes characterized by a dimensionless parameter {ital K}, which is a measure of the slippage in one gain length. We define the long-pulse limit to be when {ital K}{much lt}1 or the electron pulse length {ital L}{sub {ital e}} is much greater than a properly defined cooperation length'' {ital L}{sub {ital c}} ({ital L}{sub {ital e}}{much gt}L{sub c}). In this case we find that only the leading region of the propagating radiation pulse exhibits the usual steady-state behavior, with peak power proportional to {ital n}{sub {ital e}}{sup 4/3} (where {ital n}{sub {ital e}} is the electron-beam density). The trailing (slippage) region exhibits a spiking behavior with peak intensities reaching many times the saturated intensity predicted by steady-state theory. We define the short-pulse regime to be when {ital K}{approx gt}1 ({ital L}{sub {ital e}}{approx lt}L{sub c}). In this regime the peak power emitted by the electrons does not scale as {ital n}{sub {ital e}}{sup 4/3}, as predicted by steady-state theory, but scales as {ital n}{sub {ital e}}{sup 2}, which ismore » typical of superradiant behavior. Furthermore, energy is extracted from the electrons in a continuous way, with no steady-state synchrotron oscillatory-type behavior.« less

Wiggling optical modes in high-gain free-electron lasers.

The driving current of a free-electron laser with a uniform helical undulator is calculated by solving a linearized Boltzmann equation which includes terms, generally neglected, representing the effect of the e-beam bending due to the finite radius of the electron wiggling. The current is used for writing the wave equation for the electromagnetic field amplified along the z axis of the wiggler. The space modulation of the current induced by the e-beam bending is eliminated by using a moving frame obtained by displacing the coordinate system, with its origin at the center of the wiggler entrance section, along the central trajectory of the electron beam. In this way, a parabolic wave equation is obtained similar to the well-known equation of high-gain lasers, with the addition of a term proportional to the wiggling radius and the transverse gradient of the field, which depends sinusoidally on z. For solving this generalized parabolic equation, the laser field is represented in the moving frame as a superposition of space harmonics whose longitudinal propagation constants differ by multiples of the wiggler period (Bloch-Floquet waves). The transverse profile of the field is accounted for by expanding it in a series of Gauss-Laguerre wave functions. Then, combining Bloch-Floquet waves with Gauss-Laguerre wave functions, three-dimensional mutually orthogonal modes are obtained. In the laboratory frame these modes appear as wiggling beams, which are used as the basis for transforming the wave equation into a homogeneous set of linear equations. A simple expression for the correction of the propagation constant due to the e-beam bending is presented together with the analytic expression of the field for the case of high Fresnel numbers.

Inhomogeneous broadening effects in high-gain free electron laser operation: A simple parametrization

In this paper we present a simple parametrization of the effects of gain degradation induced in high-current FELs by the inhomogeneous broadenings due to the energy spread and emittances of the electron beam. The parametrization is based on a fitting procedure of the numerical data. The accuracy of the fit is better than 1%.

Simulations of a ring resonator free-electron laser

A relatively high gain ( approximately=25 to 40%) free-electron laser (FEL) with an optical ring resonator is simulated using the code FELEX. The laser system corresponds to the 'burst mode' FEL. The ring consists of paraboloids, grazing incidence hyperboloids, and a grating rhomb. The wiggler is 5 m in length and has an adjustable taper, while the electron beam is produced by an RF linac. The optical elements of the ring together with the FEL interaction in the wiggler are modeled in three spatial dimensions to investigate the system from start-up to saturation. Both single-frequency and finite-pulse simulations are performed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Transverse mode control in high gain free electron lasers with grazing incidence, unstable ring resonators

Grazing incidence, ring resonators have been proposed [1,2] to alleviate the problem of inordinately high irradiance on the intracavity optics in free electron lasers. Such resonators are also relatively compact, and consequently their alignment tolerances are more manageable. In this paper we present the transverse mode characteristics of an unstable, grazing incidence ring resonator under high gain conditions, and examine the issue of transverse mode control as a function of key resonator parameters.

Effects of bending on free electron laser performance

The ability of electromagnetic radiation to follow bends of the electron beam path in a high-gain free electron laser is investigated by considering the mode structure of propagation inside a bent undulator. For this purpose the mode equation, previously studied in the context of optical guiding in a straight undulator, is modified so as to account for bending. A qualitative criterion for the significance of the bending effect is given, based on the identification of the relevant dimensionless parameter. Quantitative results are then obtained by solving approximately the mode equation of a bent undulator through an extension of the Rayleigh-Ritz variational technique. Diagrams of amplification rate vs bending parameter are given.

Slippage and superradiance in the high-gain FEL

In this paper we describe the single-pulse high-gain free electron laser amplifier taking into account propagation effects (slippage). We demonstrate the existence of two different dynamical regions characterised by an adimensional parameter κ such that κ−1 is a measure of the gain of a photon on slipping through the electron pulse. We define the long pulse limit to be when κ ⪡ 1. In this case we find that only the leading region of the propagating radiation pulse exhibits the previous steady state behaviour with peak power proportional to ne43 (where ne is the electron beam density). The trailing (slippage) region exhibits a spiking behaviour with peak intensities reaching many times the saturated intensity predicted by steady state theory. The existence of the spiking may be related to the fact that the trailing region of the electron pulse experiences less radiation re-absorption than the leading region, so that slippage inhibits saturation. The energy extracted from the beam exhibits the usual oscillatory behaviour after saturation as predicted by the steady state theory. We define the short-pulse regime to be when κ ≳ 1. In this regime the peak power emitted by the electrons does not scale as ne43, as predicted by steady state theory, but scales as ne2 which is typical of superradiant behaviour. Furthermore, energy is extracted from the electrons in a continuous way, with no steady-state-type oscillatory behaviour, so that the efficiency of the superradiant FEL may be enhanced considerably.