Theory Of Free-electron Laser Research Articles

An electron wave packet in the relativistic strophotron FEL

The theory of free electron lasers (FELs) is well developed both in quantum mechanical and classical approaches. In strophotron FEL, in classical approach, resonance frequency and the gain are strongly dependent on initial parameters of electron beam. In the quantum mechanical approach considered by Zaretsky and Nersesov (1983 JETP 57 518), there is no such dependence. The correspondence between the quantum mechanical and classical approaches in a relativistic strophotron FEL is discussed. We study the initial distribution of electrons over vibrational levels determined by the expansion coefficients in relativistic strophotron FEL. It is shown, (presenting electron wave function in the form of Gaussian wave packet), that the number of the vibrational level most efficiently populated at the initial moment of time can be expressed in terms of the initial parameters of the electron beam.

Radio-Frequency Undulators, Cyclotron Auto Resonance Maser and Free Electron Lasers

We discuss a hybrid Free Electron Laser (FEL) architecture operating with a RF undulator provided by a powerful Cyclotron Auto-Resonance Maser (CARM). We outline the design elements to operate a compact X-ray device. We review the essential aspects of wave undulator FEL theory and of CARM devices.

A Review of High-Gain Free-Electron Laser Theory

High-gain free-electron lasers, conceived in the 1980s, are nowadays the only bright sources of coherent X-ray radiation available. In this article, we review the theory developed by R. Bonifacio and coworkers, who have been some of the first scientists envisaging its operation as a single-pass amplifier starting from incoherent undulator radiation, in the so called self-amplified spontaneous emission (SASE) regime. We review the FEL theory, discussing how the FEL parameters emerge from it, which are fundamental for describing, designing and understanding all FEL experiments in the high-gain, single-pass operation.

Statistical theory of a self-seeded free electron laser with noise pedestal growth

We study the impact of a spectral noise pedestal on the statistical properties of a self-seeded free electron laser (FEL). The broad pedestal is assumed to come from self amplified spontaneous emission (SASE) in the second stage of the self-seeding system and is uncorrelated with the narrowband amplified seed. An analytic description is developed based on the statistical theory of a one-dimensional FEL in the high gain linear regime. The theory shows good agreement with experimental data, which show that the presence of a SASE background can have a strong impact on the statistical behavior of self-seeding systems.

Quantum-mechanical analysis of low-gain free-electron laser oscillators

In the previous classical theory of the low-gain free-electron laser (FEL) oscillators, the electron is described as a point-like particle, a delta function in the spatial space. On the other hand, in the previous quantum treatments, the electron is described as a plane wave with a single momentum state, a delta function in the momentum space. In reality, an electron must have statistical uncertainties in the position and momentum domains. Then, the electron is neither a point-like charge nor a plane wave of a single momentum. In this paper, we rephrase the theory of the low-gain FEL where the interacting electron is represented quantum mechanically by a plane wave with a finite spreading length (i.e., a wave packet). Using the concepts of the transformation of reference frames and the statistical quantum mechanics, an expression for the single-pass radiation gain is derived. The spectral broadening of the radiation is expressed in terms of the spreading length of an electron, the relaxation time characterizing the energy spread of electrons, and the interaction time. We introduce a comparison between our results and those obtained in the already known classical analyses where a good agreement between both results is shown. While the correspondence between our results and the classical results are shown, novel insights into the electron dynamics and the interaction mechanism are presented.

Discussion and analytical test for inclusion of advanced field and boundary condition in theory of free electron lasers

By the covariant statement of the distance in space-time separating transmitter and receivers, the emission and absorption of the retarded and advanced waves are all simultaneous. In other words, for signals carried on electromagnetic waves (advanced or retarded) the invariant interval (cdt)2−dr2 between the emission of a wave and it's absorption at the non-reflecting boundary is always identically zero. Utilizing this principle, we have previously explained the advantages of including the coherent radiation reaction force as a part of the solution to the boundary value problem for FELs that radiate into “free space” (Self Amplified Spontaneous Emission (SASE) FELs) and discussed how the advanced field of the absorber can interact with the radiating particles at the time of emission. Here we present an analytical test which verifies that a multilayer mirror can act as a band pass filter and can contribute to microbunching in the electron beam. Here we will discuss motivation, conditions and requirements, and method for testing this effect.

Theoretical study of a waveguide THz free electron laser and comparisons with simulations

This paper fills a gap in the waveguide free electron laser theory by considering transverse distribution and energy spread of the electron beam.

Modelling elliptically polarised free electron lasers

A model of a free electron laser (FEL) operating with an elliptically polarised undulator is presented. The equations describing the FEL interaction, including resonant harmonic radiation fields, are averaged over an undulator period and generate a generalised Bessel function scaling factor, similar to that of planar undulator FEL theory. Comparison between simulations of the averaged model with those of an unaveraged model show very good agreement in the linear regime. Two unexpected results were found. Firstly, an increased coupling to harmonics for elliptical rather than planar polarisarised undulators. Secondly, and thought to be unrelated to the undulator polarisation, a significantly different evolution between the averaged and unaveraged simulations of the harmonic radiation evolution approaching FEL saturation.

Dispersion relation and growth rate of a relativistic electron beam propagating through a Langmuir wave wiggler

In this study, a theory of free-electron laser (FEL) with a Langmuir wave wiggler in the presence of an axial magnetic field has been presented. The small wavelength of the plasma wave (in the sub-mm range) allows obtaining higher frequency than conventional wiggler FELs. Electron trajectories have been obtained by solving the equations of motion for a single electron. In addition, a fourth-order Runge–Kutta method has been used to simulate the electron trajectories. Employing a perturbation analysis, the dispersion relation for an electromagnetic and space-charge waves has been derived by solving the momentum transfer, continuity, and wave equations. Numerical calculations show that the growth rate increases with increasing the e-beam energy and e-beam density, while it decreases with increasing the strength of the axial guide magnetic field.

Wide-Range Third Harmonic Oscillations in Free-Electron Lasers Using the Storage Ring NIJI-IV

We developed third-harmonic free-electron laser (FEL) oscillations that operated from the visible to near-infrared region. Our infrared FEL system uses the storage ring NIJI-IV, which produced the first third-harmonic storage ring FEL oscillations. By measuring the characteristics of the third-harmonic FEL oscillations, we found that behavior of the third-harmonic FEL could be explained by a one-dimensional FEL theory. We demonstrated that the higher harmonic was effective in shortening the FEL wavelength, so it will save electron-beam energy in X-ray FEL oscillators based on a cw energy-recovery linac.

Operation of higher harmonic oscillations in free-electron lasers

We report for the first time the experimental achievement of a seventh-harmonic free-electron laser (FEL) oscillation. The measured FEL gains and average FEL powers for higher harmonics were identical to those calculated by a one-dimensional FEL theory. The measured linewidths of the higher-harmonic FELs were narrower than that of the fundamental FEL owing to the narrower spectral widths of the spontaneous emissions. By applying the higher-harmonic FEL oscillation to a resonator-type FEL with an advanced accelerator, an x-ray FEL oscillator can be realized at lower electron-beam energy.

Gain length fitting formula for free-electron lasers with strong space-charge effects

We present a power-fit formula, obtained from a variational analysis using three-dimensional free-electron laser theory, for the gain length of a high-gain free-electron laser's fundamental mode in the presence of diffraction, uncorrelated energy spread, and longitudinal space-charge effects. The approach is inspired by the work of Xie [Nucl. Instrum. Methods Phys. Res., Sect. A 445, 59 (2000)], and provides a useful shortcut for calculating the gain length of the fundamental Gaussian mode of a free-electron laser having strong space-charge effects in the 3D regime. The results derived from analytic theory are in good agreement with detailed numerical particle simulations that also include higher-order space-charge effects, supporting the assumptions made in the theoretical treatment and the variational solutions obtained in the single-mode limit.

One-dimensional free-electron laser equations without the slowly varying envelope approximation

A set of one-dimensional equations has been deduced in the time domain from the Maxwell-Lorentz system with the aim of describing the free-electron laser radiation without using the slowly varying envelope approximation (SVEA). These equations are valid even in the case of arbitrarily short electron bunches and of current distributions with ripples on the scale of or shorter than the wavelength. Numerical examples are presented, showing that for long homogeneous bunches the new set of equations gives results in agreement with the SVEA free-electron laser theory and that the use of short or prebunched electron beams leads to a decrease of the emission lethargy. Furthermore, we demonstrate that in all cases in which the backward low frequency wave has negligible effects, these equations can be reduced to a form similar to the usual 1D SVEA equations but with a different definition of the bunching term.

Statistical analysis of crossed undulator for polarization control in a self-amplified spontaneous emission free electron laser

There is a growing interest in producing intense, coherent x-ray radiation with an adjustable and arbitrary polarization state. In this paper, we study the crossed-undulator scheme [K.-J. Kim, Nucl. Instrum. Methods Phys. Res., Sect. A 445, 329 (2000)] for rapid polarization control in a self-amplified spontaneous emission (SASE) free electron laser (FEL). Because a SASE source is a temporally chaotic light, we perform a statistical analysis on the state of polarization using FEL theory and simulations. We show that, by adding a small phase shifter and a short (about 1.3 times the FEL power gain length), 90\ifmmode^\circ\else\textdegree\fi{} rotated planar undulator after the main SASE planar undulator, one can obtain circularly polarized light---with over 80% polarization---near the FEL saturation.

Review of x-ray free-electron laser theory

High-gain free-electron lasers (FELs) are being developed as extremely bright sources for a next-generation x-ray facility. In this paper, we review the basic theory of the start-up, the exponential growth, and the saturation of the high-gain process, emphasizing the self-amplified spontaneous emission. The radiation characteristics of an x-ray FEL, including its transverse coherence, temporal characteristics, and harmonic content, are discussed. FEL performance in the presence of machine errors and undulator wakefields is examined. Various enhancement schemes through seeding and beam manipulations are summarized.

Quantum theory of SASE FEL

We describe a free-electron laser (FEL) in the Self-Amplified Spontaneous Emission (SASE) regime quantizing the electron motion and taking into account propagation effects. We demonstrate quantum purification of the SASE spectrum, i.e. in a properly defined quantum regime the spiking behavior disappears and the SASE power spectrum becomes very narrow.

Single-mode coherent synchrotron radiation instability of a bunched beam

The coherent synchrotron radiation instability may be driven at the shielding threshold by a single mode excited in the beam pipe. Such a problem may have general interest for other one-mode dominated problems arising in plasma, free-electron laser theory, and microwave instability. The problem may have practical interest if the steady state exists but requires the study of the nonlinear regime of instability. The results of the study, both analytic and numerical, are presented in the coasting beam approximation and for a bunched beam.

Single-mode coherent synchrotron radiation instability

The microwave instability driven by the coherent synchrotron radiation (CSR) has been previously studied [S. Heifets and G. V. Stupakov, Phys. Rev. ST Accel. Beams 5, 054402 (2002)] neglecting effect of the shielding caused by the finite beam pipe aperture. In practice, the unstable mode can be close to the shielding threshold where the spectrum of the radiation in a toroidal beam pipe is discrete. In this paper, the CSR instability is studied in the case when it is driven by a single synchronous mode. A system of equations for the beam-wave interaction is derived and its similarity to the 1D free-electron laser theory is demonstrated. In the linear regime, the growth rate of the instability is obtained and a transition to the case of continuous spectrum is discussed. The nonlinear evolution of the single-mode instability, both with and without synchrotron damping and quantum diffusion, is also studied.

Properties of the ultrashort gain length, self-amplified spontaneous emission free-electron laser in the linear regime and saturation

VISA (Visible to Infrared SASE Amplifier) is a high-gain self-amplified spontaneous emission (SASE) free-electron laser (FEL), which achieved saturation at 840 nm within a single-pass 4-m undulator. The experiment was performed at the Accelerator Test Facility at BNL, using a high brightness 70-MeV electron beam. A gain length shorter than 18 cm has been obtained, yielding a total gain of 2 x 10(8) at saturation. The FEL performance, including the spectral, angular, and statistical properties of SASE radiation, has been characterized for different electron beam conditions. Results are compared to the three-dimensional SASE FEL theory and start-to-end numerical simulations of the entire injector, transport, and FEL systems. An agreement between simulations and experimental results has been obtained at an unprecedented level of detail.

Linear Theory of Free Electron Laser with a Plasma-Loaded Cylindrical Waveguide

The dispersion characteristics of plasma–loaded free-electron laser has been analyzed using linear fluid model. The device under consideration consists of the cylindrical metallic waveguide, completely filled with background plasma and a relativistic electron beam which passes through a helical wiggler magnetic field. The result predicts that reasonable plasma density tends to improve the growth rate of the low-frequency optical wave of FEL and causes an shiftup in the operating frequency, However it has little effect on the growth rate of the high-frequency wave. In the plasma–loaded FEL, for the FEL oscillator, it may be tuned by varying the plasma density; and for the FEL amplifier, the wider frequency bandwidth is gained. A critical density ncp for the background plasma density is found.