Single-particle theory of the free-electron laser in a moving frame

We give a summary of the theory of a single electron involved in free-electron laser (FEL) operation. We use the method of transformation to a predetermined moving frame where the wiggler-laser scattering process is elastic. In this paper, we discuss the classical and quantum dynamics of such an electron and evaluate perturbatively the lowest order FEL behavior from the classical pendulum equation. The presentation is tutorial throughout and stresses analytic results and physically significant dimensionless parameters. No results are included for the dynamic evolution of the light during the laser action.     

Short-pulse effects in a free-electron laser

The Free-Electron Laser for Infrared eXperiments (FELIX) offers a unique combination of short electron bunches and long wavelengths, i.e. a slippage parameter μ_c ranging up to 10. As a consequence, pronounced short-pulse effects can be observed. In this paper the experimental observation of two of these effects is discussed, namely the occurrence of limit-cycle oscillations and the feasibility of tuning of the micropulse duration. The stable limit-cycle oscillation of the macropulse power is due to a modulation of the optical micropulse shape. This is a consequence of a combination of high optical power and short pulses. The former causes synchrotron oscillations of the electrons and the effect is, therefore, closely related to spiking phenomena. The short-pulse nature of FELIX ensures that the oscillations do not evolve into the chaotic behavior normally associated with spiking and the sideband instability. Experimental results are compared with numerical simulations     

Optical guiding in a Raman free-electron laser

A theoretical and computational study of optical guiding in a Raman free-electron laser (of wavelength ≃ 2 mm) is given. A set of basic dynamical equations is given, including the effects of space-charge and two-dimensional diffraction, both with and without a waveguide. The results from a computer code based on these equations are reported, showing optical guiding. An experiment is proposed in the Columbia free-electron laser to measure optical guiding.     

Nonlinear theory of a quadrupole free-electron laser

The nonlinear motion of electrons in a quadrupole free-electron laser is analyzed. If the betatron frequency is close to the mismatch frequency, the three-dimensional nonlinear equations can be reduced to an integrable one-dimensional equation. To enhance the efficiency, a tapered wiggler is introduced and the electron orbits in a tapered quadrupole free-electron laser are analyzed. The conditions for the particles to remain trapped as the heat wave decelerates are found.     

Simulations of a ring resonator free-electron laser

A relatively high gain (≈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     

AM mode-locking of a free-electron laser oscillator

The authors present experimental and theoretical studies of a mode-locked free-electron laser (FEL) oscillator. In the experiment the FEL uses a continuous electron beam and operates in the microwave regime. AM mode-locking is performed by modulating the attenuation of the FEL ring cavity by a PIN diode modulator. The modulation period is tuned to match the RF roundtrip time in the ring cavity. The experimental results show the evolution of a single radiation macropulse, consisting of narrow micropulses in synchrony with the sinusoidal locking signal. The micropulse period (~37 ns) equals the roundtrip time and the modulation period. The micropulse width (~5 ns) is limited by the FEL slippage time and by the dispersion in the waveguide ring cavity. The effect of the mode locking consisting in suppressing asynchronous oscillations is clearly observed in the experiment. A theoretical model of the AM mode-locked FEL oscillator operating in the small signal regime is presented. This model includes the slow time variation of the e-beam energy and waveguide dispersion. The theoretical analysis agrees well with the experimental results     

Regenerative gain in a Raman free-electron laser oscillator

A parametric study of gain in a millimeter-wave Raman free-electron laser oscillator and comparisons to linear theory are carried out. The intense (1 kA/cm²), relativistic (600-800 keV), cold [(deltagamma/gamma)_{parallel} < 1percent] electron beam employed is guided by a 9.45 kG magnetic field through a 1.45 cm period, 49.5 cm long uniform undulator. Operation at < 1 kG pump field results in a < 10 percent electron quiver velocity (upsilon_{perp}/upsilon_{parallel}) velocity. The laser power output has been mea sured at ∼ 3 MW corresponding to an efficiency of 4 percent, and tunability in the 90-170 GHz range has been achieved with a narrow linewidth (Delta lambda/lambda leq 1percent). Using a new technique, linear small-signal growth rates have been unfolded from the oscillator startup delays. Excellent agreement is found with three-dimensional small-signal calculations for both the spatial growth rate and the resonance frequency. One-dimensional theory was found to predict shorter wavelength laser output than that observed.     

The free-electron laser as a laboratory instrument

A free-electron laser (FEL) with a component cost, including the accelerator, of approximately $300k, has lased at a wavelength of 85 μm with ≈12 ps micropulse duration, achieving a power growth four orders of magnitude greater than the coherent spontaneous emission, and with a small-signal, single-pass gain of 21%. The price is about an order of magnitude less than other FELs for the far infrared, and transforms the device from the role of a national facility to that of a laboratory instrument. Cost reduction was achieved by employing several novel features: a microwave cavity gun for the accelerator, a staggered-array wiggler, and an on-axis hole in the upstream cavity mirror for electron ingress and radiation egress     

Noise in free-electron laser amplifier

The equations of the free-electron laser amplifier are generalized to include higher order modes. The density and velocity fluctuations in the entering electron beam cause noise excitation in the amplifier. The electron beam fluctuations have been studied extensively, both theoretically and experimentally, in traveling wave tubes, and hence the well-tested formalism developed for this purpose is conveniently applied to the present problem. It is found that the fluctuations put a severe constraint on the achievable exponential gain in a proposed Raman-type free-electron laser operating at optical frequencies. A1/lambda^{3}scaling law is derived.     

Characteristics of the dispersive free-electron laser

The dispersive free-electron laser (DFEL) was previously introduced as an optical klystron (OK) superimposed upon a free-electron laser (FEL). In this paper it is shown that with proper design this device provides a gain increase of the order of 4 over the gain of the OK (for equal lengths) with a gain-energy acceptance product approaching that of the FEL. Even when the transverse excursion of the electron beam exceeds the optical beam dimension, there is only a slight reduction in gain from the above value.     

Mode analysis of a dielectric-loaded Raman-type free-electron laser

The Raman-type free-electron laser consists of a relativistic electron beam contained in a dielectric-induced parallel plate waveguide and an array of permanent magnets for the wiggler. Under the influence of the periodic magnetostatic field, the coupling between the scattered electromagnetic wave of the TE mode (positive-energy wave) and the electron plasma wave of the TM mode (negative-energy wave) is investigated in detail. The following results are obtained. First, when a dielectric sheet is loaded on the waveguide, the maximum growth rate and the oscillation frequency can be greater than those for the vacuum Raman-type free-electron laser. Second, by choosing proper values for the relative permittivity of the dielectric sheet and the ratio of the beam guide, the beam energy can be greatly lowered without degrading the oscillation characteristics. Third, the growth rate decays exponentially with the oscillation frequency kept almost constant as the beam-dielectric gap increases     

Tests of a grazing-incidence ring resonator free-electron laser

The authors describe operational experience of the first free-electron laser (FEL) using a grazing-incidence ring resonator. The Boeing FEL optical cavity was changed from a simple concentric cavity using two spherical mirrors to a larger grazing-incidence ring resonator. Initial tests showed that poorly positioned ring focus and unreliable pointing alignment resulted in reduced and structured FEL output. Later efforts concentrated on improving the resonator alignment techniques and lowering the single-pass losses. FEL performance and reliability have significantly improved due to better ring alignment. The alignment procedure and recent lasing results are described. The effect the electron beam has on lasing is also discussed. Measurements are presented showing FEL temporal output and wavelength are sensitive to electron beam energy variation     

Spontaneous emission and gain in a waveguide free-electron laser

A free-electron laser (FEL) enclosed in a waveguide of narrowly spaced parallel plates has been proposed as a compact, coherent source of far-infrared radiation. The spontaneous emission and small-signal gain of such a device are analyzed. Maxwell's equations are solved for the fields of a relativistic electron beam passing through a linearly polarized undulator in the presence of a parallel-plane waveguide. The radiation intensity is resolved into its component waveguide modes for the fundamental frequency and for all harmonics. The intensity profile in a given harmonic mode is altered significantly when a parameter involving the undulator period, beam energy, and transverse dimension of the guide is such that the radiation group velocity is close to the electrons' axial velocity. The small-signal gain in the waveguide FEL is calculated and related to the spontaneous emission. Near zero slip, the gain curve is significantly different from that of a free-space FEL with the same parameters     

Phase variation in free-electron laser amplifiers

The evolution of the phase of the output radiation of free-electron laser amplifiers is investigated by means of a three-dimensional simulation code. The configuration employed consists of the propagation of a relativistic electron beam through a loss-free cylindrical waveguide in the presence of a helically symmetric wiggler and a uniform axial guide magnetic field. The analysis is fully three dimensional, and a set of model equations is discussed which describes the coupling between an ensemble of electrons and the radiation field of either the TE or TM modes. The model equations are solved numerically, and the output phase is studied with respect to variations in either frequency or electron beam energy. The output phase is found to depend sensitively on the wave frequency within the unstable bandwidth. In addition, the phase stability of the output radiation is discussed as a function of beam energy. Finally, the evolution of the phase for tapered wiggler free-electron lasers is studied.     

两维摇摆场自由电子激光的谐波特性研究

本文应用Nadey定理对两维摇摆场自由电子激光的谐波特性进行了研究。导出了这种新型摇摆场结构自由电子激光高次谐波的自发辐射功率密度和小信号增益公式。以及电子与辐射场的耦合系数的表达式。计算结果表明,采用两维摇摆场可以增强电子与辐射场之间的耦合,提高谐波的辐射强度和增益。而且在某些条件下,在轴上既可获得奇次谐波又可获得偶次谐波。     

Progress in the Hamiltonian picture of the free-electron laser

The Hamiltonian picture of the free-electron laser (FEL) is reexamined and the multielectron effects are accounted for. The conditions under which the multieleetron effect can be neglected are made precise (low-gain regime) and, in this connection, the strong signal analysis of the Stanford experiment is carried out.     

Generalized electron beam matching in the free-electron laser

Three matching schemes are presented for Gaussian profile electron beams in free-electron lasers (FELs). The three different classes of matching or symmetry conditions are (1) electron beams with separate betatron matching in each plane, (2) those with aspect ratio matching, and (3) cross-matched beams. The new schemes are distinct generalizations of well-known betatron matching and include ribbon profiles. The corresponding effective energy distributions and their Fourier transforms are obtained in analytical form. An analytical kernel produces the key Fredholm integral equation that solves the initial value problem     

Energy-loss calculation of gain in a plane sinusoidal free-electron laser

The gain of a free-electron laser (FEL) made with a plane sinusoidal undulator is calculated by the electron beam energy loss.