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Coherent enhancement of the spontaneous undulator radiation by several orders of magnitude has been observed in a free-electron laser at wavelengths from 40 to 100 /im. The coherent emission can be explained by details of the electron-beam micropulse structure. Furthermore, it has been found that the phase of the optical micropulses is fixed by the electron pulse structure and that the coherence extends over successive optical micropulses, which gives rise to interference effects as a function of the optical cavity length in a laser oscillator.PACS numbers: 41.60. Cr, 42.50.Fx, 42.72.Ai In a free-electron laser (FEL), a relativistic electron beam is passed through a periodic magnet array, the undulator, to produce electromagnetic radiation in a wavelength range determined mainly by the electron energy and the undulator period. Amplification occurs through a second-order nonlinear interaction between the optical field and the electron motion, and leads to a powerful output that can be used in a variety of experiments in physics, chemistry, and biology.A convenient description of the operation of an FEL is obtained by transforming to the rest frame of the electron beam [1]. In this frame, the undulator field transforms into an electromagnetic wave propagating toward the electrons. This wave is scattered by the electrons and appears with a Doppler upshift in the laboratory frame as the undulator radiation. In the electron frame the backscattered wave and the original wave combine to form a standing wave pattern. Enhanced stimulated scattering occurs due to the formation of a density grating in the electron distribution under the influence of the ponderomotive force associated with the standing wave. In an FEL oscillator, the radiation is trapped in an optical cavity, and through further stimulated enhancement the scattered field builds up to saturation over tens or hundreds of round trips.The initial optical field generated by scattering from the undisturbed electron beam is known as spontaneous emission. As in other instances of light scattering, the spectrum is determined by the distribution of scatterers in the scattering volume [2]. One can distinguish incoherent and coherent scattering. The incoherent contribution originates from statistical fluctuations in the number density of the scatterers, as in Rayleigh scattering or incoherent Thomson scattering, and its power is proportional to this density. The coherent contribution arises from density variations on the scale of the radiation wavelength and its power is proportional to the square of the fluctuation density. The power scattered by an ensemble of JV scatterers can be written aswhere Pi is the power for a single electron, which de-pends on the undulator parameters, and f(k) is a form factor depending on the macroscopic density distribution within the scattering volume. The first term gives the incoherent contribution and the second the coherent one. The spontaneous undulator emission in the laboratory frame is described by the same expression, with f(k...

The first experimental observation of limit-cycle power oscillations in a short-pulse free-electron laser is presented. These are due to a nonlinear modulation of the optical micropulse shape and phase by the electrons, which leads to the formation of a train of subpulses. Experimentally, the oscillations have been found to depend on the slippage distance and on the desynchronism between optical pulses and electron bunches, comparing well with theoretical predictions.PACS numbers: 41.60.CrThe free-electron laser (FEL) is a novel type of laser opening up many new applications, due to its high power, short pulse length, and wavelength tunability [1]. The FEL uses a beam of relativistic electrons injected into a periodic magnetic structure, the so-called undulator. The alternating magnetic field forces the electrons to move along sine-like trajectories and, consequently, to emit radiation. Usually this radiation, which is known as spontaneous emission, is captured in an optical cavity and amplified on successive passes through the undulator in the presence of newly injected electrons. The electrons are bent into a beam dump after they have traversed the undulator.A radio-frequency (rf) accelerator provides the electron beam in most FEL oscillators operating in the infrared and visible spectral range. This type of accelerator has the property that electrons emerge as short bunches, which are separated by fixed periods. The light wave in the FEL cavity mimics this time structure, i.e., consists of a train of short micropulses. Careful synchronization of the circulating micropulses and the electron bunches is required to achieve laser oscillation. This is done by matching the length of the optical cavity to the electron bunch repetition frequency.Electrons slip back relative to an optical micropulse on their mutual travel through the undulator, because (i) their velocity is somewhat smaller than the velocity of light and (ii) they move along an undulating path. The FEL resonance condition implies that the slippage is one radiation wavelength X per undulator period traversed and, therefore, the bunch slips back by a distance NX in an undulator consisting of TV periods [2]. In view of the fact that the amplification grows toward the downstream end of the undulator, where the electrons have shifted back relative to the front of the optical micropulse, the optical pulse peaks up at its rear end. This has the consequence that the optical group velocity is somewhat smaller than its vacuum value. Hence, in a perfectly synchronized resonator, the micropulse would continue to narrow and retard on subsequent passes through the undulator. The reduced overlap with the gain medium leads to a reduction of the gain per pass, which impedes the growth of the laser power. This effect is known as "laser lethargy" [2]. In order to restore the gain, it is necessary to slightly reduce the cavity length from the value giving perfect synchronism, so that the peak of the optical pulse is advanced relative to the peak of the electron bunch at t...

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