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Time-resolved measurements of the transverse electric field associated with relativistic electron bunches are presented. Using an ultrafast electro-optic sensor close to the electron beam, the longitudinal profile of the electric field was measured with subpicosecond time resolution and without time-reversal ambiguity. Results are shown for two cases: inside the vacuum beam line in the presence of wake fields, and in air behind a beryllium window, effectively probing the near-field transition radiation. Especially in the latter case, reconstruction of the longitudinal electron bunch shape is straightforward.

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...