A diagnostic undulator is used to measure relative electron bunch lengths. The radiation produced by the short undulator is observed off-axis so that the beam is not interrupted. Wavelengths radiated which are longer than the bunch length are coherent and may be more intense than the shorter wavelengths by a factor of up to 10 9 . The total energy radiated thus changes as the bunch length changes, and a measurement of the radiated energy provides a robust beam diagnostic. This non-disturbing diagnostic would be useful in applications where the length of short electron bunches is critical, such as singlepass FELs and linear colliders. For example, real-time bunch length measurements could be used to optimize performance of a single-pass FEL. The experiment is performed at the Source Development Lab (SDL) at Brookhaven National Laboratory. The theory and description of the experiment are reviewed, and the first experimental results are presented.
REVIEW OF THEORYThe theory of coherent off-axis undulator radiation (COUR) has been described [1]. Both a multi-mode approach and a Liénard-Wiechert approach are used to describe the electric field of the radiation produced by the accelerating electrons. It is concluded that the Liénard-Wiechert approach is the most appropriate and the most useful approach for the case described in this study [2]. A review of the Liénard-Wiechert approach follows.The electric field is derived from Liénard-Wiechert potentials: (1) R and n are the distance and direction, respectively, from the electron to the observation point. The first term, which depends on the electron's velocity, is neglected. The spectral energy is given by: are the transverse and longitudinal electron bunch densities, respectively. Eqs. 3 and 4 include the coherence effects of the radiation.A numerical simulation using this method reveals interesting characteristics of off-axis undulator radiation [1]. In particular, the effect of changes in bunch length on the total radiated energy is calculated for both a Gaussianand a top-hat-shaped bunch. The result of the calculation is shown in Fig. 1.
EXPERIMENTAL APARATUSAn experiment has been conducted at the Source Development Lab at Brookhaven National Laboratory. The purpose of the experiment is to measure coherent offaxis undulator radiation and to determine its usefulness for measuring electron bunch lengths.
The accelerator SystemThe SDL accelerator system consists of a photocathode electron gun, which produces electron bunches with up to 1 nC of charge, followed by four 2.856 GHz SLAC-type 0-7803