Undulator
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An undulator is an insertion device from high-energy physics and usually part of a larger installation, a synchrotron storage ring. It consists of a periodic structure of dipole magnets (see dipole magnet). The static magnetic field is alternating along the length of the undulator with a wavelength λu. Electrons traversing the periodic magnet structure are forced to undergo oscillations and radiate. The radiation produced in an undulator is very intense and concentrated in narrow energy bands in the spectrum. It is also collimated on the orbit plane of the electrons. This radiation is guided through beamlines for experiments in various scientific areas.
The important dimensionless parameter
where e is the particle charge, B the magnetic field, m the electron rest mass and c the speed of light, characterises the nature of the electron motion. For 
the oscillation amplitude of the motion is small and the radiation displays interference patterns which lead to narrow energy bands. If 
the oscillation amplitude is bigger and the radiation contributions from each field period sum up independently, leading to a broad energy spectrum. In this regime of fields the device is no longer called an undulator; it is called a wiggler.
Undulators can provide several orders of magnitue higher flux than a simple bending magnet and as such are in high demand at synchrotron radiation facilities.
The usual description of the undulator is relativistic but classic. That means that beside the precision calculation being tedious the undulator can be seen as a black box. An electron passes this box and an electromagnetic pulse exits through a small exit slit. The slit should be so small to let pass only the main cone, so that we do not have to deal with the side lobes. The pulses of multiple electrons do interfere. The usual pulse is a sine with some envelope. When multiple electrons come at the same time or multiple periods of this sine later or earlier, the field strength increases proportional to the number of electrons. That means the intensity increases with the square. When the electrons come with half that period, they interfere destructively, the undulator stays dark. The same is true, if they come as a bead chain. If the electrons follow the Poisson distribution a partial interference leads to a linear increase in intensity. In the free electron laser the intensity increases exponential with the number of electrons.
The figure of merit is spectral radiance.
[edit] External links
D. T. Attwood's page at Berkeley: Soft X-Rays and Extreme Ultraviolet Radiation. His lecture and viewgraphs are available online.
