An undulator is a device from high-energy physics and usually part of a larger installation, a synchrotron. It consists of a periodic dipole magnet structure. 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. This process is very similar to Thomson scattering. A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field (to turn the particles so they circulate) and the electric field (to accelerate the particles) are carefully synchronized with the travelling particle beam. ... A dipole magnet, in particle accelerators, is a magnet constructed to create a homogeneous magnetic field over some distance. ... Thomson scattering is the scattering of electromagnetic radiation by a charged particle. ...
The important dimensionless parameter
where e is the electron 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 motion of the electron can be considered linear and this is the undulator regime. If the electron motion becomes highly non-linear which leads to radiation of harmonics. This is the wiggler regime. An wiggler is an insertion device for a synchrotron. ...
External links
D. T. Attwood's page at Berkeley: Soft X-Rays and Extreme Ultraviolet Radiation. His lecture and viewgraphs are available online.
The wigglers and undulators are inserted between the bending magnets, which keep the electrons traveling around the storage ring.
Wigglers or undulators (also known as insertion devices) produce synchrotron radiation that is considerably brighter than radiation from a bending magnet.
The deflections of the beam are smaller in an undulator than in a wiggler, and the radiation's brightness can, in theory, be increased by a factor about equal to the square of the number of oscillations, but only at discrete photon energies.
the motion of the electron can be considered linear and this is the undulator regime. If 
the electron motion becomes highly non-linear which leads to radiation of harmonics. This is the 
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