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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, or it may be a component of a free electron laser. It consists of a periodic structure of dipole magnets. The static magnetic field is alternating along the length of the undulator with a wavelength
The undulator strength parameter
where e is the electron charge, B is the magnetic field,
The usual description of the undulator is relativistic but classical. This means that although a precise calculation is tedious, the undulator can be seen as a black box, where only functions inside the device affect how an input is converted to an output; an electron enters the box and an electromagnetic pulse exits through a small exit slit. The slit should be small enough such that only the main cone passes, and the side lobes of the wavelength spectra can be ignored.
Undulators can provide several orders of magnitude higher flux than a simple bending magnet and as such are in high demand at synchrotron radiation facilities. For an undulator with N periods, the brightness can be up to
The polarization of the emitted radiation can be controlled by using permanent magnets to induce different periodic electron trajectories through the undulator. If the oscillations are confined to a plane the radiation will be linearly polarized. If the oscillation trajectory is helical, the radiation will be circularly polarized, with the handedness determined by the helix.
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 exponentially with the number of electrons.
An undulator's figure of merit is spectral radiance.
History
The Russian physicist Vitaly Ginzburg showed theoretically that undulators could be built in a 1947 paper. Julian Schwinger published a useful paper in 1949 that reduced the necessary calculations to Bessel functions, for which there were tables. This was significant for solving the design equations as digital computers were not available to most academics at that time.
Hans Motz and his coworkers at Stanford demonstrated the first undulator in 1952. It produced the first manmade coherent infrared radiation. The design could produce a total frequency range from visible light down to millimeter waves.