Undulator
Encyclopedia
Insertion device
An insertion device is a component in modern synchrotron light sources. They are periodic magnetic structures that stimulate highly brilliant, forward-directed synchrotron radiation emission by forcing a stored charged particle beam to perform wiggles, or undulations, as they pass through the device...
from high-energy physics and usually part of a larger
installation, a synchrotron
Synchrotron
A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field and the electric field are carefully synchronised with the travelling particle beam. The proton synchrotron was originally conceived by Sir Marcus Oliphant...
storage ring
Storage ring
A storage ring is a type of circular particle accelerator in which a continuous or pulsed particle beam may be kept circulating for a long period of time, up to many hours. Storage of a particular particle depends upon the mass, energy and usually charge of the particle being stored...
. It consists of a periodic structure of dipole magnets (see dipole magnet
Dipole magnet
A dipole magnet, in particle accelerators, is a magnet constructed to create a homogeneous magnetic field over some distance. Particle motion in that field will be circular in a plane perpendicular to the field and collinear to the direction of particle motion and free in the direction orthogonal...
). The static magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
is alternating along the length of the undulator with a wavelength
. Electrons traversing the periodic magnet structure are forced to undergo oscillations and thus to radiate energy. The radiation produced in an undulator is very intense and concentrated in narrow energy bands in the spectrum. It is also collimatedCollimated light
Collimated light is light whose rays are parallel, and therefore will spread slowly as it propagates. The word is related to "collinear" and implies light that does not disperse with distance , or that will disperse minimally...
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 is the magnetic field,
, 
is the electron restmass and c is the speed of light, characterizes 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 wigglerWiggler (synchrotron)
A wiggler is an insertion device in a synchrotron. It is a series of magnets designed to periodically laterally deflect a beam of charged particles inside a storage ring of a synchrotron...
.
The usual description of the undulator is relativistic but classic. This means that though the precision calculation is tedious the undulator can be seen as a black box
Black box
A black box is a device, object, or system whose inner workings are unknown; only the input, transfer, and output are known characteristics.The term black box can also refer to:-In science and technology:*Black box theory, a philosophical theory...
. An electron enters this box and an electromagnetic pulse exits through a small exit slit. The slit should be small enough such that only the main cone passes, so that the side lobes may 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
more than a bending magnet. The intensity is enhanced up to a factor of N at harmonic wavelengths due to the constructive interference of the fields emitted during the N radiation periods. The usual pulse is a sine with some envelope. The second factor of N comes from the reduction of the emission angle associated with these harmonics, which is reduced as 1/N. When the electrons come with half the period, they interfere destructively, the undulator stays dark. The same is true, if they come as a bead chain.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
Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since...
a partial interference leads to a linear increase in intensity.
In the free electron laser
Free electron laser
A free-electron laser, or FEL, is a laser that shares the same optical properties as conventional lasers such as emitting a beam consisting of coherent electromagnetic radiation which can reach high power, but which uses some very different operating principles to form the beam...
the intensity increases exponentially with the number of electrons.
An undulator's figure of merit
Figure of merit
A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives. In engineering, figures of merit are often defined for particular materials or devices in order to determine their relative utility for an application...
is spectral radiance.