Editing Insertion device (section)

==Operation==
Insertion devices are traditionally inserted into straight sections of storage rings (hence their name). As the stored particle beam, usually [[electron]]s, pass through the ID the alternating [[magnetic field]] experienced by the particles causes their trajectory to undergo a transverse oscillation. The acceleration associated with this movement stimulates the emission of synchrotron radiation.

There is very little mechanical difference between wigglers and undulators and the criterion normally used to distinguish between them is the K-Factor. The K-factor is a dimensionless constant defined as:

<math>K=\frac{q B \lambda_u}{2 \pi \beta m c}</math>

where ''q'' is the charge of the particle passing through the ID, ''B'' is the peak magnetic field of the ID, ''<math>\lambda_u</math>'' is the period of the ID, ''<math>\beta=v/c</math>'' relates to the speed, or energy of the particle, ''m'' is the mass of the accelerated particle, and ''c'' is the [[speed of light]].

Wigglers are deemed to have K>>1 and undulators to have K<1.

The K-Factor determines the energy of radiation produced, and in situations where a range of energy is required the K-number can be modified by varying the strength of the magnetic field of the device. In permanent magnet devices this is usually done by increasing the gap between the magnet arrays. In electromagnetic devices the magnetic field is changed by varying the current in the magnet coils.

In a [[wiggler (synchrotron)|wiggler]] the period and the strength of the magnetic field is not tuned to the frequency of radiation produced by the electrons. Thus every electron in a bunch radiates independently, and the resulting [[Bandwidth (signal processing)|radiation bandwidth]] is broad. A wiggler can be considered to be series of [[bending magnet]]s concatenated together, and its radiation intensity scales as the number of magnetic poles in the wiggler.

In an [[undulator]] source the radiation produced by the oscillating electrons interferes constructively with the motion of other electrons, causing the radiation spectrum to have a relatively narrow bandwidth. The intensity of radiation scales as <math>N^2</math>, where <math>N</math> is the number of poles in the magnet array.

The wavelength <math>\lambda</math> of the radiation emitted by an insertion device can be calculated using the ''undulator equation'':

:<math>\lambda =  \frac{\lambda_u}{2 \gamma^2} \left(1 + \frac{K^2}{2} + (\theta \gamma)^2 \right) </math>

where <math>\gamma = \frac{1}{\sqrt{1-\beta^2}}</math> is the [[Lorentz factor]], <math>\lambda_u</math> the undulation period, ''K'' the K-factor as described above, and <math>\theta</math> the angle measured from the center of the radiated lobe. 

Despite its name the equation holds true for both undulators and wigglers.