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Extra info for Advanced Light Source - Users Handbook
And K2=3 . / are displayed in Fig. 12. Harmonic Representation Synchrotron radiation is mostly emitted from a circular accelerator, and we should expect that the radiation is made up of many harmonics of the revolution frequency. Expression (50) can be transformed into a different formulation emphasizing the harmonic structure of the radiation spectrum. The equivalence between both formulations has been shown by Sokolov and Ternov (1968) expressing the modified Bessel’s functions K1=3 and K2=3 by regular Bessel’s functions of high order.
To the propagation v of the charge and set therefore a D ak C a? Insertion into (21) splits the total radiation power into two parts, and we get the synchrotron radiation power for parallel and transverse acceleration like Pk D 23 rc mc 6 2 ˇP k ; (28) P? D 23 rc mc 4 2 ˇP ? : (29) Both expressions look similar except for the energy dependence. The radiation power for longitudinal acceleration looks on first sight higher by a factor 2 . This, however, is deceiving. At highly relativistic energies, the same acceleration force leads to much less radiation if the acceleration is parallel to the motion of the particle compared to orthogonal acceleration.
We will ignore this regime in our further discussion of synchrotron radiation because we are interested only in free radiation which is not anymore connected to electric charges. It should be noted, however, that measurements of radiation parameters close to radiating charges may be affected by the presence of the Coulomb radiation fields. Such situations occur, for example, when radiation is observed close to the source point. Related theories deal with this mixing by specifying a formation length defining the minimum distance from the source required to sufficiently separate the Coulomb regime from the radiation regime.
Advanced Light Source - Users Handbook