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Manuscript Title: Spectral intensity, angular distribution and polarisation of synchrotron radiation from a monoenergetic electron.
Authors: J. Lang
Catalogue identifier: ACQR_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 1(1970)440
Programming language: Fortran.
Computer: ICL KDF9.
Operating system: EGDON 3.
RAM: 4K words
Word size: 48
Keywords: Sychrotron, Radiation, Polarisation, Sychrotron, Radiation, Polarisation, Angular Distribution, Intensity, Intensity spectral, Absolute intensity, Absolute source, Radiometry, Relativistic electron, Circular orbit, Bessel function, Series solution.
Classification: 2.3, 21.1.

Nature of problem:
The absolute power radiated by a relativistic electron travelling in a circular orbit in a synchrotron can be calculated theoretically. This program evaluates, for an electron of specified energy and orbit radius, the power radiated round the orbit (a) as a function of wavelength (i.e. spectral distributions), (b) as a function of the angle above or below the orbital plane at any particular wavelength. These angular distributions are given for the component polarised with E-vector in a plane parallel to the orbital plane and for the component polarised with E-vector in a plane perpendicular to the orbital plane.

Solution method:
The expressions used in the calculations are those given by Tomboulian and Hartman and which were orignally given by Schwinger in a slightly different form. Olsen and Westfold have shown how the angular distribution formula also gives the polarisation. The equations contain Bessel functions of the second kind (McDonald functions) Kn(s) of order n which are calculated from series expansions. The spectral distributions involve the integration of the functions of order 5/3 and the order distributions involve the squaring of functions of order 1/3 and 2/3.

The series method of solution of the Bessel functions means that the argument of Bessel function is prevented from exceeding six. For the spectral distributions the calculation is thus cut-off when the wave- length is 2.52 times down on the wavelength of peak power, the wave- lengths higher than that of the peak power being unaffected. For the angular distributions at a fixed wavelength. The restriction introduces a cut-off as the angle above or below the orbital plane is increased. However, at this cut-off the power is down by at least two orders of magnitude on the power at the peak of the angular distribution.

Running time:
The test case compiles in 22 seconds and takes 77 seconds to run on the Glasgow University KDF9.