Intensity and Polarisation of Synchrotron Radiation from a Helical Undulator

1
Intensity and Polarisation of Synchrotron
Radiation from a Helical Undulator

• Lei Zang
• 26 March 2008

2
Undulator

• Undulator is an extension of the multipole
  wiggler
• The photon emitted in a narrow forward cone
• The photons intensity and the polarisation are
  what we feel interest

3
Kincaid Equation

• The energy radiated per unit bandwidth by one
  electron into a solid angle (brightness per
  electron)

Equation (1)
Helical orbit of electron in helical magnetic
filed, showing angles and other parameters used
in equation
4
Kincaid Equation

• we can drive equation (1) to a more practicable
  expression
• Where symbols are as defined by Kincaid.

Equation (2)
The spectrum consists of a series of harmonics of
the fundamental frequency ?1, with the intensity
of the nth harmonic given by the nth term in
series
5

• Equation (2) can be integrated over all angles to
  produce an expression for the frequency.

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Polarisation-Stoke Parameters

• Stoke parameters can be expressed in terms of the
  radiation amplitudes as follows

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Polarisation

• the polarization is given, as a function of
  photon frequency and angle, by

The overall degree, or fraction of polarisation
By J.C Sheppard
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I(?)

• From Richard Walkers notation, the expression
  for the total intensity

?/?2?0
9

• Work out the proper expression of Ax and Ay
• With help of Ax, Ay, plot the power spectrum
• Get the polarisation rate
• Consider implement of polarisation in FLUKA