Electron and Optical Physics Division

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Far Ultraviolet Physics Group / Synchrotron Ultraviolet Radiation Facility SURF III

The Far Ultraviolet Physics Group maintains and improves the Synchrotron Ultraviolet Radiation Facility SURF III.


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Synchrotron Radiation

What is Synchrotron Radiation?

Synchrotron radiation is the electromagnetic radiation emitted when charged particles travel in curved paths. Because in most accelerators the particle trajectories are bent by magnetic fields, synchrotron radiation is also called Magneto-Bremsstrahlung. The emitted spectrum is broadband from the microwave (harmonics of the driving RF field) to x-ray spectral regions. The radiation is vertically collimated and polarized. The synchrotron radiation output can be calculated if the electron energy, bending radius, electron current, angle relative to the orbital plane, the distance to the tangent point and vertical and horizontal acceptance angles are known.

Properties of Synchrotron Radiation

Schwinger derived a formalism which allows us to calculate the synchrotron radiation spectrum and other properties like its distribution in space. For SURF, the equation for the radiation power is given by
Schwinger equation
(Eq. 1)

The radiation power is a function of the wavelength λ, electron energy γ = (E/mec 2) angle relative to the orbital plane ψ0, bending radius ρ, bandpass Δλ, horizontal acceptance angle Δθ, the vertical acceptance angle Δψ, and the electron beam current IB.

The function ξ is defined by ξ(λ,ψ) = (λc /2λ) [1 + (λψ)2]2. Values for the elementary charge e0 and the electric constant ε0 can be found on the NIST Physical Measurement Laboratory Web Site Fundamental Constants. The functions K1/3[ξ(λ,γ)] and K2/3[ξ(λ,γ)] are modified Bessel functions of fractional order.

Synchrotron Radiation Spectrum

Using (Eq. 1) the synchrotron radiation spectrum for SURF can be calculated. Assuming a bandpass of 1% of the wavelength, a horizontal acceptance angle of 50 mrad, a vertical half acceptance angle of 25 mrad, 0 mrad tilt from the orbital plane, beam current 100 mA, electron energies from 380 MeV to 78 MeV, and an orbital radius of 0.8372 m the output power of SURF is illustrated in figure 1.

Calculate the synchrotron radiation spectrum using equation 1 using JavaScript !  

Synchrotron Radiation Spectrum emitted by SURF at 380 MeV, 331 MeV, 284 MeV, 234 MeV, 183 MeV, 134 MeV, and 78 MeV in comparison to a 3000 K blackbody.
Figure 1: Synchrotron Radiation Spectrum emitted by SURF at 380 MeV, 331 MeV, 284 MeV, 234 MeV, 183 MeV, 134 MeV, and 78 MeV in comparison to a 3000 K blackbody.

Vertical Angular Distribution and Polarization

Equation 1 can be used to calculate the vertical angular spread of the synchrotron radiation and its polarization. The radiation power with polarization parallel to the orbital plane is given by
Schwinger equation
(Eq. 2)

and the radiation power with polarization perpendicular to the orbital plane is given by
Schwinger equation
(Eq. 3)

Calculate the vertical angular distribution of synchrotron radiation using JavaScript !  
Vertical angular spread of the synchrotron radiation at SURF for 10 nm, 100 nm, and 1000 nm wavelength at 380 MeV.
Figure 2: Vertical angular spread of the synchrotron radiation at SURF for 10 nm, 100 nm, and 1000 nm wavelength at 380 MeV.


  1. J. Schwinger, Phys. Rev. 75, 1912 (1949).
  2. H. Wiedemann, Particle Accelerator Physics (Springer, New-York, 1993), p. 300.
  3. H. Wiedemann, Particle Accelerator Physics II (Springer, New-York, 1995), p. 229.
  4. H. Winick, Synchrotron Radiation Sources (World Scientific, Singapore, 1994).
  5. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in C (Cambridge University Press, Cambridge, 1992).

Return to: Physical Measurement Laboratory | Electron & Optical Physics Division | Synchrotron Ultraviolet Radiation Facility

Online: May 2002   Last update: June 2003
Uwe Arp.