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.



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
MagnetoBremsstrahlung. The emitted spectrum is broadband from the microwave
(harmonics of the driving RF field) to xray 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


(Eq. 1)

The radiation power is a function of the wavelength λ, electron energy
γ =
(E/m_{e}c^{ 2}) angle relative to
the orbital plane ψ_{0}, bending
radius ρ, bandpass
Δλ, horizontal acceptance angle Δθ, the vertical acceptance
angle Δψ, and the electron beam current
I_{B}.
The function ξ is defined by ξ(λ,ψ) = (λ_{c }/2λ) [1 +
(λψ)^{2}]^{2}. Values for the elementary charge
e_{0} and the electric constant ε_{0} can be found on the NIST Physical Measurement Laboratory Web Site
Fundamental
Constants. The functions
K_{1/3}[ξ(λ,γ)] and K_{2/3}[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 !


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 


(Eq. 2) 
and the radiation power with polarization perpendicular to the orbital plane is
given by 

(Eq. 3) 
Calculate the vertical angular distribution of synchrotron radiation using JavaScript !


Figure 2: Vertical angular spread of the synchrotron radiation at SURF
for 10 nm, 100 nm, and 1000 nm wavelength at 380 MeV.

References
 J. Schwinger, Phys. Rev. 75, 1912 (1949).
 H. Wiedemann, Particle Accelerator Physics (Springer, NewYork, 1993),
p. 300.
 H. Wiedemann, Particle Accelerator Physics II (Springer,
NewYork, 1995), p. 229.
 H. Winick, Synchrotron Radiation Sources (World Scientific,
Singapore, 1994).
 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.

