P kW
½ ¼ 1:266E
2
e GeV
½
I A
½ B
2
0 T
½ L m
½
ð3:65Þ
Finally, (from Kim) the power density radiated in the forward direction is:
d
2 P
d
2
ϕ
¼
Ne
2
πε 0 c
γ
4 I
e
ω u
K
2
1 þ K
2
À
Á 3
ð3:66Þ
or (from Clarke) in practical units:
d
2 P
dΩ
W mrad
À2
Â
à ¼ 4626
E
4
e GeV
½
I A
½ B
2
0 T
½ L m
½
1 þ K
2
À
Á 3
ð3:67Þ
Notice that the on-axis flux goes towards zero at high K-values, because most of the
power goes into higher harmonics, which are forbidden in the forward direction.
3.10 Other Insertion Devices
As mentioned in Chap. 2, a bevy of other insertion devices have been designed and
implemented, but none approach the popularity of the three main designs: wiggler,
planar undulator, and EPU. For more information about the radiation properties of
so-called exotic insertion devices, consult the excellent chapters by Onuki [82] and
Sasaki [80].
3.11 Suggested Exercises
1. Do the math on Δt ¼ κΔt
0
¼ (1 À β cos θ)Δt
0 to show that κ ffi
1
2
1
γ 2 þ θ
2
; θ ( 1.
2. Do the math to derive an improvement over undulator equation λ ¼ λ 0 (1 À βcosθ),
by replacing β with βÃ, starting from:
β z,av ¼ βà ¼ β 1 À
K
2
4γ 2
¼ 1 À
1
2γ 2 1 þ
K
2
2
3. Consider a dipole magnet with a field of 2 Tesla on an electron storage ring with
an electron energy of 2 GeV.
(a) What is the critical energy for the synchrotron radiation from this magnet?
(b) What is the degree of circular polarization at a vertical angle of 0.3 mrad for
100 eV photons?
66
3 Synchrotron Radiation Fundamentals
½ ¼ 1:266E
2
e GeV
½
I A
½ B
2
0 T
½ L m
½
ð3:65Þ
Finally, (from Kim) the power density radiated in the forward direction is:
d
2 P
d
2
ϕ
¼
Ne
2
πε 0 c
γ
4 I
e
ω u
K
2
1 þ K
2
À
Á 3
ð3:66Þ
or (from Clarke) in practical units:
d
2 P
dΩ
W mrad
À2
Â
à ¼ 4626
E
4
e GeV
½
I A
½ B
2
0 T
½ L m
½
1 þ K
2
À
Á 3
ð3:67Þ
Notice that the on-axis flux goes towards zero at high K-values, because most of the
power goes into higher harmonics, which are forbidden in the forward direction.
3.10 Other Insertion Devices
As mentioned in Chap. 2, a bevy of other insertion devices have been designed and
implemented, but none approach the popularity of the three main designs: wiggler,
planar undulator, and EPU. For more information about the radiation properties of
so-called exotic insertion devices, consult the excellent chapters by Onuki [82] and
Sasaki [80].
3.11 Suggested Exercises
1. Do the math on Δt ¼ κΔt
0
¼ (1 À β cos θ)Δt
0 to show that κ ffi
1
2
1
γ 2 þ θ
2
; θ ( 1.
2. Do the math to derive an improvement over undulator equation λ ¼ λ 0 (1 À βcosθ),
by replacing β with βÃ, starting from:
β z,av ¼ βà ¼ β 1 À
K
2
4γ 2
¼ 1 À
1
2γ 2 1 þ
K
2
2
3. Consider a dipole magnet with a field of 2 Tesla on an electron storage ring with
an electron energy of 2 GeV.
(a) What is the critical energy for the synchrotron radiation from this magnet?
(b) What is the degree of circular polarization at a vertical angle of 0.3 mrad for
100 eV photons?
66
3 Synchrotron Radiation Fundamentals