interference between radiation from pairs of poles with particles traveling in opposite
directions. However, the direction of this polarization varies rapidly with angle, so
that when averaging over finite angles, the degree of polarization, becomes, as given
by Kim:
P pol ¼
1 þ X
2
À
Á
K
2
2=3 η
ð Þ À X
2 K
2
1=3 η
ð Þ
1 þ X
2
À
Á
K
2
2=3 η
ð Þ þ X
2 K
2
1=3 η
ð Þ
ð3:35Þ
where X ¼ γψ and η ¼
1
2
ω
ω C
1 þ X
2
À
Á 3=2 [75]. In practice, the polarized nature of
off-axis wiggler radiation is never really used.
3.6 Undulator Radiation: A Qualitative Approach
When is an insertion device an undulator instead of a wiggler? We saw that if the
field is high and the period is long, the angular deflection of the beam is relatively
large, K is »1, and the device is called a wiggler. When K 1, δ is relatively small,
and the device is called an undulator. Although a wiggler might radiate more power,
that radiation comes from a large source and is spread out over a range of angles and
energies. In undulator mode, an insertion device puts most of its radiation in a small
range of angles and energies.
For many applications, brightness or spectral brightness is a better metric for the
quality of a synchrotron source. For a given amount of power, we can improve the
brightness by (1) decreasing the source size and (2) decreasing the beam divergence.
Furthermore, we can improve the spectral brightness by (3) putting more of the
source spectrum into a narrower bandpass. We will see below how an undulator
accomplishes all three of these goals.
We start with a qualitative analysis of planar undulator radiation. We then provide
the exact equations without detailed derivations, which are well documented in the
Fig. 3.8 The critical energy
for a wiggler source on a
3 GeV ring, as a function of
observation angle ϕ, for
different values of magnetic
field B in Tesla and magnet
period λ 0 in cm
52
3 Synchrotron Radiation Fundamentals