Chapter 3
Synchrotron Radiation Fundamentals
3.1 Introduction
Synchrotron radiation has many useful properties, including high-average power,
narrow angular collimation, and a spectral range that can include peak output
across the X-ray region. These properties all derive from the fact that the particles
are relativistic, traveling very close to the speed of light. For most users, a qualitative
understanding of the terms and concepts in the next section will suffice.
Although there are no sharp divides among synchrotron sources, for practical
purposes, we can distinguish between broadband sources, such as bend magnets and
wigglers and more narrow band sources such as undulators and free-electron lasers
(Fig. 3.1). In this chapter, we present a qualitative treatment of the broadband
sources, followed (without derivation) by rigorous equations and graphs for the
source properties. The same approach is then used for undulator radiation. We save
free electron lasers for Chap. 12.
What do we really need to know? To understand synchrotron radiation, the most
important fact is that the accelerated electrons are traveling close to the speed of
light—they are “relativisitic.” In fact, the particle speed is so close to the speed of
light that the ratio of v/c ¼ β ¼ 0.99999. . . (typically 7 or 8 9’s). Thus, a more useful
measure of the relativistic nature of an electron is the Lorentz factor γ, which can be
expressed in terms of the particle velocity and the speed of light, or as the ratio of its
total energy E to its rest mass energy m 0 c
2
.
γ ¼
ffiffiffiffiffiffiffiffiffiffiffiffi ffi
1 À
v 2
c 2
r
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffi
1 À β
2
q
¼
E
m 0 c 2 ¼
E GeV
½
0:511 MeV
½
¼ 1957E GeV
½
ð3:1Þ
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_3
39
Synchrotron Radiation Fundamentals
3.1 Introduction
Synchrotron radiation has many useful properties, including high-average power,
narrow angular collimation, and a spectral range that can include peak output
across the X-ray region. These properties all derive from the fact that the particles
are relativistic, traveling very close to the speed of light. For most users, a qualitative
understanding of the terms and concepts in the next section will suffice.
Although there are no sharp divides among synchrotron sources, for practical
purposes, we can distinguish between broadband sources, such as bend magnets and
wigglers and more narrow band sources such as undulators and free-electron lasers
(Fig. 3.1). In this chapter, we present a qualitative treatment of the broadband
sources, followed (without derivation) by rigorous equations and graphs for the
source properties. The same approach is then used for undulator radiation. We save
free electron lasers for Chap. 12.
What do we really need to know? To understand synchrotron radiation, the most
important fact is that the accelerated electrons are traveling close to the speed of
light—they are “relativisitic.” In fact, the particle speed is so close to the speed of
light that the ratio of v/c ¼ β ¼ 0.99999. . . (typically 7 or 8 9’s). Thus, a more useful
measure of the relativistic nature of an electron is the Lorentz factor γ, which can be
expressed in terms of the particle velocity and the speed of light, or as the ratio of its
total energy E to its rest mass energy m 0 c
2
.
γ ¼
ffiffiffiffiffiffiffiffiffiffiffiffi ffi
1 À
v 2
c 2
r
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffi
1 À β
2
q
¼
E
m 0 c 2 ¼
E GeV
½
0:511 MeV
½
¼ 1957E GeV
½
ð3:1Þ
© Springer Nature Switzerland AG 2020
S. P. Cramer, X-Ray Spectroscopy with Synchrotron Radiation, Biological and Medical
Physics, Biomedical Engineering, https://doi.org/10.1007/978-3-030-28551-7_3
39