1 X-Ray Sources at Large-Scale Facilities
17
The broadband bending magnet spectra for three different combinations of storage
ring energy and magnetic field strength are shown in Fig. 1.12. Particularly at low- and
medium-energy facilities, the maximum values of both these quantities are too small
to extend the spectrum far into the hard X-ray regime. However, if superconducting
magnets with larger magnetic field strengths are employed, the photon energy range
can be extended to harder X-radiation, as the critical energy is proportional to the
magnetic field strength. Moreover, the radiative power increases with the square of
the magnetic field strength B. These so-called ‘superbends’ can have magnetic field
strengths as high as 8 T.
There are two types of insertion devices, distinguished from each other by the
amount that the electrons are forced to deviate in a slalom-like path from a purely
straight path. This at first seemingly subtle distinction has a fundamental effect on
the nature of the radiation, however. For angular excursions substantially larger than
the synchrotron radiation’s natural opening angle γ
−1 , the radiation cones from each
magnet in the insertion device do not overlap. Under these conditions, the intensities
produced from each dipole are added and the ID is referred to as a wiggler, which is
briefly described below.
For gentler excursions of the order of γ
−1 , the ID is called an undulator, described
in Sect. 1.3.2.
The maximum angular deviation φ max of the electron oscillations in an ID is
defined by the dimensionless ‘magnetic deflection parameter’ K , given by
φ max = K /γ .
(1.25)
K can be expressed in terms of the maximum magnetic field B 0 as
K =
eB 0
m e ck u,w
= 0.934 λ u,w [cm] B 0 [T] ,
(1.26)
where λ u or λ w are the periods of the oscillations in the undulator or wiggler, respectively, and k u,w = 2π/λ u,w . For a wiggler, K is typically between 10 and 50, while
for undulators, K is close to unity and changes according to the size of the gap
between the upper and lower magnet arrays. The horizontal spread in the electron
beam divergence is
θ x = 2K /γ .
(1.27)
So, for example, a wiggler having K = 20, operating in a 4 GeV storage ring would
have a horizontal divergence of 5.2 mrad (0.30
◦ ).
A wiggler can be thought of as being a series of bending magnets within a straight
section of the storage ring that turns the electrons alternately to the left and to the
right. The maximum angular excursion from the central axis is larger than the natural
opening angle of the radiation, γ
−1 . For each oscillation, the electrons are twice
moving parallel to (and in reality also very close to) this axis. The radiation is therefore
enhanced by a factor of 2N , where N is the total number of wiggler periods and is of
17
The broadband bending magnet spectra for three different combinations of storage
ring energy and magnetic field strength are shown in Fig. 1.12. Particularly at low- and
medium-energy facilities, the maximum values of both these quantities are too small
to extend the spectrum far into the hard X-ray regime. However, if superconducting
magnets with larger magnetic field strengths are employed, the photon energy range
can be extended to harder X-radiation, as the critical energy is proportional to the
magnetic field strength. Moreover, the radiative power increases with the square of
the magnetic field strength B. These so-called ‘superbends’ can have magnetic field
strengths as high as 8 T.
There are two types of insertion devices, distinguished from each other by the
amount that the electrons are forced to deviate in a slalom-like path from a purely
straight path. This at first seemingly subtle distinction has a fundamental effect on
the nature of the radiation, however. For angular excursions substantially larger than
the synchrotron radiation’s natural opening angle γ
−1 , the radiation cones from each
magnet in the insertion device do not overlap. Under these conditions, the intensities
produced from each dipole are added and the ID is referred to as a wiggler, which is
briefly described below.
For gentler excursions of the order of γ
−1 , the ID is called an undulator, described
in Sect. 1.3.2.
The maximum angular deviation φ max of the electron oscillations in an ID is
defined by the dimensionless ‘magnetic deflection parameter’ K , given by
φ max = K /γ .
(1.25)
K can be expressed in terms of the maximum magnetic field B 0 as
K =
eB 0
m e ck u,w
= 0.934 λ u,w [cm] B 0 [T] ,
(1.26)
where λ u or λ w are the periods of the oscillations in the undulator or wiggler, respectively, and k u,w = 2π/λ u,w . For a wiggler, K is typically between 10 and 50, while
for undulators, K is close to unity and changes according to the size of the gap
between the upper and lower magnet arrays. The horizontal spread in the electron
beam divergence is
θ x = 2K /γ .
(1.27)
So, for example, a wiggler having K = 20, operating in a 4 GeV storage ring would
have a horizontal divergence of 5.2 mrad (0.30
◦ ).
A wiggler can be thought of as being a series of bending magnets within a straight
section of the storage ring that turns the electrons alternately to the left and to the
right. The maximum angular excursion from the central axis is larger than the natural
opening angle of the radiation, γ
−1 . For each oscillation, the electrons are twice
moving parallel to (and in reality also very close to) this axis. The radiation is therefore
enhanced by a factor of 2N , where N is the total number of wiggler periods and is of