16
P. R. Willmott
Fig. 1.11 K 2/3 (x), the
modified Bessel function of
the second kind for order 2/3
10
-2
10
-1
10
0
10
1
x
10
-12
10
-10
10
-8
10
-6
10
-4
10
-2
10
0
10
2
K
2/3
(x)
Fig. 1.12 Bending -magnet
spectra for on-axis
horizontally polarized
radiation for three different
combinations of the storage
ring energy and magnetic
field strength. Reproduced
from [3] with permission
(Copyright 2019, John Wiley
and Sons)
1
10
100
Photon energy [keV]
10
11
10
12
10
13
10
14
10
15
Photons/s/mrad
2
/0.1% BW
2 GeV, 4 T
4 GeV, 1 T
6 GeV, 1.25 T
radiation, measured in degrees, allows one to accommodate more than one so-called
‘bending-magnet beamline’ at a single bending magnet.
The spectral flux distribution is given by
ph/s
(mrad) 2 0.1% BW
= 1.325 × 10 10 I e [mA]E 2 [GeV]
E
E c
2
K 2/3
E
2E c
, (1.24)
where E c = 3eBγ
2
/2m e is the so-called critical, or characteristic, energy (which
in practical units can be expressed as E c [eV] = 665.023 B[T] E
2
[GeV
2
]), and
K 2/3 (x = E/2E c ) is the modified Bessel function of the second kind for nonintegral
order (in this instance, 2/3), shown in Fig. 1.11.
The spectral flux is thus determined by the storage ring energy and the magnetic
field strength. Increasing B (but keeping E constant) shifts the maximum of the
spectrum to higher photon energies but does not increase the spectral flux’s maximum.
In contrast, only increasing E both shifts the spectral maximum to higher photon
energies and higher values.