2.1 Backward Compton Scattering
A high energy photon beam can be produced by a head-on collision between a low energy photon beam and a high energy electron beam. Through the Compton scattering, the momentum of one electron is transferred to one incident photon and the photon is scattered in the backward direction with large momentum. This process is called backward Compton scattering (BCS). Fig.2.2.1 is a schematic view of the backward
Compton scattering.
Fig.2.2.1 Backward Compton scattering.
Since the Compton scattering is an elastic scattering, the energy of scattered photon is uniquely determined by the scattering angle as k
2

( 1
  e k
1
( 1
 cos

)

 k
1 e
)
( 1
 cos
E e

)
, where
 e
= v e
/ c and v e
is the speed of initial electron. The maximum value of k
2
is obtained for

=0 and it is written as follows. k
2
 m e
2
4 k
1
E e
2

4 k
1
E e
The energy of the BCS photon ( k
2
) becomes higher for the higher electron energy (E e
) and higher incident photon energy ( k
1
). At SPring-8, the energy of the electrons circulating in the storage ring is fixed at 8.0 GeV (7.975 GeV). The maximum energy of the BCS photon for Ee=8.0 GeV is shown in Fig.2.1.2 as a function of the wavelength of incident photon. When an ultraviolet (UV) laser (

=351 nm or 355 nm) and deep-UV
(257 nm) laser is used, the maximum photon energy is 2.4 GeV and 2.96 GeV, respectively. If we use an X-ray beam, instead of UV lasers, the energy of BCS photon becomes much higher and close to the initial electron energy. In the Fig.2.1.2, the corresponding wavelengths are pointed for some typical X-ray energy (100 eV and 1 keV).

Fig. 2.1.2 The maximum energy of the backward Compton photon beam as a function of the wavelength of incident photon.
Fig. 2.1.3 and 2.1.4 shows the cross section for the Compton scattering which is representing the energy spectra of the BCS photon beam. For the laser injection (Fig.
2.1.3), the energy distributions are roughly flat and have a peak at the maximum photon energy. This flat energy distribution is one of the advantages of the BCS photon beam over the bremsstrahlung photon because the beam does not contain large amount of low-energy photon which can be a source of background, especially for the detectors placed in the forward direction. For the X-ray injection (Fig. 2.1.4), the peaking structure is stronger.
Fig.2.1.3 Cross sections for the Compton scattering between an UV laser photon and 8-
GeV electron.

Fig.2.1.4 Cross sections for the Compton scattering between X-ray (100 eV, 1 keV) and 8-GeV electron.
When the injected photon is polarized, the polarization is transferred to the scattered photon. The polarization of the BCS photon is also uniquely determined by the scattering angle. In Fig. 2.1.5, the linear and circular polarizations of the BCS photon beam are plotted as a function of the photon energy for the laser injection case. It is assumed that the incident laser is 100% polarized. Polarizations are high at the maximum energy. Since the laser photon is 100% polarized in principle, it is easy to obtain highly (~100%) polarized gamma beam. For the linear polarization, the maximum polarization depends on the energy of the incident photon and it does not reach to 100% even at the endpoint energy. However, it is still high in the wide energy region in the laser injection case. Through the photon energies in the acceptance of the tagging system (1.5 < E  < E max
) the linear polarization can be kept high. The energy dependence of the maximum linear polarization is more significantly seen for the X-ray injection case shown in Fig. 2.1.6. The maximum polarization is only 15% for the 100eV X-ray injection and 1.5% for 1-keV X-ray. So it is hard to expect highly and linearly polarized photon beam with the X-ray injection. On the other hand, the circularly polarized beam can be obtained by using X-ray from produced by helical undulators.
Technical details of the BCS photon production are described in the following sections.

Fig. 2.1.5 Polarization of the BCS photon produced by laser injection.
Fig.2.1.6 Polarization of the BCS photon produced by X-ray injection.
(photon beam intensity has not been written

here or each (laser, X-ray) section? )
(Overview of the beamline should be written here?)