Influence of the electron beam emittance on the polarization of a laser-electron x-ray generator

In this paper we analyze the polarization of the x-ray radiation coming from laser-electron x-ray generator (LEXG). We obtain general relations connecting the polarization state of outgoing x-ray radiation to the polarization state of laser beam as well as to the parameters of electron beam. We demonstrate that finite electron beam emittance causes a partial depolarization of initially fully polarized x-ray radiation even when the laser beam is fully polarized. We demonstrate with a number of numerical experiments that finite electron beam emittance can in some cases fundamentally alter the polarization state of x-ray radiation as compared to the polarization state of x-ray radiation scattered by electron beam with a zero emittance. Possible applications of polarized LEXG’s radiation are discussed.

Figure 1

The scheme of electron beam—laser beam interaction in LEXG. Three coordinate systems used [see (32)–(37)] as well as angles, vectors, and shifts are shown.

Figure 2

The x-ray spectral brilliance for three observation angles $\theta$ and the corresponding electron beam energies. The angles and energies were chosen to produce the radiation peaks at the same energy of 30 keV.

Figure 3

The x-ray radiation polarization degree for three observation angles $\theta$ and the corresponding electron energies as function of the x-ray radiation energy. The angles and energies were chosen to produce the radiation peaks at the same energy of 30 keV, as in Fig. 2.

Figure 4

The x-ray radiation polarization degree for the three electron beam energies (and corresponding observation angles) from Fig. 3 and two x-ray energies as function of the observation angle.

Figure 5

The x-ray radiation polarization degree for the three electron beam energies (and corresponding observation angles) from Fig. 3 and two x-ray energies as function of the electron and laser beam waist radii, which were considered equal. The waist radii were varied by adjusting the beta-function and Rayleigh length.

Figure 6

The x-ray radiation polarization degree for three electron beam energies (and corresponding observation angles) and two x-ray energies from Fig. 3 as function of the relative electron energy spread $\mathrm{\Delta }\gamma /\gamma$ (top) or electron beam emittance (bottom).

Figure 7

The Stocks parameters ${\xi }_1$ and ${\xi }_3$ as well as the polarization degree as function of the x-ray energy. The observation angle was 5.6 mrad. The electron beam emittance was zero (top) or not zero (bottom).