Structured x-ray beams from twisted electrons by inverse Compton scattering of laser light

The inverse Compton scattering of laser light on high-energetic twisted electrons is investigated with the aim to construct spatially structured x-ray beams. In particular, we analyze how the properties of the twisted electrons, such as the topological charge and aperture angle of the electron Bessel beam, affect the energy and angular distribution of scattered x rays. We show that with suitably chosen initial twisted electron states one can synthesize tailor-made x-ray beam profiles with a well-defined spatial structure, in a way not possible with ordinary plane-wave electron beams.

Figure 1

Compton scattering of laser light on a beam of twisted electrons helps to generate x rays with tailor-made spatial intensity distributions. (a) The light from an optical laser is focused by a parabolic mirror and collides head on (under ${180}^{\circ }$) with electrons from a twisted beam (blue cone). The photons are mainly backscattered, frequency up-shifted to x-ray energies, and recorded on a CCD screen downstream of the beam of electrons. Plane-wave laser light is assumed with an extent in the focal plane much larger than the waist of the electron beam. (b) Definition of coordinates and angles that are used to characterize the propagation of electrons and photons in Compton scattering.

Figure 2

Energy distribution of scattered photons for Compton scattering of circularly polarized laser light with frequency $\omega =1.55$ eV on twisted electrons with initial energy $E=20.5$ MeV, i.e., $\gamma =40$, and for a cone aperture ${\theta }_p=0.05$. (a) The allowed energies ${\omega }_{-}^{\prime }\left({\vartheta }^{\prime }\right)\le {\omega }^{\prime }\le {\omega }_{+}\left({\vartheta }^{\prime }\right)$ of the scattered photons (shaded area) for the predominant scattering angles $0\le {\vartheta }^{\prime }\le 0.15$. For comparison, the dashed curve gives the known energy-angle correlation for plane-wave electrons, cf. Eq. (5). (b) Energy and angle-differential cross section $d{\sigma }_{\mathrm{tw}}/d{\Omega }^{\prime }d{\omega }^{\prime }$ for Compton scattering of plane-wave photons on twisted electrons as a function of the energy ${\omega }^{\prime }$ of the scattered photons, and for selected values of the photon scattering angle ${\vartheta }^{\prime }$.

Figure 3

Angle-differential cross section for (a) plane-wave electrons and (b) a beam of twisted electrons with aperture angle ${\theta }_p=0.05$ and with initial energy $E=20.5$ MeV, i.e., $\gamma =40$, in both cases. The laser light is linearly polarized along the $x$ axis and has the frequency $\omega =1.55$ eV.

Figure 4

Angle-differential cross section (21) for Compton scattering of plane-wave laser photons on a superposition of two equally intense beams of twisted electrons with given difference of the vortex charge $\Delta m$ and relative phase $\delta$; cf. Eq. (18). The scale of the $x$ and $y$ axes and the colors are the same as in Fig. 3. Results are shown for selected values of $\Delta m$ and $\delta =0$ for (a) circularly polarized laser light and (b) linearly polarized light along the $x$ axis. (c) The sensitivity of the cross section on the relative phase $\delta$ for fixed $\Delta m=4$ and linear laser polarization. The calculations were done for the same parameters as in Fig. 3.