Nanomodulated electron beams via electron diffraction and emittance exchange for coherent x-ray generation

We present a new method for generation of relativistic electron beams with current modulation on the nanometer scale and below. The current modulation is produced by diffracting relativistic electrons in single crystal Si, accelerating the diffracted beam and imaging the crystal structure, then transferring the image into the temporal dimension via emittance exchange. The modulation period can be tuned by adjusting electron optics after diffraction. This tunable longitudinal modulation can have a period as short as a few angstroms, enabling production of coherent hard x-rays from a source based on inverse Compton scattering with total accelerator length of approximately ten meters. Electron beam simulations from cathode emission through diffraction, acceleration, and image formation with variable magnification are presented along with estimates of the coherent x-ray output properties.

Figure 1

Schematic of the compact coherent x-ray source with rf photo-injector, electron diffraction crystal, X-band linac, EEX line and ICS laser interaction area. Entire assembly is approximately 10 m long.

Figure 2

(a) Scattering geometry for an incident particle. (b) The phase space of the incident electron bunch immediately prior to the target. (c) The calculated diffraction for the electron bunch from the rf photo-injector plotted as the relative density of electrons in the transverse phase space. With the thickness of the single crystal Si at $t=\xi /2$, 98% of the beam undergoes one scattering event (upper panel). The remaining electrons (lower panel) did not scatter.

Figure 3

(a) The single crystal Si grating. (b) The forward scattered (0th order) electron beam (with mean transverse momentum equal to the Bragg angle removed).

Figure 4

The calculated $b_0$ with $\sim 150\mathrm{nm}$ spacing for the forward scattered (0th order) electron beam.

Figure 5

(a) Individual electrons imaged after magnification and acceleration at the entrance of the EEX line. (b) Full transverse density profile of the electron bunch visualized as a two dimensional histogram of particle count in the simulation.

Figure 6

(a) The bunching factor (b) and the relative phase in radians as a function of the transverse position in the beam.

Figure 7

(a) Individual electrons imaged after demagnification and acceleration at the entrance of the EEX line. (b) The bunching factor as a function of the transverse position in the beam.

Figure 8

The relative density of the electron bunch for the longitudinal phase space (a) before and (b) after emittance exchange.

Figure 9

The bunching factor for the electron bunch modulation at 1.24 nm after the EEX line. The depth of field is 4 mm, approximately ten times the gain length or four times the nominal laser pulse length.

Figure 10

(a) Phase-contrast modulation as a function of incident angle and transverse position. (b) Integrated phase-contrast modulation over the incident electron distribution (${\sigma }_{x^{\prime }}\approx 50\mu \mathrm{rad}$) at the exit of the Si crystal.

Figure 11

(a) Added phase as a function of the angle of divergence for a focal length of 4 mm and a $\mathrm{\Delta }E/E=1.3\times {10}^{-5}$. (b) Electron population in phase-contrast image propagated through a lens with a focal length of 4 mm for the initial conditions in Fig. 10.