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.
Full exploitation of emittance exchange (EEX) requires aberration-free performance of a complex imaging system including active radio-frequency (RF) elements which can add temporal distortions. We investigate the performance of an EEX line where the
exchange occurs between two dimensions with normalized emittances which differ by multiple orders of magnitude. The transverse emittance is exchanged into the longitudinal dimension using a double dog-leg emittance exchange setup with a five cell RF deflector cavity. Aberration correction is performed on the four most dominant aberrations. These include temporal aberrations that are corrected with higher order magnetic optical elements located where longitudinal and transverse emittance are coupled. We demonstrate aberration-free performance of an EEX line with emittances differing by four orders of magnitude, textit{i.e.} an initial transverse emittance of 1~pm-rad is exchanged with a longitudinal emittance of 10~nm-rad.
