  We show using particle-in-cell (PIC) simulations and theoretical analysis
that a high-quality electron beam whose density is modulated at angstrom scales
can be generated directly using density downramp injection in a periodically
modulated density in nonlinear plasma wave wakefields. The density modulation
turns on and off the injection of electrons at the period of the modulation.
Due to the unique longitudinal mapping between the electrons' initial positions
and their final trapped positions inside the wake, this results in an electron
beam with density modulation at a wavelength orders of magnitude shorter than
the plasma density modulation. The ponderomotive force of two counter
propagating lasers of the same frequency can generate a density modulation at
half the laser wavelength. Assuming a laser wavelength of $0.8\micro\meter$,
fully self-consistent OSIRIS PIC simulations show that this scheme can generate
high quality beams modulated at wavelengths between 10s and 100 angstroms. Such
beams could produce fully coherent, stable, hundreds of GW X-rays by going
through a resonant undulator.
