  Ionization injection is attractive as a controllable injection scheme for
generating high quality electron beams using plasma-based wakefield
acceleration. Due to the phase dependent tunneling ionization rate and the
trapping dynamics within a nonlinear wake, the discrete injection of electrons
within the wake is nonlinearly mapped to discrete final phase space structure
of the beam at the location where the electrons are trapped. This phenomenon is
theoretically analyzed and examined by three-dimensional particle-in-cell
simulations which show that three dimensional effects limit the wave number of
the modulation to between $> 2k_0$ and about $5k_0$, where $k_0$ is the
wavenumber of the injection laser. Such a nano-scale bunched beam can be
diagnosed through coherent transition radiation upon its exit from the plasma
and may find use in generating high-power ultraviolet radiation upon passage
through a resonant undulator.

Plasma Physics;Accelerator Physics