  The evolution of beam phase space in ionization-induced injection into plasma
wakefields is studied using theory and particle-in-cell (PIC) simulations. The
injection process causes special longitudinal and transverse phase mixing
leading initially to a rapid emittance growth followed by oscillation, decay,
and eventual slow growth to saturation. An analytic theory for this evolution
is presented that includes the effects of injection distance (time),
acceleration distance, wakefield structure, and nonlinear space charge forces.
Formulas for the emittance in the low and high space charge regimes are
presented. The theory is verified through PIC simulations and a good agreement
is obtained. This work shows how ultra-low emittance beams can be produced
using ionization-induced injection.
