  An efficient numerical algorithm for the laser driven multi-level ionization
of high-atomic-number gases is proposed and implemented in an electromagnetic
particle-in-cell code SPACE. The algorithm is based on analytical solutions to
the system of differential equations describing ionization evolution. Using
analytical solutions resolves the multiscale issue of ionization due to
different characteristic time scales of ionization processes and the main code
time step. Algorithm efficiency is improved by using a locally-reduced system
of differential equations. The effects of the orbital quantum numbers and their
projections have been examined. The algorithm is applied to the study of
ionization injection of electrons into laser-driven plasma wakefields.
