  The ionization of xenon atoms subjected to 42fs, 800nm pulses of radiation
from a Ti:Sapphire laser was investigated. In our experiments a maximum laser
intensity of $\sim2\times 10^{15} \textrm{W}/\textrm{cm}^2$ was used. Xenon
ions were measured using a time-of-flight ion mass spectrometer having an
entrance slit with dimensions of $12\mu \textrm{m} \times 400\mu \textrm{m}$.
The observed yields $\textrm{Xe}^{n+} (n=1-7)$ were partially free of spatial
averaging. The ion yields showed sequential and nonsequential multiple
ionization and dip structures following saturation. To investigate the dip
structures and to perform a comparison between experimental and simulated data,
with the goal of clarifying the effects of residual spatial averaging, we
derived a hybrid analytical-numerical solution for the integration kernel in
restricted focal geometries. We simulated xenon ionization using
Ammosov-Delone-Krainov and Perelomov-Popov-Terent'ev theories and obtained
agreement with the results of observations. Since a large number of experiments
suffer from spatial averaging, the results presented are important to correctly
interpret experimental data by taking into account spatial averaging.
