  Non-equilibrium ionization (NEI) is a key process often times neglected when
modeling astrophysical plasmas with thermodynamical timescales much shorter
than the timescales for ionization and recombination. In this paper, we perform
NEI modeling on a magnetohydrodynamic (MHD) simulation of the solar wind during
the Whole Sun Month (Carrington Rotation 1913 from 1996 August 22 to September
18), and compare the resulting charge state distributions with in situ
measurements made with the Solar Wind Ion Composition Spectrometer (SWICS) on
Ulysses. We trace the wind trajectory back to 20$R_\odot$ using the velocity
measured by Ulysses at about 4 AU, and obtain the plasma flow trajectory within
20$R_\odot$ using the MHD simulation data performed by Predictive Science Inc.
We assume that the wind started from the solar surface and was initially in
ionization equilibrium, and analyze the time-dependent ionization state of
solar wind along each of the trajectories. In our analysis we: (1) obtain
charge state densities and ratios for slow and fast winds based on the NEI
model, and compare them with in situ observations; and (2) measure the
"freeze-in" distance for several ions observed by SWICS to determine a possible
correlation between when the ionization states become fixed and the electron
density and outward velocity of the plasma at the freeze-in height. This study
provides a stringent test on comparing charge state distributions from the
outer corona predicted from simulations with in situ measurements made in the
far heliosphere. This showcases the challenges in matching plasma conditions
near the corona to those observed in interplanetary space.
