  A physical model based on a Monte-Carlo approach is proposed to calculate the
ionization dynam- ics of warm dense matters (WDM) within particle-in-cell
simulations, and where the impact (col- lision) ionization (CI), electron-ion
recombination (RE) and ionization potential depression (IPD) by surrounding
plasmas are taken into consideration self-consistently. When compared with
other models, which are applied in the literature for plasmas near thermal
equilibrium, the temporal re- laxation of ionization dynamics can also be
simulated by the proposed model. Besides, this model is general and can be
applied for both single elements and alloys with quite different composi-
tions. The proposed model is implemented into a particle-in-cell (PIC) code,
with (final) ionization equilibriums sustained by competitions between CI and
its inverse process (i.e., RE). Comparisons between the full model and model
without IPD or RE are performed. Our results indicate that for bulk aluminium
in the WDM regime, i) the averaged ionization degree increases by including
IPD; while ii) the averaged ionization degree is significantly over estimated
when the RE is neglected. A direct comparison from the PIC code is made with
the existing models for the dependence of averaged ionization degree on thermal
equilibrium temperatures, and shows good agreements with that generated from
Saha-Boltzmann model or/and FLYCHK code.
