  The advent of x-ray free-electron lasers (XFELs), which provide intense
ultrashort x-ray pulses, has brought a new way of creating and analyzing hot
and warm dense plasmas in the laboratory. Because of the ultrashort pulse
duration, the XFEL-produced plasma will be out of equilibrium at the beginning
and even the electronic subsystem may not reach thermal equilibrium while
interacting with a femtosecond time-scale pulse. In the dense plasma, the
ionization potential depression (IPD) induced by the plasma environment plays a
crucial role for understanding and modeling microscopic dynamical processes.
However, all theoretical approaches for IPD have been based on local thermal
equilibrium (LTE) and it has been controversial to use LTE IPD models for the
nonthermal situation. In this work, we propose a non-LTE (NLTE) approach to
calculate the IPD effect by combining a quantum-mechanical electronic-structure
calculation and a classical molecular dynamics simulation. This hybrid approach
enables us to investigate the time evolution of ionization potentials and IPDs
during and after the interaction with XFEL pulses, without the limitation of
the LTE assumption. In our NLTE approach, the transient IPD values are
presented as distributions evolving with time, which cannot be captured by
conventional LTE-based models. The time-integrated ionization potential values
are in good agreement with benchmark experimental data on solid-density
aluminum plasma and other theoretical predictions based on LTE. The present
work is promising to provide critical insights into nonequilibrium dynamics of
dense plasma formation and thermalization induced by XFEL pulses.
