The ionization state of the gas in the dynamic solar chromosphere can depart strongly from the instantaneous statistical equilibrium commonly assumed in numerical modeling .
We improve on earlier simulations of the solar atmosphere that only included non-equilbrium hydrogen ionization by performing a 2D radiation-magneto-hydrodynamics simulation featuring non-equilibrium ionization of both hydrogen and helium .
The simulation includes the effect of hydrogen Lyman- \alpha and the EUV radiation from the corona on the ionization and heating of the atmosphere .
Details on code implementation are given .
We obtain helium ion fractions that are far from their equilibrium values .
Comparison with models with LTE ionization shows that non-equilibrium helium ionization leads to higher temperatures in wave fronts and lower temperatures in the gas between shocks .
Assuming LTE ionization results in a thermostat-like behaviour with matter accumulating around the temperatures where the LTE ionization fractions change rapidly .
Comparison of DEM curves computed from our models shows that non-equilibrium ionization leads to more radiating material in the temperature range 11-18 kK compared to models with LTE helium ionization .
We conclude that non-equilbrium helium ionization is important for the dynamics and thermal structure of the upper chromosphere and transition region .
It might also help resolve the problem that intensities of chromospheric lines computed from current models are smaller than those observed .