The ionization region model (IRM) is applied to model a high power impulse magnetron sputtering discharge with a tungsten target. The IRM gives the temporal variation of the various species and the average electron energy, as well as internal discharge parameters such as the ionization probability and the back-attraction probability of the sputtered species. It is shown that an initial peak in the discharge current is due to argon ions bombarding the cathode target. After the initial peak, the W+ ions become the dominating ions and remain as such to the end of the pulse. We demonstrate how the contribution of the W+ ions to the total discharge current at the target surface increases with increased discharge voltage for peak discharge current densities J (D,peak) in the range 0.33-0.73 A cm(-2). For the sputtered tungsten the ionization probability increases, while the back-attraction probability decreases with increasing discharge voltage. Furthermore, we discuss the findings in terms of the generalized recycling model and compare to experimentally determined deposition rates and find good agreement.