The ionization region model (IRM) is applied to model a high power impulse magnetron sputtering discharge in argon with a graphite target. Using the IRM, the temporal variation of the various species and the average electron energy, as well as internal parameters such as the ionization probability, back-attraction probability, and the ionized flux fraction of the sputtered species, is determined. It is found that thedischarge develops into working gas recycling and most of the discharge current at the cathode target surface is composed of Ar+ ions, which constitute over 90% of the discharge current, while the contribution of the C+ ions is always small (<5%), even for peak current densities close to 3 A cm(-2). For the target species, the time-averaged ionization probability <alpha(t,pulse)> is low, or 13-27%, the ion back-attraction probability during the pulse <beta(t,pulse)> is high (>92%), and the ionized flux fraction is about 2%. It is concluded that in the operation range studied here it is a challenge to ionize carbon atoms, that are sputtered off of a graphite target in a magnetron sputtering discharge, when depositing amorphous carbon films.