Computer simulations have been performed to describe the effect of small admixtures of hydrogen to an argon glow discharge in the Grimm-type configuration. The two-dimensional density profiles of the various plasma species (i.e., electrons, Ar + , ArH + , H + , H 2 + and H 3 + ions, H atoms and H 2 molecules, Ar metastable atoms and sputtered Cu atoms) are presented for 1% H 2 added to the argon glow discharge, and the effect of different H 2 additions (varying between 0.1 and 10%) on the species densities, the hydrogen dissociation degree, and the sputtering process, are investigated. Finally, the relative contributions of various production and loss processes for the different plasma species are calculated.