A study of the gas-phase kinetics and the plasma chemistry for an rf inductively coupled H 2 plasma discharge, in the deuterium negative ion source experiment (DENISE), has been carried out by means of a global model of the discharge implemented by the numerical code, Global Model Solver (GMS), which gives results for the spatially averaged densities of the species included in the model and the electron temperature in the steady state. The modelling of the discharge includes H − , with the production mechanism assumed to be dissociative attachment of H 2 (v). The effect of the magnetic filter in the source is taken into account for obtaining an estimate of the H − density also in the extraction chamber. The differences in the cross-section data assumed for some processes, between this paper and previous work, are pointed out, along with the consequences on H − density. The ratio between the H − density and the electron density obtained with GMS for the considered negative ion production mechanism is always far lower than 0.1, even with the most optimistic assumptions for H − production that can be put forward.