A study of the gas-phase kinetics and the plasma chemistry for an rfinductively coupled H2 plasma discharge, in the deuterium negativeion source experiment (DENISE), has been carried out by means of a globalmodel of the discharge implemented by the numerical code, Global ModelSolver (GMS), which gives results for the spatially averaged densities ofthe species included in the model and the electron temperature in thesteady state. The modelling of the discharge includes H-, with theproduction mechanism assumed to be dissociative attachment ofH2(v). The effect of the magnetic filter in the source is takeninto account for obtaining an estimate of the H- density also in theextraction chamber. The differences in the cross-section data assumed forsome processes, between this paper and previous work, are pointed out,along with the consequences on H- density. The ratio between theH- density and the electron density obtained with GMS for theconsidered negative ion production mechanism is always far lower than 0.1,even with the most optimistic assumptions for H- production that canbe put forward.