Negative hydrogen or deuterium ions are the precursor particles used to generate a high power beam of neutrals in order to heat the tokamak plasma core of magnetic fusion devices, inject current, and to some extent control instabilities. In the case of ITER, for instance, the negative ions are produced inside a high power large volume low-pressure tandem type magnetized ion source and extracted toward an electrostatic accelerator which accelerates them to 1 MeV before entering a neutralizer converting the ions into a neutral beam. This so-called neutral beam injector relies on the production of negative ions on the surface facing the plasma of the ion source extraction electrode. The latter is covered by a cesium layer in order to increase the negative ion yield. The use of cesium is currently an issue as it may diffuse outside of the source and induce secondary particle production or voltage breakdowns inside the accelerator vessel requiring a regular maintenance in a nuclear environment. In this work, we analyze numerically with a 2.5D particle-in-cell model the production rate and transport of negative ions in a linear device used as an ion source. The negative ions are generated via a dissociative attachment process with a hydrogen molecule in the volume of a magnetized cesium-free plasma. The linear device in the model has a large aspect ratio with a radius of 5 and a length of 100 cm and the magnetic field strength ranges from 100 to 400 G. We show that the shape and depth of the plasma potential profile may be controlled by biasing the end-plates which in turn strongly influence the residence time of the electrons and hence the negative ion yield. We observe the formation of large-scale rotating structures when the positive ions become magnetized with a rotation velocity in the kHz range.