The effects of a weak transverse magnetic field on negative ion (H-) extraction in a negative ion source have been studied by two-dimensional electrostatic particle simulation. A particle-in-cell model is used which simulates motion of charged particles in their self-consistent electric field. The extraction of H- ions is significantly improved by the weak transverse magnetic field in simulation as well as in experiments. Since electrons are deflected by the weak magnetic field, more H- ions arrive instead of electrons in the region close to the plasma grid in order to ensure plasma neutrality. The presence of the weak magnetic field produces important modifications in positive ion flow and, as a result, in the structure of the spatial potential which collects H- ions. © 2004 American Institute of Physics.