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Arc plasmas in switching devices are investigated in the presence of external and self-induced magnetic fields, as well as of gassing materials, using a three-dimensional computational model. The model development and validation for two- and three-dimensional arc columns with a self-induced magnetic field and natural-convection effects was presented in L. Z. Schlitz etal [J. Appl. Phys. 85, 2540 (1999)]. The present paper discusses further development of the model to enable an investigation of the effects of external magnetic fields and the presence of gassing materials. Steady-state solutions with an external transverse magnetic field (0–20 mT) imposed on a wall-stabilized air arc column are presented, followed by a study of the transient response of the arc in an open-ended arc chamber in a 0.68 ms time span. Ablation from the side walls of the arc chamber made of gassing materials (and the resulting mixing of hydrogen and air) is shown to increase the arc voltage dramatically due to the increase in heat transfer around the arc body. © 1999 American Institute of Physics.