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A Monte Carlo simulation technique has been used to model the cathode fall region of a glow discharge under the influence of a nonuniform electric field and a transverse magnetic field. It has been shown experimentally that a magnetic field can serve as an effective means for reducing the growth of discharge instabilities. The stabilization mechanism involves the dispersion of localized charged particle perturbations over the discharge area in a time less than that required for an instability to fully develop. The results of this paper provide a deeper insight into the magnetic stabilization technique, which has the potential of increasing the power output of a wide variety of gas lasers.