A self-consistent, two-dimensional hybrid Quid-particle model is presented and used to describe the electrical behavior of dc low-pressure discharges in the current range 10 -10 A in argon for products of the gas pressure and the gap spacing (pd) from 1 to 3.3 cm torr. The two-dimensional distributions of the potential, charged particle densities and ionization source term at steady state are shown to illustrate the discharge behavior during the transition from the normal to the abnormal regimes. For the larger values of pd, a positive column region as well as the cathode regions are clearly apparent. The model used here consists of Poisson's equation for the electric field coupled to the continuity equations for the electrons and ions with the important feature that the ionization source term appearing in the continuity equations is nonlocal and determined from a Monte Carlo simulation. This description yields a unified physical picture of discharge behavior in the cathode fall, negative glow, and positive column regions over a wide range of discharge currents. PACS number(s): 52.65.+z, 52.80.Hc I. INTRODUC:TlONThe goal in the work presented here has been to study low-pressure discharge behavior using a two-dimensional (2D) numerical model which is capable of yielding a selfconsistent unified description of a low-pressure glow discharge including the cathode fall, the negative glow, and the positive column. Although most of the qualitative features of the results discussed below are known from experiments and previous models, this work serves to quantify the two-dimensional aspects of steady-state glow discharges and it is intended to provide points for comparison with simpler 1D or analytical models. This work goes a step beyond previously published models in that the kinetic description of the ionization source term used here is needed to predict the field reversals on the discharge axis which occur in certain cases.A comprehensive review of previous modeling of gas discharges (dc and rf) has been recently published by Lister [1], and the book by Raizer [2] gives an excellent and detailed discussion of the physics of glow discharges. We therefore limit our discussion in this section to a summary of the context of the results presented here and refer the reader to these recent publications for a complete discussion of the physics of low-pressure discharges[2] and state-of-the-art modeling [1].Visually, self-sustained, low-pressure. glow discharges consist of several luminous regions which differ in intensity and color and which are clearly separated from each other by regions in which essentially no light is emitted.The diverse regions of emitted radiation of different intensity exist as a result of a distribution of the potential between the electrodes. That is, a large drop in the potential (typically some hundreds of volts) occurs immediately adjacent to the cathode surface in a distance on the order of several ionization mean free paths or less. This cathode fall is followed by a region of near zero and, i...

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