This paper presents a global model of micro-hollow cathode discharges working in argon gas. Inspired by experiments and two-dimensional numerical simulations, the discharge is decomposed into two main regions, labelled the cathodic region and the positive column region. The first is composed of a cathode sheath (surrounding the cathode) and a plasma in the centre, while the positive column region is essentially filled with plasma. A cathode sheath model is developed to calculate the sheath size and the power dissipated by ions and electrons in the sheath. Charged-particle transport equations are solved in one-dimensional cylindrical coordinates, in the quasi-neutral plasma region, in order to determine the radial density profiles and the electron temperature in the microhole. A global power balance is then performed in the two distinct regions in order to determine the absolute electron density. We found that the electron density is one order of magnitude higher in the cathodic region than in the positive column, showing that the power dissipation is mainly located in the cathode sheath. The calculated electron density in the cathodic region is in reasonable agreement with experiments.
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