The role of the metastable Ar atoms in a 1-cm-diameter cylindrical hollow cathode discharge ͑HCD͒ is studied self-consistently based on a hybrid model and experimental measurements in the pressure range of 0.3-1 Torr and currents of 1-10 mA. The model comprises submodels based on the principles of Monte Carlo and fluid simulations. The Monte Carlo model describes the movement of the fast electrons, fast Ar and Cu atoms, and fast Ar + and Cu + ions as particles, while in the fluid model, the slow electrons, Ar + , Cu + ions, Cu, and Ar metastable atoms are treated as a continuum. The population of the two metastable states within the 3p 5 4s configuration ͑ 3 P 2 and 3 P 0 ͒ were combined into one collective level, for which the continuity equation was written. Typical calculation results are, among others, the two-dimensional profiles of the production and the loss rates of Ar metastable atoms, as well as the metastable atom densities and fluxes throughout the complete HCD. Moreover, the calculated radial profiles ͑averaged over the axial direction͒ of the Ar metastable atom density are compared with experimental radial density profiles recorded by laser absorption spectroscopy. The relative importance of the different processes determining the Ar metastable population is analyzed, as well as the influence of pressure and voltage on them. Experimental results evidence the presence of the metastable atom production source at the cathode surface, probably originating from fast Ar + ions and Ar atoms impinging on it. Comparison between experimental and calculated Ar metastable atom densities shows a good agreement at low pressures, but at 1 Torr the calculated values differ by a factor of 2 from the measured ones. Several possible explanations for this discrepancy are discussed.
The role of the fast Ar atoms, Ar ϩ ions, and metastable Ar atoms in a cylindrical hollow cathode discharge ͑HCD͒ is studied based on a self-consistent model. The model comprises submodels based on the principle of Monte Carlo and fluid simulations. With Monte Carlo models the movement of the fast electrons, fast Ar atoms, and fast Ar ϩ ions as particles is described, while with the fluid models, the slow electrons, ions, and metastable atoms are treated as a continuum. Typical results are, among others, the fast atom, fast ion, and fast electron excitation and ionization rates, the electron, ion, and metastable atom densities and fluxes, the energy distribution function of the fast atoms, fast ions, and fast electrons, and the electric field and potential distribution. Also the relative importance of different processes determining the metastable density in an Ar HCD is analyzed, as well as the influence of the fast atoms and fast ions on the discharge properties.
A hollow cathode discharge ͑HCD͒ in He is studied based on a Monte Carlo-fluid hybrid model combined with a transport model for metastable He atoms. The Monte Carlo model describes the movement of fast electrons as particles, while in the fluid model, the slow electrons and positive ions are treated as a continuum. The continuity equations are solved together with the Poisson equation in order to obtain a self-consistent electric field. The He metastable transport model considers various production and loss mechanisms for He metastable atoms. These three models are run iteratively until convergence is reached. Typical results are, among others, the excitation and ionization rates, the electron, ion, and metastable densities and fluxes, the electric field, and potential distribution. The relative importance of different processes determining the metastable density in a He HCD is analyzed, as well as the role of He metastable atoms and He ions on the secondary electron emission at the cathode. Calculation results are compared with experimental data for the same discharge conditions, and good agreement was obtained.
Role of the fast Ar atoms, Ar + ions, and metastable Ar atoms in a hollow cathode glow discharge: Study by a hybrid modelThe role of the Cu atoms sputtered from the cathode material in a cylindrical hollow cathode discharge ͑HCD͒ and the corresponding Cu + ions are studied with a self-consistent model based on the principle of Monte Carlo ͑MC͒ and fluid simulations. In order to obtain a more realistic view of the discharge processes, this model is coupled with other submodels, which describe the behavior of electrons, fast Ar atoms, Ar + ions, and Ar metastable atoms, also based on the principles of MC and fluid simulations. Typical results are, among others, the thermalization profile of the Cu atoms, the fast Cu atom, the thermal Cu atom and Cu + ion fluxes and densities, and the energy distribution of the Cu + ions. It was found that the contribution of the Ar + ions to the sputtering was the most significant, followed by the fast Ar atoms. At the cathode bottom, there was no net sputtered flux but a net amount of redeposition. Throughout the discharge volume, at all the conditions investigated, the largest concentration of Cu atoms was found in the lower half of the HCD, close to the bottom. Penning ionization was found the main ionization mechanism for the Cu atoms. The ionization degree of copper atoms was found to be in the same order as for the argon atoms ͑10 −4 ͒.
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