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- Physics of the intermediate layer between a plasma and a collisionless sheath and mathematical meaning of the Bohm criterionPublication . Almeida, N. A.; Benilov, M. S.A transformation of the ion momentum equation simplifies a mathematical description of the transition layer between a quasi-neutral plasma and a collisionless sheath and clearly reveals the physics involved. Balance of forces acting on the ion fluid is delicate in the vicinity of the sonic point and weak effects come into play. For this reason, the passage of the ion fluid through the sonic point, which occurs in the transition layer, is governed not only by inertia and electrostatic force but also by space charge and ion-atom collisions and/or ionization. Occurrence of different scenarios of asymptotic matching in the plasma-sheath transition is analyzed by means of simple mathematical examples, asymptotic estimates, and numerical calculations. In the case of a collisionless sheath, the ion speed distribution plotted on the logarithmic scale reveals a plateau in the intermediate region between the sheath and the presheath. The value corresponding to this plateau has the meaning of speed with which ions leave the presheath and enter the sheath; the Bohm speed. The plateau is pronounced reasonably well provided that the ratio of the Debye length to the ion mean free path is of the order of 10 3 or smaller. There is no such plateau if the sheath is collisional and hence no sense in talking of a speed with which ions enter the sheath.
- Novel non-equilibrium modelling of a DC electric arc in argonPublication . Baeva, M.; Benilov, M. S.; Almeida, N. A.; Uhrlandt, D.A novel non-equilibrium model has been developed to describe the interplay of heat and mass transfer and electric and magnetic fields in a DC electric arc. A complete diffusion treatment of particle fluxes, a generalized form of Ohm’s law, and numerical matching of the arc plasma with the space-charge sheaths adjacent to the electrodes are applied to analyze in detail the plasma parameters and the phenomena occurring in the plasma column and the near-electrode regions of a DC arc generated in atmospheric pressure argon for current levels from 20 A up to 200 A. Results comprising electric field and potential, current density, heating of the electrodes, and effects of thermal and chemical non-equilibrium are presented and discussed. The current–voltage characteristic obtained is in fair agreement with known experimental data. It indicates a minimum for arc current of about 80 A. For all current levels, a field reversal in front of the anode accompanied by a voltage drop of (0.7–2.6) V is observed. Another field reversal is observed near the cathode for arc currents below 80 A.
- Near-cathode plasma layer on CuCr contacts of vacuum arcsPublication . Almeida, Nelson A.; Benilov, Mikhail S.; Benilova, Larissa G.; Hartmann, Werner; Wenzel, NorbertA model of near-cathode layers in vacuum arcs is developed. The model relies on a numerical solution of the problem of near-cathode space-charge sheath with ionization of atoms emitted by the cathode surface, and allows the selfconsistent determination of all parameters of the near-cathode layer, including the ion backflow coefficient. The dependence of the density of energy flux from the plasma to the cathode surface on the local surface temperature is nonmonotonic with a maximum, a feature that plays an important role in the physics of plasma–cathode interaction. The developed model may be used for a variety of purposes, including as a module of complex nonstationary multidimensional numerical models of plasma– cathode interaction in vacuum arcs. As a simple example, an analytical evaluation of parameters of stationary spots on copper and chromium is given. In the case of composite CuCr contacts with large grains, spots with current of several tens of amperes burning on the copper matrix coexist with spots with currents of the order of 1 A burning on the chromium grains.
- Computing anode heating voltage in high-pressure arc discharges and modelling rod electrodes in dc and ac regimesPublication . Almeida, N. A.; Cunha, M. D.; Benilov, M. S.Numerical modelling of near-anode layers in arc discharges in several gases (Ar, Xe and Hg) is performed in a wide range of current densities, anode surface temperatures, and plasma pressures. It is shown that the density of energy flux to the anode is only weakly affected by the anode surface temperature and varies linearly with the current density. This allows one to interpret the results in terms of anode heating voltage (volt equivalent of the heat flux to the anode). The computed data may be useful in different ways. An example considered in this work concerns the evaluation of thermal regime of anodes in the shape of a thin rod operating in the diffuse mode. Invoking the model of nonlinear surface heating for cathodes, one obtains a simple and free of empirical parameters model of thin rod electrodes applicable to dc and ac high-pressure arcs provided that no anode spots are present. The model is applied to a variety of experiments reported in the literature and a good agreement with the experimental data found.
- Account of near-cathode sheath in numerical models of high-pressure arc dischargesPublication . Benilov, M. S.; Almeida, N. A.; Baeva, M.; Cunha, M. D.; Benilova, L. G.; Uhrlandt, D.Three approaches to describing the separation of charges in near-cathode regions of highpressure arc discharges are compared. The first approach employs a single set of equations, including the Poisson equation, in the whole interelectrode gap. The second approach employs a fully non-equilibrium description of the quasi-neutral bulk plasma, complemented with a newly developed description of the space-charge sheaths. The third, and the simplest, approach exploits the fact that significant power is deposited by the arc power supply into the near-cathode plasma layer, which allows one to simulate the plasma–cathode interaction to the first approximation independently of processes in the bulk plasma. It is found that results given by the different models are generally in good agreement, and in some cases the agreement is even surprisingly good. It follows that the predicted integral characteristics of the plasma–cathode interaction are not strongly affected by details of the model provided that the basic physics is right.
- Kinetic Bohm criterion in the Tonks-Langmuir model: assumption or theorem?Publication . Benilov, M. S.; Almeida, N. A.New first integral is found in the collision-free Tonks-Langmuir model. The integral has a clear physical interpretation: the weighted mean inverse kinetic energy of ions, evaluated in the quasineutral approximation, equals ðkTe=2Þ 1 at all points in space. This feature is also pre sent in the full (not relying on the assumption of quasineutrality) model: for small values of the Debye length, the weighted mean inverse kinetic energy is with good accuracy equal to ðkTe=2Þ 1 in the entire region of quasineutral plasma, including in the vicinity of the space charge sheath. These results constitute a mathematical proof of the kinetic Bohm criterion and provide a new look at the problem, which has been discussed for several decades. In particular, these results show that the much-debated problem of divergence for slow ions stems from a misinterpretation. Moreover, these results explain why no unique form of kinetic Bohm criterion, modified with the account of ionization and/or collisional and/or geometrical effects in the sheath, has emerged: it cannot be postulated in a nonarbitrary way since there is simply no definite value of the inverse mean kinetic energy with which the ions enter the sheath, if these effects are non-negligible.