A model of the near-cathode plasma layer in a plasma under a pressure of the order of one or several bars is reconsidered on the basis of recent theoretical results. Physics of the near-cathode layer is analysed in the range of near-cathode voltage drops of up to 50 V, in accord to recent experimental results which have shown that the near-cathode voltage drop in high-pressure arc discharges may be that high. It is found that a non-monotony of the dependence of the energy flux density on the surface temperature at fixed values of the near-cathode voltage drop is caused by one of the three mechanisms: overcoming of the increase of combined ion and plasma electron heating by the increase of thermionic cooling as the plasma approaches full ionization; non-monotony of the dependence of the ion current on the electron temperature which is caused by the deviation of the ion current from the diffusion value; rapid increase of the plasma electron heating which is subsequently overcome by thermionic cooling. A closed description of the plasma-cathode interaction is obtained by numerically solving the nonlinear boundary-value problem for the temperature distribution inside the cathode body. Results of numerical modelling of the diffuse discharge under conditions of a model arc lamp are given and a good agreement with the experimental data is shown.

Steady-state current transfer from arc plasmas to axially symmetric cathodes is treated in the framework of the model of nonlinear surface heating. An approach is developed to calculate the bifurcation points at which three-dimensional spot-mode solutions branch off from solutions describing the diffuse mode and axially symmetric spot modes. In particular, the first bifurcation point positioned on the diffuse-mode solution has been calculated, and thus its stability limit, i.e., the current below which the diffuse mode becomes unstable. Calculation results are given for the case of a tungsten cathode in the form of a circular cylinder in high-pressure plasmas. The effect produced on the stability limit by variations of control parameters (cathode dimensions, work function of the cathode material, plasma-producing gas, and its pressure) is studied and found to conform to trends observed experimentally. The stability limit is found to be much more sensitive to variations of control parameters than characteristics of the diffuse mode are, the strongest effect being produced by variations of cathode dimensions and of the work function of the cathode material. This finding conforms to the fact that the diffuse-spot transition is difficult to reproduce in the experiment.

Solitary spots on infinite planar cathodes and diffuse and axially symmetric spot modes on finite cathodes of high-pressure arc discharges are studied in a wide range of arc currents. General features are analysed and extensive numerical results on planar and cylindrical tungsten cathodes of atmospheric-pressure argon arcs are given for currents of up to 100 kA. It is shown, in particular, that the temperature of cathode surface inside a solitary spot varies relatively weakly and may be estimated, to the accuracy of about 200-300 K, without actually solving the thermal conduction equation in the cathode body. Asymptotic behaviour of solutions for finite cathodes in the limiting case of high currents is found and confirmed by numerical results. A general pattern of current-voltage characteristics of various modes on finite cathodes suggested previously on the basis of bifurcation analysis is confirmed. A transition from the spot modes on a finite cathode in the limit of large cathode dimensions to the solitary spot mode on an infinite planar cathode is studied. It is found that the solitary spot mode represents a limiting form of the high-voltage spot mode on a finite cathode. A question of distinguishing between diffuse and spot modes on finite cathodes is considered.

A model of cathode spots in high-current vacuum arcs is developed with account of all the potentially relevant mechanisms: the bombardment of the cathode surface by ions coming from a preexisting plasma cloud; vaporization of the cathode material in the spot, its ionization, and the interaction of the produced plasma with the cathode; the Joule heat generation in the cathode body; melting of the cathode material and motion of the melt under the effect of the plasma pressure and the Lorentz force and related phenomena. After the spot has been ignited by the action of the cloud (which takes a few nanoseconds), the metal in the spot is melted and accelerated toward the periphery of the spot, with the main driving force being the pressure due to incident ions. Electron emission cooling and convective heat transfer are dominant mechanisms of cooling in the spot, limiting the maximum temperature of the cathode to approximately 4700-4800 K. A crater is formed on the cathode surface in this way. After the plasma cloud has been extinguished, a liquid-metal jet is formed and a droplet is ejected. No explosions have been observed. The modeling results conform to estimates of different mechanisms of cathode erosion derived from the experimental data on the net and ion erosion of copper cathodes.

Numerical investigation of steady-state interaction of a high-pressure argon plasma with a cylindrical tungsten cathode is reported. A whole 'zoo' of very diverse modes of current transfer is revealed. Detailed results are given for the first five (three-dimensional) 3D spot modes, four of them branching off from the diffuse mode and one from the first axially symmetric spot mode. Divergences in the general pattern of solutions, which have been present in preceding works, are resolved. Hypotheses on stability of steady-state solutions, available in the literature, are analysed. It is found that these hypotheses provide an explanation of the fact that the transition between diffuse and spot modes is difficult to reproduce in the experiment but they do not explain the indication that it is the low-voltage branch of the first 3D spot mode that seems to occur in the experiment. Thus, the question of stability of steady-state solutions remains open: an accurate stability analysis, as well as additional experimental information is required.

Three approaches to description of separation of charges in near-cathode regions of high-pressure arc discharges are compared. The …rst 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 a signi…cant power is deposited by the arc power supply into the near-cathode plasma layer, which allows one to simulate the plasma-cathode interaction in the …rst approximation independently of processes in the bulk plasma. It is found that results given by the di¤erent models are in a generally 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 a¤ected by details of the model provided that the basic physics is right.

Bifurcations and/or their consequences are frequently encountered in numerical modelling of current transfer to cathodes of gas discharges, also in apparently simple situations, and a failure to recognize and properly analyse a bifurcation may create difficulties in the modelling and hinder the understanding of numerical results and the underlying physics. This work is concerned with analysis of bifurcations that have been encountered in the modelling of steady-state current transfer to cathodes of glow and arc discharges. All basic types of steady-state bifurcations (fold, transcritical, pitchfork) have been identified and analysed. The analysis provides explanations to many results obtained in numerical modelling. In particular, it is shown that dramatic changes in patterns of current transfer to cathodes of both glow and arc discharges, described by numerical modelling, occur through perturbed transcritical bifurcations of first-and second-order contact. The analysis elucidates the reason why the mode of glow discharge associated with the falling section of the current-voltage characteristic in the solution of von Engel and Steenbeck seems not to appear in 2D numerical modelling and the subnormal and normal modes appear instead. A similar effect has been identified in numerical modelling of arc cathodes and explained.

The model of the near-cathode plasma, developed previously for the case of a single-species plasma-producing gas, is generalized for the case of multiple plasma-producing species. Results are presented of calculation of a diffuse mode of current transfer to tungsten cathodes in a mercury plasma with an addition of sodium. It is found that the presence of 1% of sodium results in a considerable expansion of the range of stability of the diffuse mode.