M. S. Benilov

Understanding and modelling plasma?electrode interaction in high-pressure arc discharges: a review

Considerable advances have been attained during the last decade in the theoretical and experimental investigation of electrode phenomena in high-pressure arc discharges, in particular, in low-current arcs that occur in high-intensity discharge lamps. The aim of this paper is to deliver a concise review of the understanding achieved and modelling methods developed.

A model of the cathode region of atmospheric pressure arcs

The paper deals with calculation of parameters in the near-cathode plasma layer, on the cathode surface and in the body of a cathode in high-pressure arc discharges. These parameters can be calculated independently of the arc column if the heat flux coming from the column to the edge of the near-cathode layer does not play a decisive role in the energy balance of the layer, which, according to the estimates presented, is a likely case. The physics of the near-cathode layer is reconsidered in view of major contradictions that have appeared in the literature recently, in particular with regard to the role of the near-cathode space charge sheath. A model of a near-cathode layer is developed that is based on a multifluid description of the plasma and takes into account multiply charged ions. The model is employed to calculate parameters of the layer as functions of the voltage drop in the layer and of the local value of the surface temperature. By means of these data, an approximate asymptotic theory of arc spots is extended to cathode spots in high-pressure plasmas. Calculated spot parameters are presented for the following combinations cathode/plasma: tungsten/argon, thoriated-tungsten/argon, thoriated-tungsten/nitrogen, and zirconium/nitrogen. The obtained results agree with the recent measurements of the spot temperature.

Modelling of low-current discharges in atmospheric-pressure air taking account of non-equilibrium effects

A model of stationary direct current discharges in atmospheric-pressure air is developed that accounts for deviation of plasma state from the local thermodynamic equilibrium. It is shown that at the current range 0.01–0.1 A a change in the dominant ionization mechanism takes place, from ionization by electron impact at low currents to associative ionization in atomic collisions at high currents. Results of the calculation of discharge parameters over a wide current range are presented. Calculated plasma parameters agree with the available experimental data.

Heating of refractory cathodes by high-pressure arc plasmas: II

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.

Steady rimming flows with surface tension

We examine steady flows of a thin film of viscous fluid on the inside of a cylinder with horizontal axis, rotating about this axis. If the amount of fluid in the cylinder is sufficiently small, all of it is entrained by rotation and the film is distributed more or less evenly. For medium amounts, the fluid accumulates on the ‘rising’ side of the cylinder and, for large ones, pools at the cylinder’s bottom. The paper examines rimming flows with a pool affected by weak surface tension. Using the lubrication approximation and the method of matched asymptotics, we find a solution describing the pool, the ‘outer’ region, and two transitional regions, one of which includes a variable (depending on the small parameter) number of asymptotic zones.

The Child–Langmuir law and analytical theory of collisionless to collision-dominated sheaths

This paper is concerned with summarizing simple analytical models of space-charge sheaths and tracing their relation to the Child–Langmuir model of an ion sheath. The topics discussed include the Child–Langmuir law and model of a collisionless ion sheath, the Mott–Gurney law and model of a collision-dominated ion sheath, the Bohm model of a collisionless ion–electron sheath, the Su–Lam–Cohen model of a collision-dominated ion–electron sheath, ion sheaths with arbitrary collisionality, high-accuracy boundary conditions for the Child–Langmuir and Mott–Gurney models of an ion sheath and the mathematical sense of Child–Langmuir type models of an ion sheath from the point of view of modern theoretical physics.

Effect of a near-cathode sheath on heat transfer in high-pressure arc plasmas

Numerical simulation of a high-pressure arc discharge has been performed with a self-consistent modelling of most of the components, including the electrodes, and the interactions between them. In particular, the arc column and the cathodic part of the discharge are simulated by means of a two-temperature hydrodynamic model and of a model of nonlinear surface heating, respectively. Simulation results are given for a free-burning arc in atmospheric-pressure argon in the range of arc currents from 10 to 200 A. It is found that the electric power deposited into the near-cathode layer is transported not only to the cathode but also to the arc column, an effect that cannot be described by the local thermodynamic equilibrium (LTE) model. The electron enthalpy transport substantially exceeds the net contribution of thermal conduction by the electrons and heavy particles and is thus the dominating mechanism of energy transfer from the near-cathode layer to the arc column. The predicted gas temperatures along the arc axis in the arc column using the LTE model are much higher than the calculated electron and heavy-particle temperatures (~1000–2000 K or higher) under the same operation conditions using the non-equilibrium model with the consideration of the near-cathode sheath for the cases studied in the present paper. Studies on the influences of the cathode shapes and metal vapour contaminations on the arc characteristics will be conducted in future work.

Unified modelling of near-cathode plasma layers in high-pressure arc discharges

A model of a near-cathode region in high-pressure arc discharges is developed in the framework of the hydrodynamic (diffusion) approximation. Governing equations are solved numerically in 1D without any further simplifications, in particular, without explicitly dividing the near-cathode region into a space-charge sheath and a quasi-neutral plasma. Results of numerical simulation are reported for a very high-pressure mercury arc and an atmospheric-pressure argon arc. Physical mechanisms dominating different sections of the near-cathode region are identified. It is shown that the near-cathode space-charge sheath is of primary importance under conditions of practical interest. Physical bases of simplified models of the near-cathode region in high-pressure arc discharges are analysed. A comparison of results given by the present model with those given by a simplified model has revealed qualitative agreement; the agreement is not only qualitative but also quantitative in the case of an atmospheric-pressure argon plasma at moderate values of the near-cathode voltage drop. The modelling data are compared with results of spectroscopic measurements of the electron temperature and density in the near-cathode region.

Multiple solutions in the theory of dc glow discharges

Multiple steady-state solutions existing in the theory of dc glow discharges are computed for the first time. The simulations are performed in 2D in the framework of the simplest self-consistent model, which accounts for a single ion species and employs the drift–diffusion approximation. Solutions describing up to nine different modes were found in the case where losses of the ions and the electrons due to diffusion to the wall were neglected. One mode is 1D, exists at all values of the discharge current, and represents in essence the well-known solution of von Engel and Steenbeck. The other eight modes are axially symmetric, exist in limited ranges of the discharge current, and are associated with different patterns of current spots on the cathode. The mode with a spot at the centre of the cathode exhibits a well pronounced effect of normal current density. Account of diffusion losses affects the solutions dramatically: the number of solutions is reduced, a mode appears that exists at all discharge currents and comprises the Townsend, subnormal, normal and abnormal discharges. The solutions that exist in limited current ranges describe patterns, and these patterns seem to represent axially symmetric analogues of the 3D patterns observed in dc glow microdischarges in xenon.

The ion flux from a thermal plasma to a surface

On the basis of a continuum multi-fluid description of a plasma, a theory is developed of an ionization layer between a plasma in ionization (Saha) equilibrium and the space-charge sheath near a surface of a cathode or of an insulating wall. The crucial parameter determining the character of the solution is the ratio of the recombination length to the mean free path ion-neutral species; if this ratio is large, then the developed theory is consistent with a conventional diffusion approach. Numerical and asymptotic solutions of a stated problem are obtained. It is found that the problem is solvable only if the degree of ionization does not exceed a certain value, which varies between approximately 0.6 and 1. Beyond this value, the equation of the pressure balance cannot be satisfied and the plasma as a whole in the considered layer cannot stay in static equilibrium. A simple approximate formula for the ion flux is obtained.