Nelson A. Almeida

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.

Novel non-equilibrium modelling of a DC electric arc in argon

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 Ohms 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.

Account of near-cathode sheath in numerical models of high-pressure arc discharges

Three approaches to describing the separation of charges in near-cathode regions of high-pressure 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.

Investigating near-anode plasma layers of very high-pressure arc discharges

Numerical and experimental investigation of near-anode layers of very high-pressure arcs in mercury and xenon is reported. The simulation is performed by means of a recently developed numerical model in which the whole of a near-electrode layer is simulated in the framework of a single set of equations without simplifying assumptions such as thermal equilibrium, ionization equilibrium and quasi-neutrality and which was used previously for a simulation of the near-cathode plasma layers. The simulation results support the general understanding of similarities and differences between plasma–cathode and plasma–anode interaction in high-pressure arc discharges established in preceding works. In particular, the anode power input is governed primarily by, and is approximately proportional to, the arc current. In the experiment, the spectral radiance from the electrodes and the near-electrode regions in xenon arcs was recorded. The derived total anode power input and near-anode plasma radiance distribution agree reasonably well with the simulation results.

Near-Cathode Plasma Layer on CuCr Contacts of Vacuum Arcs

A 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 self-consistent 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.

Physics of the intermediate layer between a plasma and a collisionless sheath and mathematical meaning of the Bohm criterion

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 l...

Transition from a fully ionized plasma to an absorbing surface

The ionization layer (presheath) separating a fully ionized low-temperature thermal plasma from the space-charge sheath adjacent to a solid surface is described by means of a (multi)fluid model. The character of the solution is governed by α, the ratio of the ionization length to the mean free path for ion–atom collisions. If α ≥ 1, the solution is determined by physically transparent boundary conditions, namely, by the Bohm criterion at the sheath edge and the condition of full ionization on the plasma side of the ionization layer. If α < 1, the latter condition becomes ineffective. An alternative boundary condition is found for a certain range of α below unity, αcr ≤ α < 1. An approximate approach which spans the whole range of α is suggested. While being incomplete theoretically, this approach is sufficient for practical purposes and gives results that are in agreement with experiment. On the other hand, the question of what is the lacking boundary condition in the range 0 < α < αcr remains open and challenging.

Boundary conditions at the plasma-cathode interface in high-pressure arcs

Summary form only given. Transport of electron energy from the near-cathode space-charge sheath into the bulk plasma is an important effect dominating heat exchange in cathodic part of high-pressure arc discharges. Therefore, a physically justified numerical model of bulk plasma in high-pressure arc discharges should take into account deviations between the electron and heavy-particle temperatures. As far as deviations from ionization equilibrium are concerned, two approaches are possible: to take them into account only in a near-cathode layer or in both the near-cathode layer and the bulk plasma. In the framework of the first approach, the model of near-cathode layer takes into account, in addition to the space charge, also non-equilibrium ionization. In the framework of the second approach, the near-cathode layer represents a space-charge sheath in which volume ionization and recombination are negligible. The two approaches have been compared1 between themselves and with the experiment on atmospheric-pressure argon arc, for which both approaches are justified. It was found that they predict values of the arc voltage which are close to each other and the experiment for arc currents between 100 and 200A, however for lower currents the second approach predicts a less constricted and colder arc attachment and, consequently, significantly higher arc voltages than those found in the experiment and predicted by the first approach. Since the second approach is at least no less accurate than the first one, its predictive capabilities with regard to the arc-cathode interaction may be improved. Physically justified boundary conditions at the interface between the bulk plasma and the cathode are needed to this end. These conditions should account for the existence of the near-cathode space-charge sheath and have not been derived up to now. A derivation and validation of these boundary conditions is the subject of this work.

Modeling near-cathode plasma layer on contacts of vacuum arcs

Summary form only given. A 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 one to self-consistently determine all parameters of the near-cathode layer, including the ion backflow coefficient, as functions of the local surface temperature Tw and the near-cathode voltage U. Evaluation results are given for Cu and CuCr cathodes. The dependence of the density of energy flux from the plasma to the cathode surface on Tw for fixed U is shown to be non-monotonic with a maximum. This feature stems from the fact that the ion heating of the cathode grows faster than the electron emission cooling at lower Tw and vice versa at higher Tw. This feature is very important theoretically and suggests that spots on cathodes of vacuum arcs may appear due to thermal instability developing in the cathode body and that stationary regimes of cathode spots in vacuum arcs are possible, similarly to what happens in the theory of cathode spots in high-pressure arc discharges.The developed model may be used for a variety of purposes, including as a module of complex non-stationary 2D and 3D numerical models of plasma-cathode interaction. As a simple example, an analytical evaluation of parameters of stationary spots on copper and chromium is performed in this work. 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 current of the order of one ampere burning on the chromium grains. This conclusion conforms to high-resolution photographs of high-current arcs between copper-chromium contacts taken at exposure times of 2υs, which revealed cathode spots with the average current of 45A similar to those on pure-copper cathodes, as well as very small and dim spots.

Unified modelling of near-electrode non-equilibrium layers in high-pressure arc discharges

This paper studies the current transfer through near-electrode layers on the basis of direct numerical simulation of the layer, without dividing it into sub-layers with different properties. Governing equations include equations of conservation and transport equations for the ions, the atoms, and the electrons, equations of energy for the electrons and the heavy particles, and the Poisson equation. The equations are solved numerically in 1D without any further simplifications, in particular, without explicitly dividing the near-cathode layer into a space-charge sheath and quasi-neutral plasma. Results of numerical simulation of near-cathode and near-anode layers in an atmospheric-pressure argon arc and in high-pressure mercury arcs with tungsten cathode are given: distributions of plasma parameters across the layer, current-voltage characteristics, energy flux from the plasma to the cathode.