Summary of research 2015-2019

Plasma-electrode interaction in high-pressure arc discharges
  • Models of plasma-electrode interaction for the LTE description of the arc bulk and a fully non-equilibrium description;
  • Effect of diffusion on current transfer in LTE and 2T plasmas;
  • Numerical simulation of changes in shape of thermionic cathodes during operation of high-pressure arc discharges.

Cathode spots in vacuum arcs and related phenomena
  • Physics of cathode spots in vacuum arcs;
  • Numerical simulation of unipolar arcing in fusion-relevant conditions;
  • Modelling of the motion of cathode spots of vacuum arcs.

Self-organization and stability of discharges on cold electrodes and related phenomena
  • The use of time-dependent and stationary solvers for simulation of complex behavior;
  • Self-organized patterns on glow cathodes in the cathode boundary layer geometry;
  • Bifurcations in the theory of current transfer to cathodes of dc discharges and transitions between different modes;
  • Numerical investigation of anode spots in a DC glow discharge;
  • Simulation of pre-breakdown discharges in high-pressure air.

Research highlights 2015-2019

Physics of cathode spots in vacuum arcs

Understanding of mechanisms of operation of cathodic spots of vacuum arc discharges, including the role of explosive electron emission, is a challenging topic of high scientific interest and importance for applications. We conducted this research on the suggestion of, and in collaboration with, colleagues from Siemens Corporate Technology (Erlangen, Germany), one of the aims being application of results to contacts of high-power vacuum circuit breakers. Our main goal was to develop a comprehensive numerical model of cathodic spots of vacuum arcs, accounting for all the potentially relevant mechanisms: the bombardment of the cathode surface by ions coming from a pre-existing 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.
All phases of life of a spot have been investigated, from ignition to extinction. The latter is accompanied by emission of a droplet. No explosions have been observed, which disproves the reigning paradigm of ectons (explosive electron emission centers). The modeling results conform to experimental data on the net and ion erosion of copper cathodes of vacuum arcs. One of the papers on this topic, which has been published in Journal of Applied Physics, was selected by the Editors for promotion through the American Institute of Physics Publishing's Scilights project.
In the future, the developed model will be used for investigation of unipolar arcs in fusion devices and of cathode erosion in other types of gas discharges.
Contact persons: Mikhail Benilov, Mário Cunha, Helena Kaufmann.

Droplet detachment from a Cu cathode of a vacuum arc. The bar is in K. The maximum temperature of copper is about 1500 K.

Numerical simulation of unipolar arcing in fusion-relevant conditions

Unipolar arcing between the plasma and the wall, triggered by plasma instabilities which deliver high energy and particle losses to the walls, is thought to be one of the mechanisms of the erosion in fusion devices. A possible mechanism of unipolar arcing is similar to the mechanism of formation of cathode spots in vacuum arcs, which was modeled previously. Our goal was to therefore apply a similar model for unipolar arcing in fusion devices. This research was started on the suggestions of, and conducted in collaboration with, colleagues from the Experimental Physics Group at IPFN.
The developed model was used for simulation of the interaction of an external energy load (laser beam) with a tungsten plate immersed in a helium background plasma. The results revealed the formation of a crater, but no jet formation or droplet detachment. The peak temperature attained varied with the size of the plate, and in the case of a small plate the potential of the plate surpasses the plasma potential. In the future, the developed model will be used for investigation of the plasma-cathode interaction and cathode erosion in other types of gas discharges and for investigation of the vacuum breakdown in conditions of accelerators (this research was started on the suggestions of, and is conducted in collaboration with, colleagues from CERN, Geneva, and other institutions).
Contact persons: Helena Kaufmann, Mikhail Benilov.

Simulation results obtained with the model of the initial stage of unipolar arcing in fusion relevant conditions. The temporal evolution of the temperature distribution in the tungsten plate and the deformation of the plate surface are shown for the case of a large plate (radius R=100mm).

The motion of cathode spots of vacuum arcs

Several hundreds of spots operate simultaneously on cathodes of vacuum arcs in high-power vacuum circuit breakers. At the macroscopic level, and in the absence of a magnetic field, the motion of a cathode spot can be described as a random walk along the cathode surface. When an external magnetic field is applied, parallel to the cathode surface, an ordered motion, directed in the opposite direction of the Amperian force exerted by the magnetic field, is superimposed over the random walk, i.e., retrograde motion.
Our goal was two-fold: to simulate the spot distribution along the contact surface by means of an approach that is based on the concept of surface density of spots and represents a natural alternative to tracing individual spots; and to propose a fresh attempt to develop a self-consistent description of the retrograde motion of cathode spots. We conducted this research on the suggestion of, and in collaboration with, colleagues from Siemens Corporate Technology (Erlangen, Germany), one of the aims being application of results to contacts of high-power vacuum circuit breakers.
In the first case, the proposed model is simple and physically transparent and correctly reproduces the trends observed in the experiments under conditions where the cathode arc attachment is diffuse. The distribution of the macroscopic current density on the cathode, given by the model, represents the boundary condition that is required for existing numerical models of vacuum arcs in high-power vacuum circuit breakers.
In the second case, three potential mechanisms of effect of transversal magnetic field on the distribution of parameters in the spot were studied: the effect of magnetic field on hydrodynamics processes in the spot, and the effect of transversal magnetic field over the motion of ions and emitted electrons in the near-cathode space-charge sheath. It was found that for typical conditions all three mechanisms are either negligible or only have a marginal effect. A phenomenological description of the retrograde motion was developed as an alternative, employing general considerations without relying on specific assumptions and the (only) unknown parameter can be determined from comparison with the experiment.
Contact persons: Mário Cunha, Mikhail Benilov.

Macroscopic motion of cathode spots during arcing. (a) Distributions of cathode spots observed at different arcing times in the experiment. (b) Computed distributions of macroscopic (averaged over individual spots) current density on the cathode; bars in Am-2. (c) Computed distributions of spot drift velocities; bars in ms-1.

Modelling of plasma-electrode interaction in high-pressure arc discharges

Efficient methods of modelling of electric arcs in high-pressure environment are of high importance for many technical devices, and the interaction of arc plasmas with electrodes, in the first place, the cathode, is currently a bottleneck. This explains a surge of interest in plasma-electrode interaction in high-pressure arc discharges in the scientific community that has occurred over the past couple of years.
Our main goal was to develop physically justified and practicable methods of modelling of interaction of high-pressure arc plasmas with refractory electrodes. This research was started on the suggestions of, and conducted in collaboration with, colleagues from Leibniz Institute for Plasma Science and Technology (Greifswald, Germany) and GREMI (CNRS/Université d’Orléans, Orléans, France).
We have developed two models of plasma-cathode interaction, relying on different descriptions of the arc bulk plasma: a description based on the assumption of local thermodynamic equilibrium (LTE) in the bulk and a fully non-equilibrium (non-LTE) description. The two models give results that are in good agreement with each other and with the experiment. Also developed was a model of plasma-anode interaction. The model employing the assumption of LTE in the bulk plasma has significant potential and may serve as a basis for development of industrial modelling tools.
Contact persons: Mikhail Benilov, Mário Cunha, Diego Santos.

Simulating changes in shape of thermionic cathodes during operation of high-pressure arc discharges

In studies of gas metal arc welding and plasma cutting, state-of-the-art arc plasma simulations, coupled with simulations of melting of electrodes and motion of the melt, rely on the assumption of LTE in the whole arc plasma computation domain up to the electrode surfaces; deviations from LTE occurring in the near-electrode regions are not considered. Our goal was to try to simulate current transfer from high-pressure arc plasmas to thermionic cathodes, including motion of the molten metal and the change in shape of the cathode, with a physically justified account of deviations from LTE occurring in the near-cathode space-charge sheath.
The model was developed on the basis of models developed previously by our group. Computation results were obtained for conditions of experiments with atmospheric-pressure argon arc with a tungsten cathode. The computed time scales conform to those observed in the experiment, indicating that the model of non-equilibrium near-cathode layers in high-pressure arc discharges predicts the cathode temperature for a given arc current with adequate accuracy. In contrast, modelling based on the assumption of LTE in the whole arc plasma computation domain up to the cathode surface does not produce a similar agreement.
Contact persons: Mário Cunha, Mikhail Benilov.

Simulation results of the evolution of the cathode shape of a thermionic (tungsten cathode) in an atmospheric-pressure argon arc. Distances in mm, temperature bar in K. (a) I=60 A. (b) 140 A. (c) 200 A. White lines: isotherm of the melting temperature (3695 K). Black lines in the first and second images in figure (a) isotherm T=3650 K.

Bifurcations in the theory of current transfer to cathodes of dc discharges and transitions between different modes

Concentration of electrical current onto the surface of electrodes of gas discharges in well-defined regions, or current spots, is often the rule rather than the exception. These spots occur on otherwise uniform electrode surfaces, a regime where one might expect a uniform distribution of current over the surface. In many cases, multiple spots may appear, forming beautiful patterns and surprising the observer. Theory of different modes to current transfer to electrodes of gas discharges is an important part of gas discharge theory in general and is needed for applications.
Modern theoretical description of spots and spot patterns on electrodes of dc glow and arc discharges is based on the multiplicity of solutions: an adequate theoretical model must in some cases allow multiple steady-state solutions to exist for the same conditions (in particular, for the same discharge current I), with different solutions describing the spotless (diffuse) mode of current transfer and modes with different spot configurations. The cornerstone of the theory is the existence of bifurcations of steady-state solutions. Unfortunately, this question has not been addressed in experimental publications on observations of transitions between spotless mode and modes with different spot configurations.
Our goal was to analyse these observations with the aim to identify eventual bifurcations. We have employed a basic numerical model of glow microdischarges, which includes a single ionization channel and a single ion species, and a detailed model, which accounts for different ionization channels, different ion and excited species, and nonlocality of electron transport and kinetics.
We have computed the relevant bifurcations and spot patterns, and found that the latter conform to spot patterns observed in the course of the corresponding transitions in the experiment. While the comparison between the theory and the experiment still remains qualitative, the agreement is convincing and lends further support to the theory.
Contact persons: Mikhail Benilov, Pedro Almeida.

Experimentally observed and computed transitions between different modes in glow microdischarges in xenon.

Modelling anode spots in a DC glow discharge

Beautiful patterns on anodes of DC glow discharges have been observed for over a century. In addition to being of significant theoretical interest by themselves, self-organized patterns on liquid anodes of atmospheric pressure glow microdischarges reveal a non-trivial cancer-inhibiting capability.
Our goal was to compute self-organized patterns of spots on a flat metallic anode of a glow discharge. We have employed a standard model of a glow discharge in a computational domain comprising the near-anode region.
We have computed multiple solutions existing in the same range of discharge current and describing the spotless mode and modes with patterns of anode spots. In contrast to dc glow and arc discharges, multiple steady-state solutions describing different modes of current transfer do not reveal bifurcations. We found that the existence of multiple solutions in this case is a consequence of the change of sign of the anode sheath voltage. The computed spots exhibit a double layer-type structure and a reversal of electric field and current density.
Contact persons: Mikhail Benilov, Pedro Almeida.

Density of ions in cross section through centre of an anode spot. Red arrows: direction of current density. Reversal of current density is apparent.

Simulation of pre-breakdown discharges in high-pressure air

High-pressure air is commonly used nowadays in high-voltage insulating switchgear. The physics of low-current gas discharges (corona, Townsend, and streamer discharges) in high-pressure gases has been understood reasonably well by now. Time-dependent solvers are virtually universally employed in gas discharge modeling but can be too heavy to be routinely used in engineering practice. Our goal was to develop a numerical model to compute low-current quasi-stationary discharges in high-pressure air based on the use of stationary solvers, which offer important advantages in simulations of steady-state discharges when compared to standard approaches that rely on time-dependent solvers. We conducted this research as a part of an applied-physics project sponsored by Siemens Corporate Technology (Erlangen, Germany), one of the aims being application of results to high-power vacuum circuit breakers.
A 'minimal' kinetic model of plasmachemical processes in low-current gas discharges has been employed, which takes into account electrons, an effective species of positive ions, and three species of negative ions. The model was validated by comparison of the computed inception voltage of corona discharges with several sets of experimental data on glow coronas. A good agreement with the experiment has been obtained for positive coronas between concentric cylinders in a wide range of pressures and diameters of the cylinders. Inception voltages of negative coronas, computed using the values of the secondary electron emission coefficient of 10⁻⁴ to 10⁻³, agree well with the experimental data.
Contact persons: Nuno Ferreira, Mikhail Benilov, Pedro Almeida.