M D Cunha

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.

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.

Space-Resolved Modeling of Stationary Spots on Copper Vacuum Arc Cathodes and on Composite CuCr Cathodes With Large Grains

A self-consistent space-resolved numerical model of cathode spots in vacuum arcs is realized on the computational platform COMSOL Multiphysics. The model is applied to the investigation of stationary spots on planar cathodes made of copper or composite CuCr material with large

Comparing two non-equilibrium approaches to modelling of a free-burning arc

({\gtrsim}{\rm 20}~\mu{\rm m})

Modelling interaction of multispecies plasmas with thermionic cathodes

chromium grains. The modeling results reveal a well defined spot with a structure, which is in agreement with the general theory of stationary cathode arc spots and similar to that of spots on cathodes of arcs in ambient gas. In the case of CuCr contacts with large chromium grains, spots with currents of the order of tens of amperes on copper coexist with spots on chromium with currents of the order of one or few amperes. The main effect of change of the cathode material from copper to chromium is a reduction of thermal conductivity of the cathode material, which causes a reduction of the radius of the spot and a corresponding reduction of the spot current.

Analysing bifurcations encountered in numerical modelling of current transfer to cathodes of dc glow and arc discharges

Two models of high-pressure arc discharges are compared with each other and with experimental data for an atmospheric-pressure free-burning arc in argon for arc currents of 20–200 A. The models account for space-charge effects and thermal and ionization non-equilibrium in somewhat different ways. One model considers space-charge effects, thermal and ionization non-equilibrium in the near-cathode region and thermal non-equilibrium in the bulk plasma. The other model considers thermal and ionization non-equilibrium in the entire arc plasma and space-charge effects in the near-cathode region. Both models are capable of predicting the arc voltage in fair agreement with experimental data. Differences are observed in the arc attachment to the cathode, which do not strongly affect the near-cathode voltage drop and the total arc voltage for arc currents exceeding 75 A. For lower arc currents the difference is significant but the arc column structure is quite similar and the predicted bulk plasma characteristics are relatively close to each other. (Some figures may appear in colour only in the online journal)

Numerical investigation of the stability of stationary solutions in the theory of cathode spots in arcs in vacuum and ambient gas

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.

Joule heat generation in thermionic cathodes of high-pressure arc discharges

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.

Simulating different modes of current transfer to thermionic cathodes in a wide range of conditions

Stability of stationary spots on cathodes of arcs in vacuum and ambient gas has been investigated by means of simulation of development in time of perturbations imposed over steady-state solutions. Two cases of loading conditions have been considered, namely, spots operating at fixed current (the case typical of small-scale experiments) and spots operating at fixed voltage (the case typical of high-power circuit breakers). Results are reported on spots on large copper cathodes of vacuum arcs and on spots on tungsten cathodes of high-pressure argon arcs. It is shown, in particular, that if the ballast resistance in a small-scale laboratory experiment with a high-current arc is insufficient, potential consequence may be a thermal explosion of a spot, if the arc burns in vacuum, and massive melting of the cathode surface, if the arc burns in ambient gas. This conclusion conforms to trends observed in the experiment.

Formation of stationary and transient spots on thermionic cathodes and its prevention

The nonlinear surface heating model of plasma-cathode interaction in high-pressure arcs is extended to take into account the Joule effect inside the cathode body. Calculation results are given for different modes of current transfer to tungsten cathodes of different configurations in argon plasmas of atmospheric or higher pressures. Special attention is paid to analysis of energy balances of the cathode and the near-cathode plasma layer. In all the cases, the variation of potential inside the cathode is much smaller than the near-cathode voltage drop. However, this variation can be comparable to the volt equivalent of the energy flux from the plasma to the cathode and then the Joule effect is essential. Such is the case of the diffuse and mixed modes on rod cathodes at high currents, where the Joule heating causes a dramatic change of thermal and electrical regimes of the cathode. The Joule heating has virtually no effect over characteristics of spots on rod and infinite planar cathodes.