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

Abstract

The stability of stationary spots on cathodes of arcs in vacuum and ambient gas is investigated by means of the simulation of the temporal evolution of perturbations imposed over steady-state solutions. Two cases of loading conditions are considered, namely, spots operating at a fixed current (the case typical of small-scale experiments) and spots operating at a 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 small-scale laboratory experiments with a high-current arc is insufficient, the 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.

Modeling Spots on Composite Copper–Chromium Contacts of Vacuum Arcs and their Stability

“…The overall pattern of stability of stationary spots on composite CuCr cathode is similar to that of spots on pure-Cu cathodes [14]: the spots are stable if they operate at a fixed current, which is the case typical of low-current arc devices and small-scale experiments; the spots are unstable if the near-cathode voltage is not appreciably affected by ignition or extinction of an individual spot, which is the case typical of high-power circuit breakers; two scenarios of development of the nonlinear phase of instability are possible, namely, thermal explosion and destruction of the spot by thermal conduction. A feature specific to spots on composite cathodes is that the time of beginning of the nonlinear phase is rather long if the grain and spot sizes are close.…”

“…In the case of positive perturbations, β > 0, the temperature maximum is shifted from the surface into the cathode volume and T max rapidly increases up to extremely high values. In the case of negative perturbations, β < 0, the spot rapidly cools down to temperatures below 2000 K. These two outcomes of the development of instability have been found also in the investigation of the stability of stationary spots on pure-Cu cathodes [14] and have been termed, respectively, thermal explosion and destruction of the spot by thermal conduction.…”

“…The sensitivity of spot characteristics with respect to properties of the cathode material can be illustrated by simulations performed for a pure-Cu cathode with the electrical conductivity of the cathode material being constant, reported in [14]. It was found that there are again visible quantitative variations in the steady-state solutions and their stability; however, there are no qualitative variations.…”

“…As far as a study of the effect of grains is concerned, one should choose a spaceresolved description of spots with at least two spatial variables; 0-D (integral) or 1-D descriptions (e.g., [1]- [4] and references therein) can hardly give meaningful information on an effect that is multidimensional by nature. 2-D numerical modeling of vacuum arc spots is reported in [5]- [14]. In particular, in [12] and [13] cathode spots on composite CuCr contacts have been studied in the case where chromium grains are large, which occurs at initial stages of life of contacts of highpower circuit breakers.…”

Physics of Spotless Mode of Current Transfer to Cathodes of Metal Vapor Arcs

“…Recently, the same approach was applied to simulation of spots on cathodes of vacuum arcs [9], [10].…”