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

Abstract

Changes in the pattern of steady-state modes of current transfer to thermionic cathodes induced by variations of the cathode geometry and temperature of the cooling fluid are studied numerically. For some combinations of control parameters, only one stable mode in a wide current range exists, which combines features of spot and diffuse modes. This mode, when attached to an elongated protrusion on the cathode surface, may be identified with the so-called super spot mode observed in experiments on low-current arcs. There is also reasonable agreement between the modelling and the experiment on cathodes of high-current arcs operating in the diffuse mode. The conclusions on existence under certain conditions of only one stable mode in a wide current range and of a minimum of the dependence of the temperature of the hottest point of the cathode on the arc current, manifested by this mode, may have industrial importance and admit a straightforward experimental verification.

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

“…24. Note that the curves T m ðIÞ shown in the mentioned figures exhibit not a loop but rather Z-shapes, similar to the one exhibited in Fig.…”

“…15, 22, and 23): (1) plasma pressure p ¼ 2.6 bar, cylindrical cathode of radius R ¼ 0.75 mm and height h ¼ 24 mm, T c ¼ 293 K, current transfer occurs in the diffuse mode; (2) p ¼ 2.6 bar, cylindrical cathode, R ¼ 0.3 mm, h ¼ 20 mm, T c ¼ 300 K, diffuse mode; (3) p ¼ 1 bar, cylindrical cathode with a hemispherical tip, R ¼ 1 mm, h ¼ 12 mm, T c ¼ 300 K, current transfer occurs in a mode which embraces states with a hot spot at low currents and states with a diffuse temperature distribution at high currents (this mode was investigated in Ref. 24 and in the following will be the termed mixed mode); (4) p ¼ 2.6 bar, cylindrical cathode, R ¼ 0.75 mm, h ¼ 20 mm, T c ¼ 300 K, the spot mode. Also reported are results on a solitary spot on an infinite planar cathode in the atmosphericpressure plasma.…”

“…6 occurs at low currents, where the Joule heating produces virtually no effect. In fact, this behavior is typical of the mixed mode of current transfer: 24 it is associated with a transition between states with a narrow current spot and diffuse-like states with a wide attachment. Again, nonstationary simulations revealed that states belonging to the retrograde section are unstable and states outside the retrograde section are stable, so the mode manifests hysteresis which, in principle, can be observed in the experiment.…”

“…We remind that this variant differs from variant 1 by a bigger cathode radius, a significantly smaller cathode height, and the cathode tip being hemispherical; the mode of current transfer occurring in these conditions was investigated in Ref. 24, embraces states with a hot spot at low currents and states with a diffuse temperature distribution at high currents, and is termed here mixed mode. Figs.…”

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

“…The eigenvalue problem governing the stability of steady-state solutions against small perturbations is self-adjoint (Hermitian) in this case [18]. This means, in particular, that the spectrum of perturbations is real, a conclusion that was confirmed by numerical calculations [19,20]. It follows that all abrupt transitions are monotonic in time.…”