Analysis of the arc-cathode interaction of free-burning arcs

Abstract

A theofetical model has been formulated describing the influence of the arc condition and the cathode material and geometry on arc cathode erosion. To arrive at a self-consistent description for the entire arc cathode attachment region, a realistic onedimensional sheath model has been used. This sheath model is supplemented by an integral energy balance of the ionization zone between the sheath and the arc, and by a differential energy balance of the cathode. For the case of a tungsten cathode in an argon arc, it h a s been shown that the ion current density is almost 50% of the total current density at low arc currents, while it decreases to about 18% of the total cunent density and the thermionic electron current density increases to about 82% of the total current density at high currents. It has also been found that heat conduction within the cathode and radiation from the cathode surface control energy transport from the cathode spot at low currents, and that dissipation by thermionic electron release dominates at high currents.

Multi-Electrode Plasma Torches: Motivation for Development and Current State-of-the-Art

“…However, due to the inherent complexity of solving the non-linear equations for the electric arc in a cross-flow of high velocity, in all the cases (steady state as well as transient) the highly non-equilibrium region very close to the cathode, including the space-charge sheath and the ionization pre-sheath, has not been implemented, unlike the more symmetric and simple transferred arc as being used in high pressure discharge lamps or in welding [39,40]. For the plasma torches, on the contrary, it is always assumed that the gas can be described everywhere as a fluid with a local welldefined one temperature and transport coefficients (local thermodynamical equilibrium LTE, i.e.…”

Maxwell's construction for non-linear heat structures and modelling of electrode spots in arc discharges

“…One gets j._,<ro+o+l We choose R in such a way that it exceeds substantially the length scale in the considered vicinity however is much smaller that the radius of the spot. Then the left-hand side may be evaluated by means of the boundary condition (8). Values g, (-R, 0) and r (R, 0) for such R are outside the range in which the function q is localised, hence the interval of integration on the right-hand side includes the whole of this range.…”

“…Such an approach has been widely employed and has given interesting and useful results (see, e.g., reviews [1,2] and references therein; we mention also recent studies [8,9]). Unfortunately, this approach is still incomplete.…”

“…Unfortunately, this approach is still incomplete. The above-mentioned recent works represent a typical example: the voltage drop in the near-cathode plasma layer is considered in [9] as an empirical parameter instead of being calculated; in [8], the 'principle' of minimum voltage is invoked, which does not follow from the governing equations.…”

What is the mathematical meaning of Steenbeck's principle of minimum power in gas discharge physics?

“…This principle has been extensively invoked in investigations of many gas discharge phenomena, in particular cylindrical arcs [4], effect of normal current density on glow cathodes [5], cathode spots in arc discharges [6]. Steenbeck's principle has still been used in the literature, e.g., [7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”