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

Abstract

It is shown that Steenbeck's principle of minimum power, or voltage, for discharges with fixed current is a not a corollary of the principle of minimum entropy production, in contrast to what is frequently assumed; besides, the latter principle itself does not provide a reasonable approximation in gas discharge physics. Similarly, Steenbeck's principle is not a corollary of mathematical models of gas discharges. Hence, this principle contradicts the mathematical models. A methodically correct evaluation of the error caused by the use of Steenbeck's principle requires a comparison of a solution obtained with the use of this principle with an exact solution to the same problem, rather than with experimental results or results deemed reasonable from the point of view of common sense. Such comparison is performed for two examples from the theory of a cylindrical arc column. The examples show that the error incurred by the usage of Steenbeck's principle is uncontrollable and may be unacceptably high.

A simplified model for the determination of current-voltage characteristics of a high pressure hydrogen plasma arc

“…We consider here a positive column of arc plasma burning and conned inside a cylindrical tube which walls are maintained at a constant temperature. This boundary condition, with a rotationally symmetric geometry, allows us to formulate the channel arc problem without involving the Steenbeck's minimum principle [11] which mathematical meaning in gas discharge physics has also been questioned [12]. The stronger the connement, the larger the gradients in the plasma arc.…”

Effects of laser induced metal vapour on arc plasma during laser arc double sided welding of 5A06 aluminium alloy

“…8, it can be seen that the Al and Mg atoms are ionised more easily than the Ar atoms. According to Steenbeck's minimum principle,33, 34 larger ratios of Al and Mg to Ar atoms ionise, allowing for relatively lower ionisation energy of the arc plasma during LADSW. The effect of laser induced metal vapour on the arc plasma was much stronger closer to the workpiece, and consequently, the arc will be stabilised and constricted in this region, as shown in Figs.…”

How Hydrogen Admixture Changes Plasma Jet Characteristics in Spray Processes at Low Pressure

“…Steenbeck's minimum principle [48] postulates a minimum arc voltage for a given arc current, working gas flow rate, and torch configuration. Although, this is a controversial issue [49], the fact is that the arc adjusts to a certain radial and longitudinal size. This leads also to the well-known restrike phenomenon [50].…”