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

M S Benilov (1) , G V Naidis (2)

1 Departamento de Física
2 Joint Institute for High Temperatures of the Russian Academy of Sciences

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.

Mots clés: Physical Sciences

M S Benilov, G V Naidis. What is the mathematical meaning of Steenbeck's principle of minimum power in gas discharge physics?. Journal of Physics D: Applied Physics, 2010, 43 (17), pp.175204. ⟨10.1088/0022-3727/43/17/175204⟩. ⟨hal-00569590⟩