Positive Column of High-Pressure Arcs Elenbaas-Heller Equation

Positive Column of High-Pressure Arcs Elenbaas-Heller Equation 

The temperature distribution in a long cylindrical steady-state thermal plasma colunm stabilized by walls in a tube of radius R is described by the Elenbaas-Heller equation, assuming heat transfer across the positive coliunn provided by heat conduction with the coefficient X(T). According to a Maxwell equation, cur IE = 0 and the electric field in a long homogeneous arc colunm is constant across its cross section. Radial distributions 

This equation is known as the Elenbaas-Heller equation. Boimdary conditions for (4-55) are dT jdr = 0 at r = 0, and T = at r = i . The experimentally controlled parameter is current  

The Elenbaas-Heller equation (4-55) together with (4-56) permits calculations of the function E I), which is the cmrent-voltage characteristic of the plasma coluttm determined by two material functions electric conductivity a T) and thermal conductivity X(T ). To reduce the number of material functions, it is convenient to introduce, instead of temperatine, the heat flux potential (T)  

Using the heat flux potential, the Elenbaas-Heller equation can be simphfied  

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