Jens Wendelstorf:     Models

2. Physical models for the individual parts of the electric arc discharge


The details of this work can be be found in a consistent and scientifically elaborated form in my dissertation. The following introduction is short, but somewhat outdated.
The computation of a specific discharge configuration requires mathematical models of the individual discharge regions and algorithms for the iterative linking between them:
Physical regions of the arc plasma

2.1 Modelling complex chemical equilibria

For calculating the physical properties of a specific plasma gas, first the thermodynamic properties have to be determined. Since our applications lie in the field of thermal plasmas, we assume [partial] local thermodynamic equilibrium ([p]LTE). That means, local particle densities only depend on local temperature.

However, the distinction of electron and heavy particle temperature is often important (partial LTE). A practical implication of the pLTE is the need to calculate the partition functions, as these are tabulated for LTE only.
For the simple case of a single gas plasma (neutral particles, electrons and the individual ionization states), elementary thermodynamic data can be calculated and visualized on-line (on-line plasma Calculator OPLACALC - sorry, access is limited) .

2.2 Calculation of the transport coefficients in (partial) LTE

If the densities and thermodynamic state variables of the respective gas mixture are known, the electric and thermal conductivities etc. can be calculated with the help of various cross sections or interaction potentials. The resulting transport coefficients are functions of the local temperatures (and pressure).
In particular for lamp plasmas, there is also substantial effort needed to calculate the radiation phenomena. State of the art is the separation in optically thin (net emission coefficient) and optically thick (additional heat conductivity) radiation.

2.3 Modelling the plasma column

Knowing the temperature-dependent transport coefficients, enables us to calculate the flowing [p]LTE plasma of the arc column. Depending upon application, continuity equation, Navier Stokes equation and energy transfer equation have be considered. For a [p]LTE plasma two coupled energy balances are to be set up. For the case of large Reynolds numbers (plasma torches) turbulence models are needed also. At lower pressures or currents (some lamps) some additional transport equations have to be implemented (segregation effects).

2.4 Modelling the non equilibrium layers in front of the electrodes

The assumption of local thermodynamic equilibrium is not justified some hundreds of micrometers in front of the electrodes. These areas are called cathode- and anode-fall and are forming a skin over the surface of the electrode solid. They are responsible for the transition from metallic solid to thermal plasma, which in general shows substantially higher temperatures than the solid surface. Here we have substantial effects from space charges, ionization and (ambipolar) diffusion.

2.5 Modelling of the electron emission processes

To some extend, the electron emission properties of the hot (tungsten) cathode are modelled by the Richardson-Schottky equation. For higher local electric fields, we have thermal field emission calculation codes and tables, which were developed at the Institute for Theoretical Physics that TU-Braunschweig.

2.6 Modelling of the electrode solid

In the electrode solid, we are computing thermal conduction and current transport. However, temperature-dependent material properties are necessary.
Additionally, the transport and high temperature chemistry of activator substances (e.g. ThO_2) and the reactions between electrode material and orifice gas can become important.
Perhaps, you may want to see, how these electrodes look like?

Last modified: 10.10.1998
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