ABSTRACT
MODEL EQUATIONS AND BOUNDARY CONDITIONS Our time dependent two-dimensional model includes the entire plasma (local thermal equilibrium (LTE) plasma column, hot plasma spots in front of electrodes, constriction zones, non-LTE-plasma) as well as anode and cathode and interactions between plasma and electrode surface! Using a non-LTE electrical conductivity, no subdivision of the discharge space into different regions (e.g. space charge layer, ionization zone, plasma column) is necessary. The discharge is described by the electric potential V, the plasma temperature T„, and the electrical conductivity a. Additionally we calculate the temperature distribution TF in anode and cathode. The electric potential V(r,z,t) in the plasma is determined by current continuity (1). The temperature T(r,z,t) is calculated by means of the power balance in the discharge (2) and the electrodes (3), taking the specific heat of plasma and electrodes into account. To calculate the electrical conductivity a(r,z,t) we use an approach first proposed by Fischer [I], which includes strong diffusion of electrons near anode and cathode due to a large gradient in the electron concentration (4). Eq. (4) is applicable for LTE regions as well as for non-LTE plasma regions close to the electrodes in high-pressure plasmas. More details concerning the model can be found in [2].
