The plasma boundary layer of HID-cathodes: modelling and numerical results

From the experimental finding that the cathodic plasma boundary layer in front of a thermionically emitting cathode is independent of the bulk plasma, the conclusion is drawn that the power flux density and the current density from the boundary layer to the cathode can be reduced to functions which depend only on the cathode temperature and the cathode fall. To advance the calculation of these so called transfer functions an already existing model of the cathodic plasma boundary layer consisting of a space charge sheath and a pre-sheath is reconsidered. The latter is split into a zone in which the ion current is formed and into an ion acceleration zone. A closed expression is deduced for the ion current density with regard to the back diffusion of neutralized particles from the cathode but with disregard of mass inertia. The electron temperature in the boundary layer is related to the cathode temperature and the cathode fall by the power balance of the electrons in the boundary layer. Special properties of the cathodic boundary layer of an argon arc are given. They are calculated with rate coefficients which are evaluated with cross sections from the literature. Numerical results are presented showing the dependence of the transfer functions on the cathode fall, gas pressure, work function of the electrode material and on the properties of the rare gases neon, argon, krypton and xenon.