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

Abstract

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.

Investigating the dependence of the temperature of high-intensity discharge (HID) lamp electrodes on the operating frequency by pyrometric measurements

“…For a more detailed discussion the cathode and the anode have to be considered separately. The current density in front of the cathode is composed of the density of a thermionically emitted current j em (T electrode ), the density of an ion current j i (T es ) and the density of an electron back diffusion current j ep (T es ) from the plasma boundary layer to the cathode [10]:…”

“…The third term considers the heat transfer from the heavy particles in the boundary layer with the temperature T h in front of the electrode surface to the cathode. α is an empirical heat transfer coefficient [10]. The term (j em − j ep )(Φ − ∆Φ) gives the power which is needed to lift the electrons from the conduction band within the electrode into free space reduced by the power which is released within the cathode by the back diffusing electrons.…”

“…with noble gases or mercury. It is on one hand an outcome of intense theoretical studies and on the other hand of experimental investigations, mainly at a model lamp, within the last years [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. The description of the dc operation of anodes in HID lamps is less advanced, but at least a qualitative understanding has been achieved for cold and to some extent also for hot HID anodes [16,17,18,19].…”

“…The layer decouples the cathode from the bulk plasma. Accordingly, its properties are completely determined by the cathode fall U c and the temperature of the cathode surface T c [10,11]. The power balance of the system plasma boundary layer -cathode has different solutions beneath a distinct arc current corresponding to the experimentally observed diffuse and spot mode of cathodic arc attachment.…”

Investigating the gas phase emitter effect of caesium and cerium in ceramic metal halide lamps in dependence on the operating frequency

“…If pure tungsten electrodes are used the temperature of the electrode tip is raised up to its melting point, T m = 3695 K, to supply a sufficiently high thermionic electron emission for a diffuse attachment of the lamp arc on the electrodes [9,10,11,12,13,14,15]. But the work function and with it the electrode temperature can be substantially reduced if a dipole layer consisting of a monolayer of atoms being electropositive with respect to tungsten is deposited on the tungsten surface.…”