Numerical investigation of time-dependent electrode-plasma interaction in commercial HID lamps

Abstract

High-intensity discharge (HID) lamps capture more and more the markets for automotive headlight lamps (D2 lamp), video projection (UHP lamp), street/industrial lighting, floodlighting, etc. They are normally very small (typically 0.7-10 mm electrode gap) and have short time scales, leading to difficulties during experimental investigations. Thus, numerical simulations of HID lamps are an important tool to understand, improve, and develop new HID lamps. Especially the interaction between electrodes and plasma is a very localized and fast process, still not understood satisfactorily. Lamps are usually operated on alternating current (ac); the electrodes switch alternately from anode to cathode phase. Therefore, time dependent simulations that include realistic anode and cathode models are essential. We present a model having the ability to address all these challenges.Index Terms-Anode, cathode, electrodes, high-pressure discharge, lamp, plasma, non-local thermal equilibrium (LTE), time dependent simulations. W ITHIN this paper, a model first proposed in [1] and substantially improved in [3] is used. This model accounts for the special conditions in high pressure discharge lamps, needs no artificial division of the near-electrode plasma into different layers, includes plasma, anode, and cathode and the interactions between them. It predicts operating properties like temperature distribution within plasma and electrodes, heat fluxes to electrodes and quartz wall, electrode losses, type of arc attachment to the electrodes, etc. even for time-dependent lamp currents (alternating current (ac) operation). The model uses a complete energy balance for plasma temperature (1) and electrode temperature(2), and electric current continuity (3). As a special feature, an additional differential equation (4) accounting for deviations from local thermal equilibrium (LTE) due to strong diffusion of electrons and ions close to the electrodes is used (due to large particle density gradients between hot plasma spot and "cold" near-electrode plasma, cf. Fig. 2). The result is a non-LTE electrical conductivity [4].(1)(2) Manuscript

Understanding anode and cathode behaviour in high-pressure discharge lamps

“…Thus a special focus of the model is the investigation of the lamp as a whole and the results cover many details of the lamp. The many possibilities of the model are outlined in [9][10][11][12][13].…”

“…Nevertheless, the high pressure within the discharge of HID lamps leads to a collision-dominated plasma where radiation processes do not disturb the LTE noticeably, which is established by the countless collisions between the plasma constituents. In a similar manner, the three-body recombination with an electron as the third particle (inverse reaction of collisional ionization 9 A more serious problem for this radiation will be the passage of the quartz walls. Furthermore, this high energy radiation might heat the electrodes or release an electron from the cathode.…”

“…The model equations described above are solved using the finite element method on an unstructured grid assuming rotational symmetry [34]. One important advantage of this method is that regions with large gradients (temperature, electric field, electrical conductivity) can be spatially resolved with a much finer mesh than other regions, leading to a very fine mesh in the vicinity of the electrode tips (very high spatial gradients of temperature, electron density and electric field) and a rather low density of mesh points elsewhere [9,12,13,34]. Furthermore, it is possible to consider arbitrary rotationally symmetric electrode and quartz vessel shapes.…”

The plasma modelling toolkit Plasimo

“…It is straightforward to generalize the method to systems in which multiple components and saturated gases are present, for details we refer to [31, section 6.7]. The authors have not been able to find another discussion of this technique in the scientific literature; it seems that most authors simply take the pressure as input to the model, see for example [58].…”

Investigations on the influence of pressure, current and electrode gap in high-pressure mercury lamps

“…A model first proposed in [7] and further improved in [8][9][10][11][12] predicts such operating properties allowing even time-dependent lamp currents (ac operation, [8][9][10][11]). This model uses a complete energy balance for plasma and electrodes (equations ( 1) and ( 2)), electric current conservation (equation ( 5)), and, as a special feature, an additional differential equation accounting for deviations from LTE-conditions due to strong diffusion of electrons and ions in close proximity to the electrodes (equation (7)).…”