The subject of this paper is a novel modelling method for dc operated high-pressure discharge lamps including both electrodes. No subdivisions of the discharge space into different regions (e.g. space charge layer, ionization zone, plasma column) is necessary. Starting from general diffusion equations, this goal is achieved by using a differential equation for a non-LTE electrical conductivity which is applicable for local thermal equilibrium (LTE) regions as well as non-LTE plasma regions close to electrodes. This novel approach is valid only for high-pressure conditions, where the product of electron mean free path and electric field is such that the mean energy gain of electrons is considerably less than the ionization energy of the discharge gas, so that the same local kinetic energy distribution can be assumed for the electron, the ion, and the neutral gas components anywhere within the discharge. Boundary conditions for this non-LTE electrical conductivity at cathode and anode are derived. We present modelling results for Hg- and Xe-discharge lamps (p⩾1 MPa). Comparison with results from traditional models using plasma layers will be presented and discussed. Convective flow within the lamp is not included yet, as the emphasis of this paper is on the regions close to anode and cathode.

The subject of this paper is the modelling of d.c. and a.c. high-intensity Hg-discharge lamps with differently shaped electrodes. Different arc attachments on the electrodes are studied and insight for the development of new electrodes is gained. The model includes the entire discharge plasma (plasma column, hot plasma spots in front of electrodes, near-electrode non-LTE-plasma) as well as anode and cathode. No subdivision of the discharge space into different regions is necessary (like space charge layer, ionization zone, plasma column). This is achieved by using a differential equation for a non-LTE electrical conductivity which is applicable for local thermal equilibrium (LTE-)regions as well as for non-LTE plasma regions close to the electrodes in a high pressure plasma. Modelling results for a 0.6 MPa mercury discharge considering six different electrode shapes (anode and cathode) are presented and compared with experimental results. The electrodes have different diameters and different electrode tips, such as hemispherical, flat, or conical tip with 60˚or 90˚apex angle. Furthermore, an electrode with a larger diameter in the mid section of the rod is investigated.

The 35 W D2 automotive headlight lamp with an electrode gap of around 4 mm is a well known example of a short-arc high-intensity discharge (HID) lamp. It has a filling of xenon, mercury, and sodium/scandium iodide and is driven by a rectangular-wave current of 0.4 A, 400 Hz. Other fields of application of HID lamps are video projection (UHP), street and industrial lighting, floodlighting, etc. Due to their small size and short timescales, HID lamps are often experimentally difficult to investigate or even inaccessible. Thus modelling gets more and more important. The challenges in modelling such lamps are e.g. the important plasma–electrode interaction, the time dependence (electrodes change with 400 Hz from anode to cathode phase and vice versa in the case of D2 lamps), and the complex plasma composition (Xe, Hg, NaI, ScI3 in the case of D2 lamps). Additionally the electrodes might change their well-defined tip geometry during operation, causing substantial changes in electrode temperature or electrode fall voltages. This paper intends to address all these questions and compare results of numerical simulations with measurements of plasma and electrode temperatures. Special focus is directed towards the important electrode–plasma interaction, which, even after seven decades of HID lamps, has not been understood satisfactorily. The results presented in this paper are very important for a better understanding of dc and ac HID lamps including the treatment of complex plasma compositions, the choice of the work functions, and the effect of different electrode geometries. Furthermore the results of the numerical simulations will lead to improved or new HID lamps.

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High-intensity discharge (HID) lamps have widespread and modern areas of application including general lighting, video/movie projection (e.g. UHP lamp), street/industrial lighting, and automotive headlight lamps (D2/xenon lamp). Even though HID lamps have been known for several decades now, the important plasma–electrode interactions are still not well understood. Because HID lamps are usually operated on ac (electrodes switch alternately from anode to cathode phase), time-dependent simulations including realistic and verified anode and cathode models are essential. Therefore, a recently published investigation of external laser heating of an electrode during anode and cathode phase in an operating HID lamp [28] provided the basis for our present paper. These measurements revealed impressive influences of the external laser heating on electrode fall voltage and electrode temperature. Fortunately, the effects are very different during anode and cathode phase. Thus, by comparing the experimental findings with results from our numerical simulations we can learn much about the principles of electrode behaviour and explain in detail the differences between anode and cathode phase. Furthermore, we can verify our model (which includes plasma column, hot plasma spots in front of the electrodes, constriction zones and near-electrode non-local thermal equilibrium-plasma as well as anode and cathode) that accounts for all relevant physical processes concerning plasma, electrodes and interactions between them. Moreover, we investigate the influence of two different notions concerning ionization and recombination in the near electrode plasma on the numerical results. This improves our physical understanding of near-electrode plasma likewise and further increases the confidence in the model under consideration. These results are important for the understanding and the further development of HID lamps which, due to their small dimensions, are often experimentally inaccessible. Thus, modelling becomes more and more important.