Lars Dabringhausen

Different modes of arc attachment at HID cathodes: simulation and comparison with measurements

Based on a model for the plasma boundary layer of high intensity discharge cathodes, simulations are performed and compared with experimental results. To solve the power balance of the cathode body different methods are used, namely a 1D integral solution as well as 1D, 2D and 3D finite-element calculations. The simulations are done for cylindrical tungsten cathodes operated in different pure noble gas discharges (0.1–1.0 MPa) and with currents between 0.5 and 10 A. Under these conditions different modes of arc attachment are found, both in simulations and experiments. For the diffuse mode of arc attachment an excellent quantitative agreement between measurements and the simulations is obtained, reflecting an improved accuracy of measurements and simulation. In addition, different spot modes are found. At least one of these modes is also observed in the experiment. Also for this spot mode the agreement between measurements and simulation for the integral quantities is good. There are still some open questions concerning the spot mode of cathodic arc attachment. Varying the geometric dimensions of the cathode, the proper simulation of the heat conduction problem of the cathode body is shown. Variations of the plasma properties, like gas type and pressure, prove the conceptional capability of the boundary layer model for the simulation of different modes of arc attachment. Evaluating the cathode fall characteristics, regions of existence for the different modes are found, which are similar to the experiments.

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.

Arc attachment at HID anodes: measurements and interpretation

Anodes for high intensity discharge lamps made of cylindrical tungsten rods and the plasma in front of them are investigated in a special lamp filled with argon and other noble gases at pressures of 0.1–1 MPa. The arc attachment on these anodes takes place in a constricted mode. The temperature is measured pyrometrically along the electrode axis and the anode fall electrically. The electron temperature, Te, and the electron density, ne, within the anodic boundary layer are determined spectroscopically with high spatial resolution. It is found that the power input into the anode increases nearly linearly with the arc current. The proportionality constant is mainly determined by the work function of the electrode material and Te but is independent of the electrically measured anode fall and scarcely dependent on the electrode dimensions. The constriction is more pronounced in cold anodes, with maxima of Te and ne in front of the electrode surface, than on hot anodes with thermionic electron emission and vaporization of the electrode material. The distances of the Te- and ne-maxima from the anode surface are increased and Te is reduced in front of the anode with increasing anode temperature. The experimental findings may be explained by a model of the anodic boundary layer consisting of a thin sheath in front of the surface and a more extended constriction zone. The current and voltage are anti-parallel within the sheath. The power which is needed to sustain the sheath is supplied by an enhanced electrical power input into the constriction zone.

The boundary layers of ac-arcs at HID-electrodes: phase resolved electrical measurements and optical observations

Arcs are operated in noble gases with sinusoidal and switched dc currents of different frequencies in a model lamp between tungsten electrodes with properties appropriate for high intensity discharge lamps. The sum of the cathode and anode fall, called electrode sheath voltage ESV(t) = uc(t) + ua(t), is determined by a variation of the arc length and the anode fall ua(t) by probe measurements along the arc axis and an extrapolation procedure. It is found that ua(t) adopts low, approximately constant values within a half cycle. Therefore the time variation of the ESV reflects that of uc. It was observed by high speed photography that a high value of uc after current zero crossing (CZC) may initiate a transition of the initially diffuse mode of cathodic arc attachment into a spot mode. It is accompanied by a breakdown of uc causing the formation of a voltage peak starting at current zero crossing. It is a prominent example of the so-called commutation peak (CP). By an adjustment of the operation conditions to a low uc the cathodic arc attachment remains diffuse during the whole half-cycle. It is also indicated by high speed photography that the arc constriction in front of the anode is relieved with increasing operation frequency. It is illustrated by measurements that commutation peaks may be removed by an increase in the arc current, a decrease in the electrode cooling, a reduction of the filling gas pressure and an increase in the operation frequency. Moreover it is demonstrated, that the formation of a CP is sensitively dependent on the electrode surface structure.