Table of contents

This special issue is concerned with a better understanding of the mechanisms in plasmas of the types found in the discharge lamps used for lighting. Most of these papers originate from presentations made at the 9th International Symposium on the Science and Technology of Light Sources held at Cornell University on 12--16 August 2001. A small number of papers from closely related studies have also been included in this special issue.

Arc terminations and particularly cathodes present major challenges for modellers and experimentalists alike. For the experimenter the difficulties are that most of the action takes place in very thin layers and that it is usually only global quantities such as electrode fall and power dissipation that can be measured without ambiguity. For the modeller, the difficulties lie in the complex geometries, the poorly known materials constants and, above all, the wide range of scale lengths involved.

The editors particularly welcome a group of papers from the Ruhr University in Bochum describing work on arc electrodes that was funded by the German government. These describe careful measurements of very wide interest on model arcs in an `ideal' high-pressure argon plasma. The construction of the electrodes and the experimental technique allow comparisons to be made between various theoretical models. The result of this extensive work is a very substantial improvement in the understanding of the termination regions, at least in argon arcs. Papers from other institutions describe detailed observations on electrodes in more complicated atmospheres.

Other related papers refer to the modelling of the complete arc with its terminations, ignition, and the radiation transport within discharges. Many arcs, both in low and high-pressure discharges, depend on surface layers of low work function and a number of the papers address this.

The editors hope that bringing this group of papers together will provide a resource for those aiming for a more complete understanding of the complex behaviour of discharge lamps.

A Koedam β factor makes it possible to compute the total output power in line radiation from a positive column discharge using a single radiance measurement normal to an aperture in the wall. The results of analytic derivations of β factors are presented for columns with uniform (β = 1.0) and parabolic (β = 0.75) excitation rates per unit volume and with negligible opacity. A Monte Carlo code for simulating radiation trapping with a spatially uniform density of absorbing atoms is then used to determine β factors as a function of opacity. The code includes partial frequency redistribution and a Voigt line shape with radiative broadening, resonance collisional broadening, and Doppler broadening. The resulting β factors are found to be nearly independent of opacity over a wide range of column radii for spectral line shapes dominated by Doppler broadening or by resonance collisional broadening. Additional Monte Carlo simulations are used to study β factors as a function of a non-uniform density of absorbing atoms from radial cataphoresis with line shapes dominated by Doppler broadening, foreign gas broadening, and resonance collisional broadening. Radial cataphoresis is found to increase β factors in all cases. Geometrical effects, refraction, and imperfect transmission at the glass wall are studied and found to decrease β factors.

To verify models describing the near-electrode regions electrodes of pure and doped tungsten for high intensity discharge lamps are investigated in a special model lamp. It can be operated with arc currents of 1 A to 10 A, DC or AC with arbitrary waveforms up to a few kHz. Argon and xenon, at pressures from 0.1 MPa to 1 MPa, are used as fill gases. A large variety of electrodes can be inserted. To perform spatially resolved measurements they are displaced reproducibly within the discharge tube during lamp operation.

Spatially resolved pyrometric measurements of the electrode surface temperature in the case of DC operation are presented. From the temperature distribution the power loss of the electrodes by thermal radiation and heat conduction is determined. It increases almost linearly with the arc current at the anode and less than linear at the cathode. A relation is deduced between the cathode fall and the power fed into the cathode setting up the power balance of the cathodic current transfer zone. The resulting cathode falls show a strong dependence on the electrode diameter. Electrical measurements of separate cathode and anode falls are given in a subsequent paper. The outcomes of both methods and of modelling are compared in a third paper.

A special measuring method with Langmuir probes was established which yields the plasma potential in high-pressure plasmas to determine separate cathode and anode falls of HID electrodes. The probes consist of two tungsten wires which are inserted via side arms into the discharge tube of a model lamp. Their bended ends form together a full circle which surrounds the arc at its boundary. One probe is operated at floating potential with the other one a current-voltage characteristic of the probe is recorded. Its shape corresponds to that taken with a plane probe in a low-pressure plasma. Taking into account the radial voltage drop between the axis and the boundary of the arc, it was shown that the inflection point between the retarded electron current and electron saturation current represents the plasma potential in the arc axis. The electrode falls were determined by an extrapolation of the plasma potential which was measured along the arc axis towards the electrodes. Cathode and anode fall measurements at tungsten electrodes of different diameters are presented which were performed with an arc in argon at 0.26 MPa at currents between 1.5 and 6 A.

Electrodes of pure and doped tungsten for high intensity discharge lamps are investigated in a special model lamp. Our intention is to obtain experimental data to verify models describing the near-electrode region. For the DC case, we have two totally independent methods to determine the cathode fall separately from the anode fall. The first method is based on the spatially resolved measurement of the cathode surface temperature and a treatment of the cathodic power balance. The second method uses Langmuir-probe measurements to determine the plasma potential at known distances from the cathode.

The comparison of both methods shows good agreement which justifies the assumptions and simplifications introduced. Parameter studies yield a strong dependency of the cathode fall on the cathode diameter and the material. The cathode length and the fill gas pressure seem to have only minor influence. Comparing the results of our experiment with outcomes of models by several authors, the values for the cathode fall show good agreement, too. However, concerning the total power loss of the cathode, differences between experiment and theory were found.

Electrodes made of pure and doped tungsten are operated in a special model lamp with a DC current of 1-10 A in argon or xenon atmosphere within the pressure range of 0.1-1 MPa. Cylindrical electrodes with different designs are investigated with regard to the mode of cathodic arc attachment. Three modes are observed: a diffuse mode, a spot mode and a super-spot mode. The major difference between the diffuse and the spot mode is the current density, which is low in the case of the diffuse mode and high in the spot mode. The diffuse mode is favoured by high current, low pressure and weak cooling of the electrode, the spot mode by the opposite conditions. In a transition region the cathode changes statistically between these modes. Whereas the global electrode temperature and the cathode fall of the diffuse and the spot mode differ slightly, the super-spot mode is associated with a significantly decreased global electrode temperature and cathode fall at similar parameters. SEM pictures show that the surface structure of the electrodes has wide influence on the mode of cathodic arc attachment. Due to the significant difference between the super-spot mode and the two other modes this paper is concentrated on the comparison between the spot and the diffuse mode.

Usually two modes of arc attachment to cathodes for high intensity discharge (HID) lamps are observed, the spot mode for high pressure, low currents and large electrode diameters and the diffuse mode for the opposite conditions. Recently, a very constricted attachment to cathodes was observed both in real HID lamps and in Bochum's model lamp. In the model lamp, the extremely constricted arc attachment was observed in argon and xenon atmosphere at a pressure p = 0.26 MPa and for currents I = 1-6 A. Whereas the global electrode temperature and the cathode fall of the diffuse and the spot mode differ only slightly, the extremely constricted arc attachment (so-called `super spot mode') is associated with a significantly decreased global electrode temperature at similar parameters. The reduction in electrode temperature implies low cathode falls and low electrode losses, respectively. Scanning electron micrographs show that the surface structure of the electrodes has substantial influence on the mode of cathodic arc attachment.

Spatial profiles of electrode temperatures and plasma temperatures have been measured on `real' HID lamps filled with a commercial metal-halide compound. The absolute accuracy of pyrometric determination of electrode tip temperatures was ±30 K, while the determination of plasma core temperatures, using a modified Bartels method, has an accuracy of ±100 K.

We could deduce a close correlation between the plasma temperature in front of an electrode T_pand its tip temperature T_t due to the influence of the cataphoresis. If T_p is reduced at the cathode the T_t value has also lowered, whereas T_p at the anode is raised together with its T_t data. This correlation disappears at ballast frequencies above 100 Hz, whereas the cataphoresis influence on T_p continues up to 500 Hz. Based on the latter limit, a rough estimation of the cataphoresis velocity delivers 700 cm s^-1. As a tentative interpretation, we suggest that the connection between T_p and T_t is caused by an increase of the ion part of the total current at the cathode due to Na accumulation before it. Thus, the cathode has to emit fewer electrons and works at a lower temperature.

Further results are the temporal behaviour of T_t depends on the ballast type. For vertical operation the strong influence of convection on T_t has also to be taken into account. Above 100 Hz, where only convection plays a role, the upper electrode T_t exceeds the T_t value of the lower electrode by nearly 400 K. This discrepancy one may explain, tentatively, by convection heating of the upper electrode and convection cooling of the lower one.

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.

Experimental and theoretical investigations have been performed on the ignition process of low-pressure mercury-noble gas fluorescent lamps operating on a 50 kHz electronic driver circuit. In case the electrodes of the lamp are not heated prior to the ignition process, the ignition process can, under certain conditions, lead to premature fracture of the coiled-coil electrode, which means that the lamp ceases to operate before the emitter is consumed completely. Experimental studies of this process have shown that the erosion process responsible for this premature end-of-life consists of localized sputtering of the tungsten electrode by energetic ions from the glow discharge that is present during the ignition process. In order to understand the basic process that leads to localized sputtering of the electrodes in a glow discharge, a simple glow-discharge fluid model, in combination with a finite-element model of the heat transport in the electrode, has been built. The model shows that thermionic emission can supply a significant fraction of the electrons already at temperatures far below the normal operating temperature in fluorescent lamps. This thermionic emission is responsible for a contraction process. After the beginning of the discharge contraction it takes typically a few milliseconds before the glow-to-arc transition is observed in the lamp voltage and the normal electrode operating temperature is reached. During this time localized sputtering takes place, which eventually leads to coil fracture.

The arc attachment on electrodes is investigated in 50 Hz high-pressure mercury and sodium discharges between 50 and 150 W. In the cathode and also in the anode phase the discharges are constricted towards the electrodes, and in case of mercury a spot is formed at the electrode. For sodium a diffuse attachment is found in both phases. Side-on intensities in the electrode region are measured with an intensified CCD camera connected to a spectrograph. This leads to a spatial resolution of ~10 µm. The plasma temperature is determined from absolute line intensities of optically thin lines. A rapid temperature increase to nearly 11 000 K is found for mercury within 200 µm in front of the cathode. The same tendency is found in case of sodium but the sheath is smaller and the temperatures are lower compared to mercury.

A new method for the determination of the cathode fall voltage of fluorescent lamps is shown. The cathode fall voltage can be determined by measurement of the lamp operating voltage at constant lamp wall temperature, constant discharge current and variation of the electrode heating current. Commercial lamps, which do not need to be specially prepared, can be used for the measurement. The results show good correlation to other measurements of the cathode fall voltage at various discharge currents by means of capacitive coupling. The measured values of the cathode fall voltage are used for determining the minimum, target and maximum setting of the sum of the squares of the pin currents of one electrode (the so-called SOS value) as a function of the discharge current in fluorescent lamp dimming.

The depletion of emitter from the oxide cathodes during the glow switch starting of the discharge in 50 Hz operated low-pressure mercury/noble gas discharge lamps (fluorescent lamps) has been studied. It follows from pulse ignition studies and computer-controlled ignition experiments that two plasma modes exist during ignition: a glow discharge and a vapour-arc discharge. The occurrence of these modes depends on the point of interruption with respect to the phase of the 50 Hz preheat current. The vapour arc appears to be the dominant mechanism of emitter depletion. The average emitter loss per vapour-arc pulse has been quantified by radioactive Ba tracer experiments. The nature of the vapour arc has been studied by fast photography and SEM. The vapour arc involves dielectric breakdown over the non-conducting oxide mass and gives rise to explosive emitter vapourization.

The cathodic region of atmospheric pressure arcs is dominated by a number of different mechanisms. This makes a theoretical model extremely difficult. A description of this region based on fundamental physical principles is given. Using a previously published model of the inhomogeneous boundary layer of a Saha plasma (Schmitz H and Riemann K-U 2001 J. Phys. D: Appl. Phys.34 1193), the description is set on a firm theoretical basis. A number of equations including the energy balances of plasma boundary and cathode body lead to a maximum closure of the system. The values for the boundary conditions toward the plasma column could be motivated by a simple minimum principle argument thus eliminating all arbitrary fitting parameters. Results are given for a variety of external parameters and three different discharge gases. The comparison with experimental results shows excellent agreement.

A model of the near-cathode plasma layer in a plasma under a pressure of the order of one or several bars is reconsidered on the basis of recent theoretical results. Physics of the near-cathode layer is analysed in the range of near-cathode voltage drops of up to 50 V, in accord to recent experimental results which have shown that the near-cathode voltage drop in high-pressure arc discharges may be that high. It is found that a non-monotony of the dependence of the energy flux density on the surface temperature at fixed values of the near-cathode voltage drop is caused by one of the three mechanisms: overcoming of the increase of combined ion and plasma electron heating by the increase of thermionic cooling as the plasma approaches full ionization; non-monotony of the dependence of the ion current on the electron temperature which is caused by the deviation of the ion current from the diffusion value; rapid increase of the plasma electron heating which is subsequently overcome by thermionic cooling. A closed description of the plasma-cathode interaction is obtained by numerically solving the nonlinear boundary-value problem for the temperature distribution inside the cathode body. Results of numerical modelling of the diffuse discharge under conditions of a model arc lamp are given and a good agreement with the experimental data is shown.

Under certain conditions alkali vapours form dipole monolayers on metallic electrodes that can lower the work function of the bulk material. In this case, the power balance of the electrode, the electrode fall voltage and the electrode loss power can change considerably. To verify this effect a pyrometric technique was adapted and optimized for the diagnostics of tungsten electrodes in high pressure sodium discharges. Using an already verified model of thermally emitting cathodes the effect was observed in a Na DC discharge and the range of existence was investigated. An interpretation of the results is given using a Langmuir description of forming the Na monolayers and first-principles electronic structure calculations using a pseudopotential plane wave method to solve the Kohn-Sham equations of density-functional theory.

By observation of arc attachment on the cathode of an ac high-pressure mercury discharge, a transition from a diffuse mode at low current to a spot mode at higher current was found. The transition was accompanied with a sudden decrease in the arc voltage of about 10 V. At decreasing current there is a reverse transition with a voltage increase. A recent cathode-fall model shows quite a similar behaviour. Further, the electrode sheath voltage (essentially the sum of anode and cathode fall) was measured and compared with the calculated cathode fall. The obvious differences especially during the current rise were ascribed to the anode fall which should attain highly negative values in the order of 10 V.

The time dependences, up to 200 s, and the noise power spectrum (0.005-10 Hz) in the electron transport response at bias up to 300 mV of Co/Al₂O₃/Ni₈₀Fe₂₀ magnetic tunnel junctions (MTJs) and of Co/Al₂O₃⟨δ(Fe)⟩/Ni₈₀Fe₂₀ (with Fe δ dopants of thickness 1.8 Å inside the barrier) were investigated. The magnetic field was changed between +100 and -100 G in steps of 1 G. The measurements were carried out at different temperatures between 77 and 300 K for the samples with large tunnel magnetoresistance (exceeding 14% at 300 K). We found that the magnetization reversal of the Co and permalloy electrodes, as detected from the time response near the coercive field, occurs via relaxation on the timescale of about 10² s with sudden jumps in the resistance (ΔR/R~10^-2-10^-3). We link this noise to the depinning of the domain walls. In addition to the magnetic noise, in some of the studied MTJs with Fe δ dopants, we observed a two-level-system telegraph-type noise, which was independent of the magnetic field, indicating its relation to the trapped charges inside the insulating barrier. For MTJs, the noise power spectrum has 1/f^α character for a wide frequency range below a few Hz. At low bias and parallel state the exponent α is close to 1-1.5, but at higher bias or in the antiparallel state the exponent increases to 2. We link these effects to non-equilibrium noise in magnetic structure of the electrodes in the antiparallel state and to non-equilibrium transport inside the barrier at high bias.

Some peculiarities of the spatial distribution of magnetization _S inside stripe domains near the planar grain boundaries in the sheets of soft magnetic alloys such as Fe-3%Si with orientation (01) in demagnetized state are investigated. By means of solution of the Landau-Lifshitz equation, the equilibrium magnetization configurations are calculated and mechanisms of their formation are discussed. An existence of 180° domain walls bending under the action of the magnetostatic fields at the grain boundary was theoretically grounded.

A recently developed method for the solution of the space-dependent electron Boltzmann equation in higher-order accuracy has been adopted to study the behaviour of the electrons in the anode region of a dc glow discharge. This method is based upon a multiterm approximation of the Legendre polynomial expansion of the electron velocity distribution function. Generalizing the boundary conditions, in particular for the partially absorbing anode, the impact of the anode fall and the influence of the electron absorption at the anode on the spatial behaviour of the electron kinetic properties have been investigated in various approximation orders. The analysis has shown that the simplified treatment of the kinetic equation using only the first two terms of the velocity distribution expansion can lead to considerable falsifications of the convergent behaviour. In general, the convergent solution of the significant components of the electron velocity distribution and all important macroscopic quantities is obtained by a multiterm approximation including six to eight terms of that expansion. The discrepancies between the two-term and convergent results are found to depend sensitively on the parameters of the anode fall. In addition, the multiterm results are compared with corresponding ones obtained by accurate Monte Carlo simulations. Very good agreement between the convergent eight-term Boltzmann and Monte Carlo simulations is found.

The argon positive column has been investigated by means of a complementary diagnostic approach, which combines the CW laser collisionally induced fluorescence (LCIF) technique with kinetic models for the excited-state populations and emission line ratios. The conditions ranged from pressures of 0.30-8.0 Torr and currents of 1-10 mA, equivalent to reduced axial electric fields of 1.7-53 Td. Fitting theory to experimental observations of the 1s densities and 2p-1s emission intensities allows determination of the electron temperatures relating to the high-energy electrons in the tail of the electron energy distribution function. The tail temperatures vary from 0.9 to 1.9 eV over the range of conditions investigated. Examination of CW LCIF for 1s₅-2p₂ (696.5 nm) laser excitation along with the traditional optical absorption and emission techniques provides specific information on the collisional kinetics involving the metastable states.

A theoretical analysis is presented for the processes involved in natural lightning attachment to earthed structures. This analysis is based on physical criteria for upward leader inception and propagation during the approach of the downward lightning leader. Analytical expressions for the equivalent voltages and their time variation are obtained for earthed structures before and after upward leader inception. Equivalent voltages in lightning rods of varying height are calculated for different values of the peak stroke current of lightning, taking into account the process of upward leader development. Significant values of equivalent voltages and their derivatives at the final jump phase of a downward leader are predicted. It is shown that there is a time interval between the moment of upward leader inception and the time when the upward leader propagation condition is fulfilled. The implications of these results for testing in a high voltage laboratory are also discussed.

A model is developed for electron-ion recombination in a gas capacitor in which the cathode is irradiated simultaneously by an electron beam and a defocused flux of soft-landing ions, under conditions such as encountered in variable pressure scanning electron microscopes (SEMs). The model describes the dependence of the secondary electron (SE) emission current (injected into the gas from the cathode) on the distance above the cathode, and the effects of SE-ion recombination on electron imaging signals utilized in SEMs. The model is tested experimentally, and is used to construct a simple procedure for quantification of the effects of SE-ion recombination on emissive signals in a gas capacitor. The presented method allows for quantification of electron emission current measurements obtained in a variable pressure SEM.

This paper presents an advection-diffusion model to describe the stagnation of normal grain growth in thin films. The underlying advection-diffusion model describes grain growth in a two-dimensional topological-class/size space. Grain boundary grooving and the correlation between neighbouring grains are introduced into the model to represent stagnation. Grain boundary grooving causes the stagnation of grain growth, and the correlation between neighbouring grains accelerates the effects of stagnation. Numerical solution of continuity equations gives a grain size distribution that is close to log-normal, and fits experiments well. The time development of average grain size also shows the stagnation of grain growth.

The experimental measurements of spatial distribution of copper vapour flux from a two-dimensional source (D = 10.4 mm; L = 97 mm) was carried out by impinging electron beam from 130 mm strip electron gun. The copper vapour was generated in the transition flow regime of rarefied gas dynamics and experimental measurements were carried out by using deposition technique, at locations (r), where free jet expansion is expected to show three-dimensional behaviour (D<<L~r). Reported analytical expressions based on Knudsen's cosine law for two-dimensional sources with uniform temperature were reviewed and used for the interpretation of experimental data. The inadequacy of these expressions is pointed out by noting the systematic deviation of the calculated values from the observed ones with receding position of the vapour collector from normal line of the source. Attempts are made to interpret experimental data by dividing source area into small elemental areas and integrating contribution from each such area on to the collectors. The experimental data could be best fitted within ±5% with cos ⁿψ distribution with n = 1.77 and uniform source temperature of 1694 K or with n = 1.75 with temperature distribution along and across the focal strip with an average temperature of 1687 K as compared to the measured value of 1685 K.