Chairman:G.C. Dijkhuis
J.J. Lowke


J.A.M. van der Mullen and J. Jonkers

Department of Applied Physics,Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, the Netherlands

For monitoring plasma processes the plasma characterization is in many cases realized by simple spectroscopical techniques; often with the aim to find or follow the temperature. Very popular is the 2-l method in which the temperature is determined by measuring the ratio of two (atomic) lines. In the presence of LTE this temperature can be used to determine the electron density and other plasma properties. The justification of the LTE assumption is in many studies guided by the Griem criterion, which predicts the critical electron density above which the influence of the escape of radiation can be neglected.

However, what is seldom realised is, that fulfilling the Griem criterion, although needed in most cases, is hardly ever sufficient. Even at high ne values there might be other equilibrium disturbing mechanisms such as the outward transport of charged particles. Just like the escape of radiation this can affect the atomic state distribution function so that the application of the 2-l method might give wrong results. This is mostly handled by introducing (qualitatively) more temperatures; such as excitation-, ionization- translation- and-so-on- temperatures.

The aim of this study is to come to a more quantitative treatment of equilibrium departures and plasma characterization by relating the responsible transport fluxes to the corresponding equilibrium restoring processes. Therefore we use the following recipe.

First of all it is realized that for a system in full equilibrium (TE) the principle of DB applies, stating that equilibrium is present on each stage or level in the sense that each forward process (collisional or radiative) is balanced by the corresponding backward process acting along the same channel (but in the opposite direction). Thus a plasma in TE can be seen as an ensemble of Bilateral Relations: 'generalized levels' or system parts linked up by forward and backward processes. Second, the departure from equilibrium can be described as a disturbance of one or more of these bilateral relations by one or more transport fluxes.

Thus the departure can be visualized by disturbed bilateral relations DBR, each between two "generalized levels" a and b. In steady state we have for the level b the balance


stating that the rate of the forward reaction (Nanf where Na is a 'density' and nf a frequency), equals that of the backward reaction Nbnb plus the (transport) 'leak', the efflux ft = Nbnt. For ft = 0 (or nt = 0) the principle of DB states that


which can be divided on eq.(2), giving:


in which the parameter b = N/Neq is introduced to express the densities in units of the corresponding equilibrium values. Depending on the application it can be useful to choose either b(a) = 1 or b(b) = 1. Note that it is assumed that the equilibrium departure does not change the frequencies nf and nb. This is justified if the departure is not too large.

The generalized levels a and b of the DBR can play various roles; such as that of 1) two atomic levels, 2) two subsequent ion stages, 3) two energy intervals in the electron energy space or on an even higher stage 4) a can refer to the group of electrons {e} and b to that of the heavy particles {h}. The transport leak ft can be (related to) 1) the escape of photons, 2) electron-ion pairs leaving the plasma, 3) the fast electrons which are removed due to inelastic collisions or 4) the heat loss from the heavy particles {h} to the environment.

The simple equation (3), which has a large application field, expresses that the equilibrium departure of the specific DBR is related to nt/nb, the ratio of the transport and backward frequency at the leak-side b. It can in many cases be used to predict (parts of) distribution functions and serves as a general formulation for equilibrium criteria: There is equilibrium provided nt/nb << 1 or nttb << 1. Or in words: equilibrium is (almost) established if the number of leaks-per-balance-time is much less than unity. More specifically one can define the presence of equilibrium quantitatively by stating that for equilibrium the relation nttb < 0.1 must hold. In this way a general (quantitative) boundary criterion is introduced. It should be noted that the Griem criterion in which the escape of radiation (efflux) is compared to the equilibrium restoring collisional processes, has the same structure.

If the leak can be neglected we have a so-called proper balance; a balance of forward and corresponding backward processes (Na nf = Nb nb), whereas if the leak dominates (in steady state) a so-called improper balance is present in which the number of processes arriving at the leak-side b equals that of the 'outward' processes leaving this a-b system ((Na nf = Nb nt).

Depending on the nature of the equilibrium restoring processes, we can distinguish between proper balances of the Maxwell (elastic energy transfer), Boltzmann ((de)excitation), Saha (ionization/recombination) and Planck (absorption/emission) type.

It is very well possible that equilibrium of a certain type is (almost) established whereas others are not. We then speak of partial equilibria. For instance pLSE (partial local Saha equilibrium) refers to the situation in which an upper part of the atomic system is ruled by a Saha balance (ionization/recombination) in equilibrium.

In some cases eq. (1) can be used for describing the plasma as a whole by casting the electron energy and particle balance in this DBR form. Especially for small plasmas with consequently steep gradients this leads to a relatively simple characterization. The main reason is that because of the fact that the plasma is so small and thus largely influenced by the environment it is possible to find a relation between control parameters such as power, volume and pressure which externally determine the plasma and the specific internal properties of the plasma like ne, Te and the departure from equilibrium. However, apart from the influential external properties also atomic properties of the main gas are of importance. If e.g. the well-known Ar is replaced by the ten times lighter He, the influence of the escape of charged particles will be enhanced. The consequence is that, apart from having roughly a factor of two larger electron temperature, a He plasma will also have an electron density which is about 10 times smaller whereas the departure from equilibrium can easily be 4 orders of magnitude larger than that of an equi-operational argon plasma.

Results from laser diagnostics will used to support this study on the influence of equilibrium departures induced by steep gradients.


S. Cavadias and J. Amouroux

Laboratoire de Genie des Procedes Plasmas - ENSCP - UPMC, 11 rue P. et M. Curie 75231 Paris cedex 05

In the general theory of heat transfer between a gas and a surface there is a tacit hypothesis: that is the gas surrounding the surface prevails thermodynamic equilibrium, as well as between the gas and the surface. However number of interesting systems does not comply with this hypothesis, as for example upper atmosphere, plasma chemistry, laser chemistry etc. In these cases the gas is out of thermodynamic equilibrium, and molecules have intense internal excitation. This non-equilibrium character (thermal or chemical) plays an important role in the heat transfer during gas-surface interactions. As the temperature grows the Ea/RT factor approaches unity, molecular bonds begin to break. The atoms or radicals formed begin to recombine and to rearrange to form other molecules. The solid surface from a kinetic viewpoint may be considered as a system with an infinite degree of freedom and can be the place where some excess of kinetic (translational energy may be deposited and recombination of atoms may occur. The energy released during this recombination is shared between the produced molecules and the surface. Thus besides the heating of the surface by transport there is an additional heating due to the recombination leading to the increase of temperature and acceleration of the surface heating.

The study of non-equilibrium heat transfer must answer some key questions:

Is there any influence of the nature of the surface in the rate of the recombination?
How is the exothermic energy shared between desorbing products and the surface?
What happens at the surface during these reactions?

An attempt to answer these questions is presented here through the example of the recombination of oxygen atoms on metals such as copper, silver, zinc, gold, steel and ceramic materials like silicon carbide or silica. In this case the total energy transferred to the surface depends on the recombination of oxygen atoms and the accommodation of the energy released during this recombination at the surface.

The operating procedure consists of the production of an atomic oxygen flux in a low-pressure (diffusion regime) plasma reactor.

The recombination coefficient, which is the ratio of the recombined atoms to the sticking atoms in the surface, can be measured by Actinometric Optical Emission Spectroscopy. The use of a pulsed discharge allows very short plasmas (a few hundreds of milliseconds). Thus there is no thermal exchange between the plasma and the surface and the modification of the chemical composition of the surface can be followed by different ex-situ analyses, for different exposure times.

The accommodation coefficient which is defined as the ratio of the energy transferred to the surface to the total energy released by the recombination is measured by a calorimetric method for different temperatures of the surface.

As already mentioned the chemical structure of the surface during the recombination changes inducing a variation in the rate of the recombination coefficient, accelerating or reducing the heat transfer.

Surface analyses of the surfaces show a very fast oxidation of the metals (except gold) and the ceramic surfaces that means a quick ageing of the material.

The recombination and accommodation coefficients depend on the nature and the temperature of the metal or ceramic oxides. The recombination coefficient increases with temperature leading to a higher heat transfer and the heating of the surface. Also at higher temperatures the change of the oxidation mechanism can accelerate the heating of the surface.

Finally in agreement with literature on the electronic properties of the metallic oxides relationship between the catalycity of the material and its electronic nature has been established. Indeed the p-type semiconductors oxides like Ag20 or Cu~O are strongly catalytic, whereas the n-type such as SiO2 or Zn0 are poorly catalytic. Moreover, the higher the optical gap the lower the catalycity of the semiconductor.


Bakhtier Farouk

Professor of Mechanical Engineering, Drexel University, Philadelphia, PA 19104, U.S. A.


The design and control of reactive low pressure plasmas for materials processing are becoming difficult as the wafer and liquid crystal display sizes are increasing, and to the contrary, the size of etched trench or deposition layers are decreasing every year. This results in a great expense in research and development of plasma reactors. The design of reactors based only on experimentally obtained know-how is rather time consuming and expensive. A definitive solution to this problem is to develop computer codes for the analysis of the physics and chemistry within the reactor. However, this solution is not simple either. Phenomena in low pressure non- equilibrium plasma reactors are rather complicated. For example, there are electrons, positive and negative ions, radicals, gas molecules and reaction products in depositing/etching plasma reactors. To predict the distribution of deposition/etch rate on wafer, one has to simulate the production, consumption, diffusion and flow of all of the above species in multi-dimensional electric and magnetic fields.

Recent advances on the development of simulation tools for the prediction of plasma characteristics and deposition/etch behavior on wafers will be reviewed. Both particle and fluid models (along with hybrid models) are now under intense development by scientists and engineers to model reactive low pressure plasma reactors and their deposition/etching behavior. Results from a recently developed PIC/MC (particle-in-cell/Monte-Carlo) model will be presented for low pressure radio-frequency (RF) glow discharges for carbon film deposition [1-3]. Understanding the mechanisms of glow discharge such as electron and ion transport, gas phase reaction, deposition, is important to optimize the glow discharge systems. Particle model is a powerful means to simulate such non-equilibrium phenomena. While charged particle motion and collisions are traditionally modeled, the present model includes neutral motion and collisions. The model was extended to CH4 (polyatomic gas) plasma and predicted the carbon film deposition. Radio frequency CH4 plasma has been recently used for diamond-like-carbon (DLC) deposition. The model considers the motions of CH4, CH4+ , CH3, C2H5, H2, H and electrons. Detailed information such as space and time dependent results, energy distributions, will be presented for CH4 plasma. Deposition behavior, obtained by sampling impinging particles to the electrode, shows radicals are major species for deposition as previous studies reported.

Though particle models are most suitable for the prediction of non-equilibrium low pressure plasmas, such models are computationally intensive, especially for multi-dimensional reactive plasmas where a large number of reactive species (ionized and neutral) are present. Fluid models solve Poisson's equation for electric potential and one or more moments of Boltzmann's equation to obtain the density, momentum, and energy of each charged species. The models assume a continuum, and are applicable for low Knudsen number discharges (the mean free path of electron-neutral collision is much less than the characteristic dimension of the discharge). Fluid models require relationships between the electron impact rate coefficients and transport coefficients with known quantities such as reduced electric field or mean electron energy. These models execute rapidly and can predict collective plasma phenomena like deposition rate, and power consumption quite well. Recent applications [4-7] of a self-consistent two-dimensional fluid model of both capactively coupled and inductively coupled methane glow discharge will be presented. The simulations provide insights to charged-species dynamics and investigate their effects on deposition in a polyatomic gas discharge. Swarm data as a function of electron energy are provided as input to the model. The necessary dc bias for the discharge is also predicted consistently such that the cycle-averaged current to the powered electrode becomes zero. The predictions provide a comprehensive understanding of the various processes in methane discharges found in plasma assisted chemical vapor deposition (PACVD) reactors for the deposition of carbon films. The effects of discharge pressure on discharge variables will be presented.

Finally, the future challenges and opportunities in modeling low pressure non-equilibrium plasma reactors will be addressed.


  • Nagayama, K., Farouk, B. and Lee, Y. H. , Neutral and Charged Particle Simulations of Ar Plasma, Plasma Sources Science and Technology, Vol. 5, pp 685-695, 1996
  • Nagayama, K., Farouk, B. and Lee, Y. H. , Modeling of RF Plasma Discharge of Methane for Carbon Film Deposition, IEEE Transactions on Plasma Science , Vol. 26, No. 22, pp 125-134, 1998
  • Nagayama, K., Farouk, B. and Lee, Y. H. Particle Simulation of CH4/H2 Radio-Frequency Glow Discharges for Diamond-like Carbon Film Deposition", Proceedings International Conference on Fluid Engineering, Vol. II, (JSME Centennial Grand Congress, Tokyo) pp 977-981, 1997
  • Bera, K., Farouk, B. and Lee, Y. H., Modeling of RF Methane Glow Discharge in a Cylindrical PACVD Reactor", JSME International Journal, Special Issue on Fluids Engineering, Vol. 41, 1-2, pp 132-138, 1998
  • Bera, K., Farouk, B. and Lee, Y. H., Two-Dimensional Modeling of RF Methane Glow Discharge", (in press, Plasma Sources Science and Technology)
  • Bera, K., Farouk, B. and Lee, Y. H., Simulation of Thin Carbon Film Deposition in a Radio- Frequency Methane Plasma Reactor", (in press, Journal of the Electrochemical Society)
  • Bera, K., Farouk, B., Yi, W. J., and Lee, Y. H., "Simulation of Two-dimensional Radio- Frequency Methane Plasma: Comparison with Experiments", with (submitted for publication), IEEE Transactions on Plasma Science


P. Buchner, H. Schubert, J. Uhlenbusch, M. Weiß, K. Willée

Institut für Laser- und Plasmaphysik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany


The application of thermal plasmas, especially for the production of high performance materials is a rapidly developing field in plasma technology with a growing number of publications and patents. The radio frequency generated thermal plasmas offer a 10000 K hot region free from electrode contamination. The long residence time for particles injected into this kind of plasma jet makes it suitable for the production of ultrafine particles and coatings. Many of these processes deal with gases and liquids as starting materials. However, the use of solid precursors is given attention in the so-called plasma flash evaporation method1 due to the low costs for the starting materials and the prevention of unwelcome reaction products. Boiling point and heat of evaporation are often much higher for the solid starting materials compared to other precursors, so special care has to be taken for the complete evaporation of the particles. The coarse grained precursor particles disturb the structure of produced films and reduce the desired properties of nanosized powders. Especially for materials with high melting and evaporation temperatures such as zirconia (melting temperature: 2950 K, evaporation temperature: 4548 K) the evaporation of the precursor is problematic.


The complete evaporation of zirconia powders injected in a thermal rf plasma is investigated in this paper. Both model calculations and experimental techniques such as optical emission spectroscopy (OES) and laser Doppler anemometry (LDA) are used to study the evaporation behaviour. Precursor powders are axially injected into a thermal rf plasma powered by a 35 kW rf generator operated at 3.5 MHz. Details of the process are described elsewhere2-3. Two different injection modes are used:

  • dry powder feeding (high feeding rate: approx. 60 g/h) by means of a rotary wheel powder feeder. Agglomerated spray-dried YSZ powder (mean agglomerate size: 30 µm, Tosoh) is used and the carrier gas flow is 5 slm (standard liter per minute) in this mode.
  • feeding of aqueous YSZ powder suspensions (low feeding rate: < 10 g/h YSZ) using an atomizer. YSZ powders of 5µm particle size (Unitec) and deagglomerated spray-dried YSZ powder (particle size: < 1µm) are used in these experiments. The atomizer gas flow is about 3 slm.
The light emitted by the argon/zirconia plasma is imaged onto an optical fiber. The fiber entrance optics is mounted on a y-z-stage, so that lateral and axial scans of the plasma can be performed. The fiber is coupled to a spectrograph, where an OMA system detects the spectrally resolved signals. Gas temperatures and velocity distributions are determined numerically from conservation laws and Maxwell equations4-6. The influence of plasma and particle parameters on the thermal history of entrained particles is investigated.

The unevaporated particles predominantly present in the upstream region of the plasma are investigated by laser scattering. An argon ion laser (Spectra physics, maximum power approx. 1.5 W for the line at l=514.5 nm) and a commercial LDA head (Polytec) are used for the measurments. The Doppler signals are detected with a digital storage oscilloscope (LeCroy). Velocity distributions are deduced from the Doppler signals by means of a Fourier Transform. The velocity values are compared to the results of the modeling.


According to model calculations, ZrO2 can be completely evaporated up to diameters of 15 µm under all investigated plasma conditions, larger particles can be evaporated when the residence time is increased (reduced discharge pressure and/or carrier gas flow). Especially a reduction in carrier gas flow should improve the evaporation, as can be seen from Figure 1, where the evaporated mass fraction at the plasma exit is shown for different plasma conditions and initial particle diameters d0.

Axial emission profiles obtained by OES and numerically are in qualitative good agreement, showing a continuously growing intensity in case of incomplete evaporation (large particles) and intensity profiles with pronounced maxima in case of complete evaporation (smaller particles). Asymmetrical Abel inversion8 is applied for spectroscopic evaluations to detect asymmetric emission profiles of argon, zirconium and hydrogen to determine the temperature distributions in the plasma source. This technique provides improved results in cases, where slight asymmetries in the measured profiles would cause severe errors in conventional symmetrization. In addition, the profiles can be used to optimize process parameters to avoid asymmetric plasma conditions.

During powder injection, no significant cooling effect on the plasma is detected at an axial position downstream the induction coil. Since no Zr vapour is found in the rf energy coupling zone inside the induction coil and the evaporated particles concentrate near the plasma axis, as has been shown by emission spectroscopy, this result seems quite reasonable. The Zr emission profiles broaden towards the plasma exit from 5 mm (FWHM) to 9 mm due to convective and diffusive transport (see Figure 2a and b).

Measurements of axial velocities by LDA show good agreement between calculated and measured values. A comparison of the results for the on-axis region is drawn in Figure 3. In this case the dry powder feed mode is applied.


The task of achieving complete particle evaporation of high-melting materials in a thermal rf plasma requires careful adjustment of relevant parameters, such as particle size and gas velocities. Numerical modeling in combination with diagnostics of line emission of evaporated species and scattered light from the injected precursor particles promote the understanding of the evaporation process.


  • T. Yoshida, Mater. Trans. 31, 1 (1990)
  • P. Buchner, H. Ferfers, H. Schubert, J. Uhlenbusch, Proc. Gas Discharges & Their Applications, (ed. G. Babucke, Greifswald), 300 (1997)
  • P. Buchner, D. Lützenkirchen-Hecht, H.-H. Strehblow and J. Uhlenbusch, submitted to Journal of Materials Science, 1998
  • M.I. Boulos 1976, IEEE Transactions on Plasma Science PS-4 (1976)
  • P. Proulx, J. Mostaghimi, M.I. Boulos, Journal of Heat and Mass Transfer 28, 1327 (1985)
  • P. Buchner, H. Ferfers, H. Schubert, J. Uhlenbusch, Plasma Sources Scence. and Technology 6., 450 (1997)
  • P. Buchner, H. Schubert, J. Uhlenbusch, K. Willée, submitted to Plasma Chemistry and Plasma Processing, 1998
  • M.W. Blades, Applied Spectroscopy 37, 371 (1983)


Özlem Mutaf Yardimci, Alexei V. Saveliev, Alexander A. Fridman, Lawrence A. Kennedy

Department of Mechanical Engineering, The University of Illinois at Chicago, Chicago, IL 60607-7043 USA

There are two different kinds of plasmas used in practical applications. Thermal plasmas, with low electric field and high electron densities, are able to deliver high power at high operating pressure. Non-thermal plasmas, operating at the high electric fields and low electron densities, offer high selectivity and efficiency in chemical processes, but usually at limited pressure and power. At present, the challenge is to combine these two basic systems to obtain continuous non-thermal powerful discharges with high plasma concentrations and high electric fields.

These requirements are met in non-equilibrium Gliding Arc Discharge, which is investigated in this study. This discharge consists of periodic fast self triggered transitions of thermal arc discharge with temperature about 3000-5000 K into non-equilibrium one1. During the transition, the plasma cools rapidly to a gas temperature of about 1000 K and less, while the electron temperature can go up to 1 eV, and vibrational temperature of molecular gas can be sustained on the level of 3000-5000 K. Electric field reaches values typical for cold discharges, and electron densities remain on the thermal plasma levels. Meanwhile ionization mechanism changes from a thermal to nonequilibrium one, sustained by direct electron impact. According to our theoretical model, the main part of the gliding arc power (up to 75-80%) can be dissipated in a cold non-equilibrium zone2.

In this work, we specify the transition of thermal arc into non-equilibrium gliding discharge. We consider the discharge geometry and evolution of plasma dimensions, time and space dependent parameters of the electrical circuit, and local plasma parameters such as plasma temperatures (electron temperature, vibrational temperature and gas temperature) reduced electric field values, and local plasma concentrations.

The schematic of the experimental setup is given in Fig. 1. Gliding discharge reactor consists of two very thin diverging steel electrodes, fixed in a transparent container. In order to investigate the plasma dragging independent from the flow patterns a slender rectangular cross-section parallel flow gliding discharge reactor was built. The processing gas is passed through stages of different size fillings and flow diffusers before it is introduced to the section with blades to ensure parallel flow around the blades with controllable flow rate. The power is delivered by low-ripple (0.1%) power supply (Universal Voltronics, Inc.) with internal resistance variable from 25 to 150 k and no-load voltage settings from 1 to 10 kV.

The evolution of plasma column was recorded continuously by using a high-speed video camera (Kodak EktraPro Motion Analyzer, Model 1000 FIRC) which has a recording rate of up to 1000 frames per second and adjustable exposure rate of 0.05 to 1 millisecond. In order to obtain the time-resolved length and position diagnostics of moving plasma channel, digitally stored images are subsequently analyzed in a personal computer by using a image processing and analysis software (Image AnalystTM, AM 3300). Superimposed images of discharge as taken by the camera can be seen in Fig. 2.

A digital oscilloscope (HP 54616B, 500 MHz, 2GSa/s) is used to record the electrical characteristics of plasma column during its evolution. Digitized electrical waveforms are transferred to a personal computer via GPIB interface and then processed using software (HP34801A, BenchLirik Scope) that handles the oscilloarams and gives output as time-amplitude pairs for further processing. A typical voltage-current histogram is shown in Fig 3. An external trigger circuit is used to synchronize the electrical and visual recordings.

The oscillograms are analyzed to obtain discharge electrical characteristics such as average current and voltage values, average power, histogram of these parameters; together with the time dependent length, position and diameter values of the moving plasma channel. Finally, the coupling of the electrical and geometrical parameters provides necessary information for developing theoretical or numerical models to relate these parameters to each other for several working conditions.

One of the crucial parameters that we used to describe the transition is the change in electric field strength. This information is obtained by coupling the voltage measurements with geometrical arc characteristics obtained from direct video imaging. An example of such a transition can be seen in Fig. 4. For this particular case, reduced electric field is 0.9 V/cm-Torr for equilibrium zone before transition, and 2.4 V/cm-Torr for non-equilibrium zone after transition.

A theoretical model has been developed to "define the transition parameters, based on energy balance, Ohm's law and change of ionization mechanism from thermal one to cascade ionization by direct electron impact.

In this study, it was concluded that powerful non-equilibrium plasma can be generated from initially equilibrium thermal gliding arc discharge.


  • Fridman, A.A., Petrousov, A., Chapelle, J., Cormier, J.M., Czernichowski, A., Lesueur, H., and Stevefelt, J., Modele Physique de L'Arc Glissant, J. Phys. III France Vol 4, pp 1449-1465, 1994
  • Fridman, A.A. Nester, S., Kennedy, L.A., Saveliev, A.V. Mutaf-Yardimci, O., "Gliding Arc Gas Discharge" J. of Progress in Energy and Combustion Science, Vol.25, pp. 211-232, 1999.


E.A.H. Timmermans, I.A.J. Thomas, J. Jonkers, M.J. van de Sande,D.C. Schram and J.A.M. van der Mullen

Eindhoven University of Technology, Department of Physics, P.O. Box 513, 5600 MB Eindhoven, the Netherlands


The time-dependent behavior of emission lines during a temporary removal of the plasma power can provide information on the population mechanisms of the corresponding radiative levels[1]. These so-called Power Interruption (PI) experiments have been used to compare three plasma sources which are used for analytical spectrochemistry[2]:

  • A 100 MHz ICP (Inductively Coupled Plasma)[3]. Typical operational settings are: power input P=1 kW and argon flow [Ar]= 20 slm. The plasma has a radius rp of approximately 1 cm.
  • A 2.45 GHz microwave induced plasma called "TIA" (from "Torche à Injection Axiale", using the terminology of Moisan et al.[4], the developers of the torch). the TIA produces needle-like plasmas (rp~1 mm) which expand into the open air (P=1.5 kW and [Ar]= 5 slm)[5,6].
  • A 2.45 GHz microwave induced plasma called "MPT" ("Microwave Plasma Torch", developed by Jin et al.[7]). This plasma torch deviates from the TIA by its low power and gas consumption and its separate central gas channel through which analytes can be introduced (similar to the ICP). Typical settings are P=200 W, [Ar]= 0.5 slm and the flame-like plasma has a diameter rp~2 mm.

More insight in the mechanisms responsible for the excitation of analytes which are studied in atomic emission spectroscopy might contribute to a better understanding of phenomena which are not yet fully understood, e.g. matrix effects or the effect of aerosol introduction on an argon plasma.


In RF plasmas the energy is mainly absorbed by electrons, which on their turn heat the heavy particles: {RF power}->{electrons}->{heavy particles}->{surroundings}. Because this latter energy transfer is a rather inefficient process, there is a difference between the electron temperature Te and the gas temperature Tg: Te>Tg. If the power supply is suddenly stopped, the electrons will almost instantaneously thermalize with the (much) cooler heavy particles and as a result Te will drop (tcool<1 ms). On a larger time scale the plasma will vanish due to recombination and diffusion processes[8] . During PI measurements the power supply is repeatedly switched off (for typically 200 ms) and switched on again (typically 10 ms). The photon counting signal of selected emission lines is measured with a multi-channel scaler, having 4096 channels with a time resolution of 2 ms. Therefore the line intensities can be monitored during the complete power-off cycle and part of the power-on cycle.


In these equations e denotes electrons, A and B heavy particles, the subscript (+) the corresponding ion and the subscripts (p), (q) and (1) excited levels p, q and the ground state level respectively. Strictly spoken, the heavy particles having the subscript (1) do not necessarily have to be in the ground state, but in general interactions with the (ion) ground state are dominant due to the high concentrations of (ion) ground state particles.

A sudden decrease of the electron temperature (i.e. a sudden decrease of the number of fast electrons), will effect levels governed by these three balances differently:

  • If radiative level p is populated by electron excitation, the emission of level p will decrease since the Boltzmann balance shifts to the left.
  • If radiative level p is populated by three particle recombination, the emission of level p will increase since the Boltzmann balance shifts to the right.
  • If level radiative p is populated by excitation transfer, the radiation of level p will remain unchanged since the excitation transfer balance is electron temperature independent.
  • If radiative ion level p is populated by charge transfer, the emission of level p will initially remain unchanged (but increase steadily afterwards due to recombination processes[3].
If immediately after the power removal the emission of a radiative level increases, it is said that the response is Saha-like. If the intensity immediately decreases, the response is called Boltzmann-like. Examples of a Saha- and a Boltzmann-like response are given in figure 1.


For all studied plasma sources it is found that in the active zone of a pure argon plasma in general argon lines (which have high excitation energies) show a Saha-like PI response. However, if aerosols are introduced into the plasma, the argon lines no longer show a Saha-like response, but a Boltzmann-like response instead. Analytes and molecules show a Boltzmann-like response as well. Apparently the introduction of water has a strong effect on the excitation mechanisms in the plasma. Similar results are found if molecular gases are introduced into argon discharges produced by the TIA: the Saha-like response of argon-lines changes into Boltzmann-like if more than 0.5% of molecular gases are introduced into the plasma[9].

Large differences are found for the decay times of emission lines in the active zone of the plasma (due to diffusion and recombination processes). Whereas a typical decay time for the ICP is a few hundred microseconds, for the microwave discharges this is only a few microseconds. This shows that in the microwave discharges diffusion is a very fast process. The shortest decay times (<3 ms) are found for the TIA. Probably the turbulent mixing with ambient air is the main reason for the rapid loss of electrons. This given outline is valid for the active zones in the plasmas only. In the recombination zones of the plasma totally different responses to PI are observed. Analytes show hardly any instantaneous response to PI and decay times are significantly longer than diffusion times of free electrons. This can only be explained if electrons play no dominant role and that heavy particle interactions (like Penning excitation) must be responsible for analyte excitation in this zone.

Figure 1: A typical Boltzmann- (left) and Saha-response (right) to power interruption (at t=100ms) as measured from plasmas created by the MPT.


  • J.W. Olisek and K.R. Bradley, Spectrochimica Acta 42B, 377 (1987).
  • P.W.J.M.Boumans, Ed. Inductively Coupled Plasma Emission Spectroscopy. Part 1, Methodology, Instrumentation and Performance. Part 2, Applications and Fundamentals. Wiley, New York (1987).
  • F.H.A.G. Fey, W.W. Stoffels, J.A.M. van der Mullen, B. van der Sijde and D.C. Schram, Spectrochimica Acta 46B, 885-900 (1991).
  • M. Moisan, G. Sauvé, Z. Zakrewski and J. Hubert, Plasma Sources, Sci. and Technol. 3, 584 (1994).
  • E.A.H. Timmermans, J. Jonkers, J.A.M. van der Mullen and D.C. Schram, "Microwave induced plasmas for the analysis of molecular compounds in incinerator gases", Progress in Plasma Processing of Materials 1997, Proceedings of the TPP4 conference, July 15-18 1996 Athens, Begell House inc., 299 (1997).
  • J. Jonkers, L.J.M. Selen, J.A.M. van der Mullen, E.A.H. Timmermans and D.C. Schram, Plasma Sources, Sci. and Technol.6533 (1997).
  • Q.Jin, C.Zhu, M.Borer and G.Hieftje, Spectrochimica Acta 46B, 417-430 (1991).
  • J.A.M. van der Mullen and J.M. de Regt, Fresenius J. Anal. Chem., 355, 532-537 (1996).
  • E.A.H. Timmermans, I.A.J. Thomas, J. Jonkers, A. Hartgers, J.A.M. van der Mullen and D.C. Schram, accepted for publication in Fresenius J. Anal. Chem., (1998).


K.T.A.L. Burma, D.C. Schrama, and W.J. Goedheerb

a)Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven
b)F.O.M. Institute for Plasma Physics 'Rijnhuizen', P.O. Box 1207, 3430 BE Nieuwegein


The object of this paper is the study of a cylinder symmetric plasma expansion from a high density source with small dimensions into a low pressure vessel with large dimensions. The gas dynamic theory of Prandtl-Meyer flows is used as a guide to get a better understanding of the flow behaviour of the expanding plasma. In gas dynamics, the expansion from the exit pressure to the background pressure takes place through a series of expansion waves just beyond the arc and is followed by a shock1-3. A plasma behaves similar. Using gas dynamic theory, the shock position and the Mach number at the shock have been estimated for an argon plasma.


For the deposition of surface layers expanding plasmas admixed with deposition gases are used. To optimise these surface layers a high source strength, knowledge of how to control the expanding flow, and information about the mixing of the deposition gas with the carrier gas is needed. Therefore it is necessary to have basic knowledge of the here investigated expanding argon plasma.

The considered argon plasma source is a D.C. wall-stabilised thermal cascaded arc4. The power dissipation is typically of the order of 5 kW, using an arc current of 50 A. The cascaded arc produces a thermal argon plasma at (sub)atmospheric pressure, characterised by an electron temperature of 1 eV and high electron densities of 1022-1023 m-3. Flows are typically between 10 and 150 sccs5,6. The unit 1 sccs is equivalent to 2.5*1019 particles/s. The arc channel has a length of 34 mm and a constant diameter of 4 mm.

The expansion chamber7 is a low pressure vessel at a varying downstream pressure of 20 Pa - 10 kPa. The plasma is 'under-expanded' (the pressure in the exit plane can be as large as 103 times the background pressure1). The dimensions of the vessel are 1 m. diameter and 1.5 m. length.


Experiments7 show that due to the increase in diameter the plasma expands supersonically, and that in the expanding plasma a stationary shock occurs at a relatively short distance from the arc outlet. Observation on argon plasmas by van de Sandeng confirm that the density in rarefied plasmas and the shock behaviour of plasmas follow the gas dynamic laws for the expansion of gases.
Several authors have determined the position of the stationary shock front after the supersonic expansion of a free jet as an function of the ratio of the stagnation pressure at the outlet, po,e, and the background pressure, pb. Ashkenas et al.9 obtained an empirical relation between ds and po,e/pb:

where C equals 0.67 and is independent of g. This same relation has been derived by Young10 using the entropy and pressure balances. Young finds a somewhat higher constant which depends slightly on g: C ~ 0.76 for g = 5/3.
Further, from gas dynamic theory of disturbances1 (Mach waves and expansion fans) we know how a sudden increase in diameter induces supersonically expanding gases. A sudden increase in diameter causes an increase in Mach number M and velocity v, and a decrease in pressure p and density r. From the combination of conservation of mass, momentum and energy with the first derivative of the Mach number, we get:

where d is (and dd a infinitesimal sinall part of d) the angle the flow is turned through. Integrating expression (2) over the total expansion angle, while dropping the negative sign for negative angles, yields1:

where the initial boundary condition is taken as the sonic arc outlet boundary condition, i.e. d=0, M = l. The here discussed expanding gas flows are so-called Prandtl-Meyer flows. The behaviour of such gas flows is described by diverging Mach waves, i.e. a fan.
In the above described set up with a sudden increase in diameter at the outlet of the cascaded arc, we are interested in the flow behaviour of an argon plasma in the preshock region and in the location of the shock front. We used the gas dynamic theory of Prandtl-Meyer flows on an argon plasma to get a better understanding of the behaviour of an expanding plasma.


To obtain the results discussed here we used the expressions from gas theory with an adapted isentropic exponent. The isentropic exponent of an argon plasma is lower than that of an argon gas11. From expression (6), we estimated that in our set up (90 degree angle) an expanding argon plasma will have a Mach number of 4.l. This number is in good agreement with estimations from experimental data.
In the area between the Mach wave at the outlet (M1) and the maximum Mach wave of 4.1 (M2) the plasma accelerates. In accordance with gas dynamics, when Mach number M2 is reached there is no reason to accelerate the plasma any longer, therefore a shock (if it occurs) may occur after the position where the two M2 wave lines intersect each other compressively. If we neglect bending of the Mach wave lines in the pre-shock region, we can obtain an estimation of the pre-shock region length. For an argon plasma flowing out of a 4 mm diameter straight cascaded arc we estimated a pre-shock region length of about 32 mm, which is in good agreement with experimental data, and which is in good agreement with estimations in which expression (1) is used.


According gas theory, a gas flow will expand supersonically into the low pressure vessel when the outlet diameter of the arc increases suddenly, and a stationary shock will occur at a relatively short distance from the arc outlet. Such gas flows are socalled Prandtl-Meyer flows. The series of Mach waves that occur diverge forming a fan.
A plasma is assumed to behave similar as a gas in our set up. In the expansion, the Mach number and the velocity will increase, and the pressure and the density will decrease. Using the Prandtl-Meyer flow theory for an argon plasma the shock position and the Mach number at the shock have been estimated and were compared with experiment and theory.


We thank A. Leroux, J.A.M. van der Mullen, and M.C.M. van de Sanden for their support.


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W.L. Ng*, O.R. Tutty* and J.W. McBride**

*Computational Engineering and Design Centre (CEDC)
**Department of Electrical and Mechanical Engineering University of Southampton, Southampton SOl7 lBJ, United Kingdom


There is a wide spectrum of arc applications, for example in the field of electric circuit breakers, electric arc gas heaters, space-vehicle re-entry simulation, high temperature chemistry and material processing. The present work covers arc phenomena during the breaking of two current carrying electric contacts. If one or both electrodes are movable, electrode contact may be established after an electric potential is applied to the electrodes. Even with a macroscopic clean metallic surface, metallic contact occurs at a small number of asperities and the current flowing through the contact is constricted. Due to the current constriction, the contact point may be heated to a temperature sufficent for electrode to melt. Upon the breaking of two contacts, the molten metal is then drawn into a molten metal bridge. The rupture of this molten metal bridge will generate ions and electrons across the electrode gap. These electrons and ions provide the necessary charge carriers for developing an arc upon the breaking of two electric contacts. There is a minimum current level in which an arc is established. This threshold current is a function of electrode materials.

Arc erosion of electrical contacts is a very complex phenomena involving many branches of physics: fluid mechanics, electromagnetism, solid state physics and heat transfer mechanism. Due to the complexity of the physical phenomena involved, it is not surprising that very little theoretical work has been done in this field. It seems that there will not be any general theory to describe the arc erosion as long as the amount of input arc energy into the contact material remains unknown.

The arc-electrode interaction has been studied by many authors 1,2,3,4,5,5,7 using many different approaches. Much of the progress has been motivated by the need to understand the erosion process in electrical contact. Some of them attempt to predict electrode erosion using the experimental data such as arc current, arc voltage, current density 3,5,6. The input arc energy into the electrode is a pre-requisite for this approach. Unfortunately, there is still no quantitative theory to determine how much arc energy is fed into electrode surface during the arcing process. Therefore there is a growing need to solve the energy balance equation on the cathode surface coupled with influence of the electric arc. Some of the existing theoretical models have included the local thermodynamic equilibrium (LTE) arc column 7 while others considered the non-equilibrium sheath region next to the electrode surface 1,2. It is the latter approach that the present work will adopt.

This work has been undertaken to develop a numerical model of interaction between electric arc and electrodes. It is hoped that this model will provide some insight into the arc erosion process through the amount of arc energy fed into the electrical contacts. A full mathematical model is developed to describe gas flow between two electrodes during switching operation. Significant temperature discrepancies between electron and heavy species occurs at the electrode region. Therefore, multi-species, two temperature Navier-Stokes equations were used in the model together with some kinetic theory equations and Maxwell's equations.


A standard technique for solving complex nonlinear systems of differential equations is to use an operator splitting approach where the equations are broken down to a sequence of much simpler equations which are relatively easy to solve. As a result, different numerical solvers (implicit or explicit method) can be used on each part of the governing equation as appropriate. The overall time step of the numerical scheme is then determined by the requirements of the independent solvers. The numerical scheme used here adopts a convection-diffusion-ionization operator splitting scheme which has previously been used for reacting gas flows8, with extra operations for the electromagnetic effects. The Navier-Stokes equations are divided into separate PDE that describe respectively the convective, diffusive, ionization, electromagnetic effects separately, to give

where U is the vector of conversed variables (density, momentum, energy), (F, G) are the convective fluxes, (Fv, Gv) the diffusive fluxes, are the species source terms from the ionization scheme, M represents the electromagnetic effects, and Re is the Reynolds number of the flow. Here it has been assumed that the problem is axisymmetric, and A gives the extra terms generated in the momentum equations in this coordinate system.

A further geometric operator splitting is applied, in which the various parts of the equations are reduced to a sequence of one-dimensional problems along grid lines, which are relatively easy to solve. The convective solver for (1) is based on the explicit HLLC approximate Riemann solver which is well established for the solution of gas dynamics problems. The viscous solver (2) use a mixed implicit/explicit scheme, in which the cross derivative terms are handled explicitly, and the other terms implicitly along grid lines. The reactive/ionization solver (3) uses a point implicit method. The electromagnetic terms (4) are also handled implicitly. With this formulation, the stability condition on the scheme comes from the well known Courant condition from the explicit convective solver for (1). This gives a time step that is small enough for a time accurate solution, but not too small to make the computing requirements prohibitively expensive.


The system of equations outlined above are solved for a simple axisymmetric electrode as shown in Figure 1.
Initially the gas is pure molecular Nitrogen N2. It is assumed that the plasma is initiated by the application of a potential between the electrodes which gives rise to a strong electric field which draws electrons from the cathode, which then generates a nonlinear response in the gas, involving fluid and reactive effects through the usual flow mechanisms and the ionization scheme. To complete the model, effects from the evaporation and ionization of the electrode material at the electrode surface should also be included. Currently a model of electrode erosion is being developed, which will eventually be incorporated into the plasma model, but the work presented here concentrates on the formation of a plasma in the gas due to the applied potential and the subsequent heating of the electrodes. Results will be presented showing the development of the plasma, including the change in species concentrations, and diagnostics such as the time dependent heat transfer rate to the electrodes.


  • X. Zhou, J. Heberlein, E. Pfender, "Model predictions of arc cathode erosion rate dependence on plasma gas and on cathode material", in 39th IEEE HOLM Conference On Electrical Contacts, pp. 229-235, 1993.
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  • S. N. Kharin, "Mathematical model of arc erosion in electric contacts", in l6th International Conference On Electrical Contact, (Loughborough, England), pp. 205-209, 1992.
  • M. Sun, Q. Wang, M. Lindmayer, "The model of interaction between arc and AgMeO contact materials" , IEEE Transactions On Components, Packaging and Manufacturing Technology, vol. 17, no. 3, pp. 490-493, 1994.
  • J. Swingler, J. W. McBride, "Modelling of energy transport in arcing electrical contacts to determine mass transfer", IEEE Transactions On Components, Hybrids and Manufacturing Technology, vol. 21, no. l, pp. 54-60, 1998.
  • J. J. Gonzalez, A. Gleizes, P. Proulx, M. Boulos, "Mathematical modelling of a free-burning arc in the presence of metal vapour", Journal of Applied Physics, vol: 74, no. 5, pp. 3065-3070, 1993.
  • S. R. Amaratunga, A numerical study into surface catalytic effects in non-equilibrium reacting viscous laminar hypersonic flow. PhD thesis, Department of Aeronautics & Astronautics, Southampton University, 1998.


Miran Mozetic

Institute of Surface Engineering and Optoelectronics,Teslova 30, 1000 Ljubljana, Slovenia

Experimental vacuum system for study of interaction of hydrogen plasma with a variety of samples is described. Hydrogen plasma is created by the use of inductively coupled RF generator with the output power from 100 up to 300 W. Plasma parameters are measured with electrical and catalytic probes. The system proved useful for a variety of experiments from basic studies on plasma–surface interaction to discharge cleaning of archeological artifacts.


The vacuum system is shown in Figure 1. It is pumped with a mechanical rotary pump with the pumping speed of 2.2 l/s and the base pressure of 0.1 Pa, and a Hopkins trap cooled with liquid nitrogen with the pumping speed for vapors of at least 80 l/s. Both the discharge vessel (forced air cooled) and the connecting tube are made of Schott 8250 glass which has the recombination coefficient for hydrogen atoms of 1 10-4 at room temperature. Plasma is created with an inductively coupled RF generator with the frequency of 27.12 MHz and the nominal power of 700 W. The output power of the generator is varied from 100 to 300 W by changing dimensions of the RF coil. Commercially pure hydrogen is leaked into the discharge vessel through a precise leak valve. Pressure is measured away from the discharge vessel with Pirani gauges calibrated to hydrogen.
Figure 1. Schematic of the vacuum system.
1–rotary pump, 2–high vacuum valve, 3–molecular sieves trap, 4–Hopkins trap, 5–Pirani gauge, 6–air inlet valve,
7–connecting tube, 8–discharge vessel, 9–leak valve, 10–high pressure valve, 11–hydrogen flask.



Plasma parameters are measured with a double Langmiur probe and a catalytic probe. The Langmuir probe is mounted in the discharge vessel, while the catalytic probe is placed on a moveable holder in the connecting tube in order to assure its operation also at high atomic hydrogen density. A typical characteristics of the Langmuir probe is shown in Figure 2(a) and the plasma density versus pressure at the RF power of 200 W and 300 W in Figure 2(b). Both gold and nickel catalytic probes are used for determination of the density of hydrogen atoms. A probe is shown in Figure 3(a) and the H density in the discharge vessel versus pressure in Figure 3(b).


The experimental system is used for a study of heterogeneous recombination of neutral hydrogen atoms on a variety of samples. The recombination process can be monitored by measuring the temperature of a small disc of the material exposed to a flux of atomic hydrogen. Assuming the recombination coefficient is constant, the temperature of the disc increases well over the ambient temperature and in a short time after turn on the H source and reaches the constant value. In the case the recombination coefficient is not constant, the T(t) curve has a more complex shape. A typical behavior of the temperature for the first case is plotted in Figure 4(a), and for the second case in Figure 4(b). In the case of normal behavior the T(t) curve can be used to determine the recombination coefficient of a material. Monitoring the H distribution along the connecting tube enables determination of the recombination coefficient for the material the tube is made of.


The system is used to perform experiments on discharge cleaning of a variety of samples including contact materials, chip housings, and archeological artifacts. Thin layers of oxidizing impurities are effectively reduced in a few seconds while thicker layers may take hours to be removed. Figure 5(a) shows AES depth profile of the surface of a silver strip used as contact material before discharge cleaning, and Figure 5(b) shows the profile after cleaning. In the case of archeological artifacts EMPA is used for determination of surface composition instead of AES. Figure 6(a) shows the EDX spectrum of the surface of an old silver coin before cleaning in the system, and Figure 6(b) after successful cleaning. The system is suitable for a study of discharge cleaning of a base of a chip made of Fe60Ni40 alloy. Samples are taken directly from the production line. The AES depth profile of the surface layer of a sample is shown in Figure 7(a). The surface is covered with a layer of oxide and right on top there is a layer of carbon (probably oil or grease). Samples are exposed to hydrogen plasma for a different period of time. The AES depth profile of a sample exposed to plasma for 20s is shown in Figure 7(b). After the treatment, the surface is just clean, as in other cases of discharge cleaning experiments.


Ludek Krejci, Vladimir Dolinek, Pavel Sopuch*, Vâclav Nenicka, Jan Hlina **

* Institute of Thermomechanics CAS, Dolejskova 5, 182 00 Praha 8, Czech Republic
** Institute for Electrical Engineering, CAS, Dolejskova 5, 182 00 Praha 8, Czech Republic

The most important events responsible for effective practical utilization of thermal plasma plume energy are the heat and mass transfer processes taking place in the plume initial (core) region. However, the advanced thermal plasma technologies are often performed in oscillating transitional plasma plumes. And when it comes to prediction of heat and mass transfer processes in the core of such plumes, we are in trouble. Using the "classical" approach to turbulent flows we are generally not close to corresponding experimental data - we are far from the reality here, most probably.

The solution of this problem requires a thorough truthful phenomenological understanding of hydrodynamic events controlling the plume core heat and mass transfer during the core laminar-turbulent transition, first of all. But the complexity of the problem causes that only a supporting mathematical modeling of the whole transition process should enable use to grasp the problem thoroughly. Unfortunately, seemingly reasonable phenomenological as well as mathematical models of the processes taking place during the plume core transition to turbulence do not exist, up to now. Direct numerical simulation of processes discussed does not represent a realistic possibility and in any event simulation by itself does not bring understanding, of course. The solution of such problems requires more sophisticated modeling of them.

In the paper presented, the experimental facts that justify our proposal to solve this problem by the use of methods of the theory of nonlinear dynamic systems are summarized and analyzed. And on the basis of the facts submitted, the approach enabling us to construct the appropriate mathematical model of the plasma plume core behavior during its transition to turbulence is proposed.

Our experiments were performed in argon plasma plumes generated by a cascaded arc heater. The results gained show that during the transition process, the core dynamics and the related heat and mass transfer events are principally controlled by the plume shear layer vortex system formed and evolved owing the shear layer instability. The changes of the morphology of this system play the crucial role in the "strange" metamorphoses of the core dynamics. And each vortex system configuration (identified by distinct plume core oscillations spectrum) links tightly with particular type of nonlinear heat transfer process in the core. During the core laminar-turbulent transition, there appear two distinct types of this process, identified by the changes in core cusp stagnation point heat flux and the arc heater exit average enthalpy relationship. Just before the self sustained, fully turbulent plume sets up a violent heat flux enhancement appears first. Increasing the mass flow rate more over, this enhancement is followed by rapid heat flux decrease. The state determined then by the minimum heat flux value identifies the end of the core (and plume) transition; the further mass flow increase results in abrupt formation of the self-sustained, fully turbulent plume, causing also a corresponding plume core heat flux increase. In principle, there are also two dominant events, which induce the effects mentioned. The core heat flux enhancement produces probably the energy seperation (Eckert-Weise) effect controlled by specific shear layer vortex system pattern; the following heat flux decrease cause resonance events in the arc chamber cavity - they induce such a shear layer vortex system change which enhances the entrainment of surrounding medium into the core.

The body of informations gained enabled us to formulate a complex conceptual model (scenario) of the events governing both hydrodynamic as well as thermal processes taking place in the plasma plume core during its transition to turbulence. The scenario suggests that the transition evolves in our "open" plasma plume dynamic system in the same manner as the transition in a "closed" one. Just on the basis of this fact we feel, that the methods of nonlinear dynamic systems theory will provide us the appropriate theoretical approach enabling us to build a relatively realistic low-dimensional mathematical model of the core transition process.

The methods used in the analysis of dynamic systems are now acknowledged to have a useful role to play also in the study of closed fluid systems (e.g. of Taylor-Couette flow or Rayleigh-Benard convection) in which relatively few spatial modes are active. Thus we propose that such low dimensional dynamic systems can also provide models for - and hence contribute to the understanding - of the dynamically similar behavior of a transitional plasma plume core. The tools enabling to analyze the behavior of nonlinear dynamic systems are usually very far from the methods applied in the classical hydrodyamics. However, the principles of global vector field reconstruction - the topic of growing interest between the specialists in nonlinear dynamics now - provide very important advantage just in the solution of our problem. They should allow one to obtain a global model of the commlex dynamics by the measurements of a single measured quantity - of its scalar time series - exploiting a very powerful redundancy pririciple.

The first step in the analysis will then consist the reconstruction of phsical picture of our vortex system dynamics - the reconstruction of its attractor in corresponding embedding phase space. This reconstruction may be carried out in a number of ways - and we will use severally known techniques because non of them alone is fool proof. Once we have reconstructed the attractor, the next step is to obtain a set of equations which - modelling the evolution of the attractor - models in principle our plume core vortex system dynamics, too. And the behavior of this set of differential equations should also describe the evolution of the whole transition process as the external or modelling parameters vary.


Vanden Abeele, G. Degrez, P. Barbante, J.P. Mellado González

von Karman Institute for Fluid Dynamics Steenweg-op-Waterloo 72, 1640 St. Genesius-Rode, Belgium


In an inductive plasma torch, a gas is heated in an electrodeless manner to a plasma state with peak temperatures of about 10 000 K. The non-polluted plasma thus obtained is well suited to a wide variety of industrial and scientific applications.1 In the aerospace industry, air inductive plasmas are used to test thermal protection systems for re-entry space vehicles. To properly simulate re-entry flight conditions, inductive plasmas need to be operated at pressures below 0.1 atm, where thermal and chemical non-equilibrium effects are known to be important.2

As a step in the development of a model of the 1.2 MW 'Plasmatron' wind tunnel at the von Karman institute,3 this contribution presents a numerical model of multi-component inductive plasmas (e.g. air) under chemical non-equilibrium. To the authors' knowledge, continuum models of argon inductive plasmas under non- equilibrium have been presented by Mostaghimi et al.4 (1987), by Semin5 (1991) and by Benoy6 (1993). Unfortunately, these models can not be easily extended to more general multi-component mixtures.

Whereas argon plasmas can be modeled by a straightforward three-component formalism, a full multi-component formalism (e.g. multi-component diffusion model, ...) is required to simulate e.g. air plasmas. Moreover, the evaluation of the thermodynamic and transport properties of a multi-component plasma mixture is usually very costly, due to the large number of chemical components involved. The traditional models are no longer feasible, as they converge through a large number of semi-implicit iterations, where the cost of a single iteration can be of the order of several minutes on a modern workstation. Instead, a fully implicit model should be used to limit the number of iterations to a minimum.


A finite mixture of atoms (molecules), ions and electrons is used to represent the plasma. The concentration of each species in the mixture is given by a corresponding species continuity equation. Production and destruction of plasma species due to chemical reactions (ionization) is modeled by Arrhenius-type source terms.7 The plasma thermodynamic properties are determined through statistical mechanics and the plasma transport properties are computed with the well-known method of Chapman and Enskog.8

Multi-component species diffusive fluxes are obtained from the full Stefan-Maxwell equations9 by means of a straightforward iterative procedure.10 The electron concentration is obtained from the electron species continuity equation, rather than by explicitly imposing quasi-neutrality. Provided the global and species continuity equations are discretized with care, it is shown that quasi-neutrality automatically holds. An elegant algorithm, in which no distinction needs to be made between electrons and heavy particles, is thus derived.


The torch is modeled by a fully axisymmetric configuration. To this end, the outer inductor is represented by a series of parallel current-carrying rings. The physics of the problem may then be described by the axisymmetric equations of magnetohydrodynamics, where the flow variables are assumed not to vary in time and the electromagnetic variables are pure Fourier modes at the torch operating frequency. The governing equations are discretized in a second order accurate finite volume manner on a structured mesh.11

The low Mach number flow field is solved with a pressure-stabilized CFD technique on a collocated mesh. The electromagnetic field is solved on a dual far field mesh, which coincides with the flow field mesh inside the torch, yet extends into the space beyond the torch boundaries. The discretized system of equations is solved with a fully coupled damped Newton method.11 Modern Krylov subspace methods are used to efficiently solve the linear systems arising from the Newton linearization. Fully converged computations for air inductive plasmas on fine meshes are computed in several hours on up-to-date workstations.


The performance of the model is evaluated by calculating an atmospheric nitrogen plasma flow in the VKI mini-torch.11 A fine inner mesh of 53 by 24 cells and a far field mesh of 65 by 44 cells were used. For the second order discretization used, results were found to be grid-converged. The equilibrium solution is first computed and then used as an initial guess for the non-equilibrium model. Both the equilibrium and non-equilibrium model converge in about 100 damped Newton iterations to machine accuracy. Each run requires about 1 hour of CPU time on a modern (235 Mflops) workstation.

Figure 1 shows the computed temperature field. At the atmospheric pressure level used for the calculation, the plasma was found to be very close to chemical equilibrium. A similar conclusion was drawn earlier by Mostaghimi et al. in their study of argon plasmas.4 When computing air inductive plasma flows, unexpected stability problems frequently occur at the time of writing. The precise reason for these instabilities still needs to be investigated. Once the remaining problems with air mixtures will be solved, thermal non-equilibrium effects will be brought into the code and calculations will be performed for lower pressure levels.

Figure 1: Computed temperature field in the VKI mini-torch (6 kW, 27 MHz, 1 atm)

  • 1 Boulos, M. I., The inductively coupled radio frequency plasma. Pure & Appl. Chem., 57(9), pp. 1321-1352, 1985.
  • 2 Kolesnikov, A. F., Aerothermodynamic simulation in sub- and supersonic high-enthalpy jets: experiment and theory. In proc. 2nd European Symposium on Aerothermodynamics for Space Vehicles. ESTEC, Noordwijk, the Netherlands, 1994.
  • 3 Bottin, B., Carbonaro, M., Vander Haegen, V., Paris, S., Predicted and measured capability of the VKI 1.2 MW Plasmatron regarding re-entry simulation. ESA SP-426, ESTEC, Noordwijk, the Netherlands, 1999.
  • 4 Mostaghimi, J., Proulx, P., Boulos, M. I., A two-temperature model of the inductively coupled radio frequency plasma. J. Appl. Phys., 61(5), pp. 1753-1760, 1987.
  • 5 Semin, V. A., Theory of non-equilibrium inductive high frequency discharge in a gas flow. Fluid Dynamics (translated from Russian), 2), pp. 282-288, Plenum Publ. Corp., New York, 1991.
  • 6 Benoy, D. A., Modeling of thermal argon plasmas. Ph.D. Thesis, Tech. Univ. Eindhoven, the Netherlands, 1993.
  • 7 Gnoffo, P. A., Gupta, R. N., Shinn, J. L., Conservation equations and physical models for hypersonic air flows in thermal and chemical non-equilibrium. TP-2867, NASA, 1989.
  • 8 Bottin, B., Vanden Abeele, D., Carbonaro, M., Degrez, G., Sarma, R. S., Thermodynamic and transport properties for inductive plasma modeling. J. Thermophys. Heat Transf., accepted.
  • 9 Kolesnikov, A. F., Self-consistent Stefan-Maxwell relations for multi-component ambipolar diffusion in two-temperature plasma mixtures. TN-196, von Karman Institute, St. Genesius-Rode, Belgium, 1999.
  • 10 Sutton, K., Gnoffo, P. A., Multi-component diffusion with application to computational aerothermodynamics. TP 98-2575, AIAA, Albuquerque, New Mexico, 1998.
  • 11 Vanden Abeele, D., Degrez, G., n efficient model for inductive plasma calculations. TP 98-2825, AIAA, Albuquerque, New Mexico, 1998.


Ludek Krejcí, Vladimír Dolínek, Pavel Sopuch*, Václav Nenicka, Jan Hlína **

* Institute of Thermomechanics CAS, Dolejškova 5, 182 00 Praha 8, Czech Republic
** Institute for Electrical Engineering, Dolejškova 5, 182 00 Praha 8, Czech Republic

In many advanced technologies, the thermal energy needed for their realization is supplied from oscillating thermal plasma plumes. The oscillations of them are ascribed mainly to the events arising in the arc chamber cavity or in the arc itself – e.g. to the arc-restricting etc. Such oscillations are of particular interest long time already. On the other hand, very strong plume oscillations may arise in the plume itself, too; they did not attract a special attention up to now, however. The oscillations induced by the plume shear layer instability and evolving during the plume transition to turbulence hold an unique position among them. And the salient features of such oscillation show up most vividly just as remarkable heat and mass transfer effects in the plume core region. From these events – which are of importance in the plume thermal energy utilization in most technological applications – the effects induced by the self-sustained (resonant) oscillations are of crucial significance.

The aim of the paper presented is to give an insight into the plume core dynamic phenomena bringing the resonant events in the plasma column into play.

The experiments were performed in a transitional plume generated by a cascaded arc heater. In such a plume we can establish very good controllable experiments in which the dynamic states may be unambiguously controlled reproduced and detected. The plume core shear layer dynamics as well as the core and plasma column global oscillations have been reflected by the core light and arc voltage oscillations as well as by corresponding plume acoustical emission data. The related heat transfer effects were detected of the flow stagnation point heat flux data measured in the core cusp region.

The results show that in the interplay between the plume core dynamics and the thermal energy transport through the core the crucial role plays the coupling of the plume core vortex system induced global plasma column oscillations with the organ-pipe acoustical oscillations in the arc chamber cavity. And just this coupling provides also a means for most effective utilization of the plume thermal energy. Synchronized periodic oscillations of the whole plasma column result in unexpected core heat flux enhancement in the first place – under such conditions the core heat flux attains in general its maximum value at all. The further evolution of self sustained oscillations of the plasma column system, taking place during the next phase of the plume transition process, results on the contrary in rapid heat flux decrease owing the remarkable entrainment of the environmental – or injected – medium. And the fact, that the onset and the extent of those core heat flux changes may be simply controlled by the operating – by arc current – and by design – by arc chamber length – parameters suggests that the practical application of these events will find suitable use certainly. In addition the synchronized oscillations in the whole plasma column represent essentially a dynamic closure of this hydrodynamic system. The dynamic closure results in firm control of the whole transition process and in good reproducibility of it, of course.

On the contrary, the absence of such control results in the generation of an unstable flamming plasma plume. Our results suggest, that the process bifurcation at the onset of the non-linear phase of the core transition to turbulence is responsible for such plume behavior – characterized both by low efficiency of the plume thermal energy utilization as well as by poor reproducibility of whole transition process (or – in other words – by poor reproducibility in establishing the desired flow behavior conditions under the prescribed arc heater working conditions).


S. Mazouffre, M.G.H. Boogaarts, I.S.J. Bakker, J.A.M. van der Mullen and D.C.Schram

Departement of Applied Physics, Eindhoven University of Technology, Department of Physics, P.O. Box 513, 5600 MB Eindhoven, the Netherlands

In an expanding plasma created by a cascaded arc from a Ar-H2 mixture, spatially resolved densities, temperatures and velocities of ground state atomic hydrogen are obtained by applying two-photon excitation laser induced fluorescence. The axial velocity profile of H shows a strong coupling between Ar and H atoms, however atomic hydrogen density and temperature profiles can not be fully described in term of supersonic expansion model in contrast with the profiles of Ar. There are several indications that hydrogen atoms can escape the supersonic domain by a scattering process.


When a cascaded arcl created plasma is expanded into a vacuum vessel, a versatile high quality particle beam is obtained. Such an expanding plasma beam has many applications2 like e.g. fast deposition of thin layers, etching of microstructures and atoms or ions source in the field of nuclear fusion. In all these applications atomic species play a key role and specially atomic hydrogen. Furthermore argon gas is often used as a carrier gas. Thus from a technological point of view, but also from a fundamental perspective, it is of interest to study the properties of the beam generated from a mixture of Ar and H2 and to understand them in terms of transport öf hydrogen atoms from a reservoir to a processed surface.

Ground state atomic hydrogen atoms are spatially probed by using a two-photon excitation laser induced fluorescence process3,4 (TALIF). H is excited with two 205.14 nm photons from the 1s2S ground state to the 3d2D and 3s2S states. The excitation is monitored by detection of the fluorescence yield on the Balmer-a line at 656.3 nm.

Figure 1 shows a typical spectral scan of the two-photon transition. Integration of the line profile allows the determination of the relative H density. In order to obtain absolute number density the LIF set-up has to be calibrated. This is accomplished via a titration with N02 in a flow tube reactor5. Assuming Doppler broadening to be the main broadening mechanism, H temperature can be determined from the full width at half maximum. In addition, the velocity component in the direction of the laser beam is obtained from the absolute Doppler shift of the peak.

2 Experimental TALIF set-up

A simplified scheme of the experimental set-up is depicted in figure 2. The cascaded arc plasma source has already been described in detail elsewhere. In this experiment the arc is operated on 40 A dc current and with a cathode voltage of 100 V. A gas flow of 3.0 slm Ar and 0.5 slm H2 is used. The UV laser beam generation has been extensively described. A tunable 50 Hz Nd-YAG pumped dye laser delivers radiation around 615 nm. The output of the dye-laser is frequency-tripled using non-linear optical crystals resulting in 0.8 mJ of tunable UV light around 205 nm. The UV beam is focused into the plasma jet and the resulting fluorescence photons at Balmer-a line are collected with a photo-multiplier tube. The delivered signal is then processed using a computer.
The laser frequency is calibrated by simultaneous recording of the absorption spectrum of molecular iodine6,7.

3 Results and discussions

From the adiabatic supersonic expansion theory8,9, a value of 4000 m.s-1 is obtained for the velocity of an Ar-H mixture with a source temperature of 1 eV. Figure 3 shows a measured H atoms axial velocity profiles (at 16 Pa) where the measured maximum speed is about 3800 ms-1. This implies a complete coupling of Ar and H atoms. From the measured translational temperature the speed of sound is calculated. The Mach number ahead the shock front equals 5. Axial temperature profiles depicted in figure 4 show that both position and thickness of the shock front depend on the background pressure. Using Hankine-Hugoniot10 relations, a Mach number of 4 is deduced from the temperature jump at 16 Pa.

As shown in figure 5, there is no density jump. Using Mach number equals 5, Hankine-Hugoniot relations give a density ratio, ahead and behind the shock, of 3.6 as it is for the velocity. This disagreement can be explained by the fact that H mean free path11 increases while Ar density decreases along the beam axis. Ahead the shock the mean free path is already larger than the shock thickness. Thus the argon stationary shock front is transparent to H atoms. This also means that the rise in temperature across the shock is due to heat conduction between hot H atoms from the background gas and cold H atoms from the supersonic expansion domain.

But more interesting is the fact that the slope of the sharp part of the density decay depends on the background pressure. This means that H atoms from the plasma jet core receive information about the background, which is impossible in a supersonic expansion. The only way to explain such a phenomenon is to account for diffusion of H atoms outside the supersonic domain meaning that H is not perfectly confined inside the argon jet.

4. Conclusion

Behind the sonic exit of thye cascaded arc the hydrogen mean free path becomes soon larger than the shock front thickness and then the Ar shock front is transparent to H atoms. Because of the mass difference between argon and hydrogen, H atoms can radially escape the plasma beam by a scattering process. The study of radial density, temperature and velocity profiles as well as measurements at high background pressure (100 Pa) confirm the previous inferences.


This work is financially supported by the Netherlands Technology Foundation (STW) and by the Netherlands Fundamental Research on Matter Foundation (FOM).


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