SESSION 5
NONEQUILIBRIUM
Chairman:  G.C. Dijkhuis
J.J. Lowke

NONEQUILIBRIUM EFFECTS INDUCED BY MOBILITIES ALONG STEEP GRADIENTS
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 2l 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 n_{e} 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
2l method might give wrong results. This is mostly handled by introducing (qualitatively) more temperatures;
such as excitation, ionization translation andsoon 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
(1)
stating that the rate of the forward reaction (N_{a}n_{f}
where N_{a} is a 'density' and n_{f} a frequency),
equals that of the backward reaction N_{b}n_{b} plus the
(transport) 'leak', the efflux f_{t} = N_{b}n_{t}. For
f_{t} = 0 (or n_{t} = 0) the principle of DB states that
(2)
which can be divided on eq.(2), giving:
(3)
in which the parameter b = N/N_{eq} 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 n_{f} and n_{b}. 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 f_{t} can be (related to) 1) the escape of photons, 2) electronion 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
n_{t}/n_{b}, the ratio of the transport and backward frequency at
the leakside 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 n_{t}/n_{b} << 1
or n_{t}t_{b} << 1. Or in words: equilibrium is
(almost) established if the number of leaksperbalancetime is much less than unity. More specifically one can define the presence of
equilibrium quantitatively by stating that for equilibrium the relation n_{t}t_{b} < 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 socalled proper balance; a balance of forward and corresponding backward processes
(N_{a} n_{f} = N_{b} n_{b}),
whereas if the leak dominates (in steady state) a socalled improper balance is present in which the number of processes arriving at the
leakside b equals that of the 'outward' processes leaving this ab
system ((N_{a} n_{f} = N_{b} n_{t}).
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 n_{e}, T_{e} 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 wellknown 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 equioperational argon plasma.
Results from laser diagnostics will used to support this study on the influence of equilibrium departures induced by steep gradients.
HEAT TRANSFER BETWEEN A NONEQUILIBRIUM PLASMA AND A SURFACE
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 nonequilibrium character (thermal or chemical) plays an important role
in the heat transfer during gassurface interactions. As the temperature grows the E_{a}/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 nonequilibrium 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 lowpressure (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 exsitu 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 ptype semiconductors oxides like Ag_{2}0 or Cu~O are strongly
catalytic, whereas the ntype such as SiO_{2} or Zn0 are poorly catalytic. Moreover, the higher the optical gap the lower the
catalycity of the semiconductor.
PARTICLE AND FLUID MODELS OF RADIO FREQUENCY DISCHARGES FOR THIN FILM DEPOSITION
Bakhtier Farouk
Professor of Mechanical Engineering, Drexel University, Philadelphia, PA 19104, U.S. A.
ABSTRACT
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 knowhow 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 multidimensional
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 (particleincell/MonteCarlo) model will be presented for
low pressure radiofrequency (RF) glow discharges for carbon film deposition ^{[13]}.
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 nonequilibrium phenomena. While charged particle motion and
collisions are traditionally modeled, the present model includes neutral motion and collisions. The
model was extended to CH_{4} (polyatomic gas) plasma and predicted the carbon film deposition.
Radio frequency CH_{4} plasma has been recently used for diamondlikecarbon (DLC)
deposition. The model considers the motions of CH_{4}, CH_{4}^{+} , CH_{3}, C_{2}H_{5}, H_{2}, H and electrons.
Detailed information such as space and time dependent results, energy distributions, will be
presented for CH_{4} 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 nonequilibrium low pressure
plasmas, such models are computationally intensive, especially for multidimensional 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
electronneutral 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 ^{[47]} of a selfconsistent twodimensional
fluid model of both capactively coupled and inductively coupled methane glow discharge will be
presented. The simulations provide insights to chargedspecies 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 cycleaveraged 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 nonequilibrium plasma
reactors will be addressed.
REFERENCES
 Nagayama, K., Farouk, B. and Lee, Y. H. , Neutral and Charged Particle Simulations of Ar
Plasma, Plasma Sources Science and Technology, Vol. 5, pp 685695, 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 125134,
1998
 Nagayama, K., Farouk, B. and Lee, Y. H. Particle Simulation of CH4/H2 RadioFrequency
Glow Discharges for Diamondlike Carbon Film Deposition", Proceedings International
Conference on Fluid Engineering, Vol. II, (JSME Centennial Grand Congress, Tokyo) pp
977981, 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, 12, pp 132138, 1998
 Bera, K., Farouk, B. and Lee, Y. H., TwoDimensional 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 Twodimensional Radio
Frequency Methane Plasma: Comparison with Experiments", with (submitted for
publication), IEEE Transactions on Plasma Science
DIAGNOSTICS AND MODELING OF A THERMAL RF PLASMA PROCESS USED FOR THE FLASH EVAPORATION OF ZIRCONIA POWDERS
P. Buchner, H. Schubert, J. Uhlenbusch, M. Weiß, K. Willée
Institut für Laser und Plasmaphysik, HeinrichHeineUniversität Düsseldorf,
Universitätsstr. 1, D40225 Düsseldorf, Germany
INTRODUCTION
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
socalled plasma flash evaporation method^{1} 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.
EXPERIMENTAL
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 elsewhere^{23}. 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 spraydried 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 spraydried 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 yzstage, 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 equations^{46}. 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.
RESULTS AND DISCUSSION
According to model calculations, ZrO_{2} 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 d_{0}.
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 inversion^{8} 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 onaxis region is drawn in Figure 3. In this case the dry
powder feed mode is applied.
CONCLUSION
The task of achieving complete particle evaporation of highmelting 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.
REFERENCES
 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. LützenkirchenHecht, H.H. Strehblow and J. Uhlenbusch, submitted to Journal
of Materials Science, 1998
 M.I. Boulos 1976, IEEE Transactions on Plasma Science PS4 (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)
NONEQUILIBRIUM EFFECTS IN GLIDING ARC DISCHARGES
Özlem Mutaf Yardimci, Alexei V. Saveliev, Alexander A. Fridman, Lawrence A. Kennedy
Department of Mechanical Engineering, The University of Illinois at Chicago,
Chicago, IL 606077043 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. Nonthermal 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 nonthermal powerful discharges with high plasma concentrations and high electric fields.
These requirements are met in nonequilibrium 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 30005000 K into nonequilibrium one^{1}. 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 30005000 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 7580%) can be dissipated in a cold nonequilibrium zone^{2}.
In this work, we specify the transition of thermal arc into nonequilibrium 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 crosssection 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 lowripple (0.1%) power supply (Universal Voltronics, Inc.) with internal resistance variable from 25 to 150 k and noload voltage settings from 1 to 10 kV.
The evolution of plasma column was recorded continuously by using a highspeed 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 timeresolved 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 Analyst^{TM}, 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 timeamplitude pairs for further processing. A typical voltagecurrent 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/cmTorr for equilibrium zone before transition, and 2.4 V/cmTorr for nonequilibrium 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 nonequilibrium plasma can be generated from initially equilibrium thermal gliding arc discharge.
REFERENCES
 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 14491465, 1994
 Fridman, A.A. Nester, S., Kennedy, L.A., Saveliev, A.V. MutafYardimci, O., "Gliding Arc Gas Discharge" J. of Progress in Energy and Combustion Science, Vol.25, pp. 211232, 1999.
EXCITATION BALANCES IN ATMOSPHERIC ARGON RF DISCHARGES STUDIED BY POWER INTERRUPTION EXPERIMENTS
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
INTRODUCTION
The timedependent 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 socalled 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
r_{p} 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
needlelike plasmas (r_{p}~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
flamelike plasma has a diameter r_{p}~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.
POWER INTERRUPTION EXPERIMENTS
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 T_{e} and the gas temperature T_{g}: T_{e}>T_{g}. If the power
supply is suddenly stopped, the electrons will almost instantaneously thermalize with the
(much) cooler heavy particles and as a result T_{e} will drop (t_{cool}<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 multichannel scaler, having 4096 channels with a time resolution
of 2 ms. Therefore the line intensities can be monitored during the complete poweroff cycle and part of the poweron cycle.
EXCITATION BALANCES AND THEIR RESPONSES TO POWER INTERRUPTION
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 Sahalike. If the intensity immediately decreases, the response
is called Boltzmannlike. Examples of a Saha and a Boltzmannlike response are given in
figure 1.
EXPERIMENTAL RESULTS
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 Sahalike PI response.
However, if aerosols are introduced into the plasma, the argon lines no longer show a
Sahalike response, but a Boltzmannlike response instead. Analytes and molecules show
a Boltzmannlike 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 Sahalike response
of argonlines changes into Boltzmannlike 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 Saharesponse (right) to power interruption (at t=100ms) as measured from plasmas created by the MPT.
REFERENCES
 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, 885900 (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 1518
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, 417430 (1991).
 J.A.M. van der Mullen and J.M. de Regt, Fresenius J. Anal. Chem., 355, 532537 (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).
PLASMA EXPANSION WAVES IN THE PRESHOCK REGION
K.T.A.L. Burm^{a}, D.C. Schram^{a}, and W.J. Goedheer^{b}
^{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
ABSTRACT
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 PrandtlMeyer 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 shock^{13}. 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.
INTRODUCTION AND SET UP
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. wallstabilised thermal cascaded arc^{4}. 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 10^{22}10^{23} m^{3}. Flows are typically between 10 and 150 sccs^{5,6}. The unit 1 sccs is equivalent to 2.5*10^{19} particles/s. The arc channel has a length of 34 mm and a constant diameter of 4 mm.
The expansion chamber^{7} is a low pressure vessel at a varying downstream pressure of 20 Pa  10 kPa. The plasma is 'underexpanded' (the pressure in the exit plane can be as large as 10^{3} times the background pressure^{1}). The dimensions of the vessel are 1 m. diameter and 1.5 m. length.
EXPANDlNG FLOWS
Experiments^{7} 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, p_{o,e}, and the background pressure, p_{b}. Ashkenas et al.^{9} obtained an empirical relation between d_{s} and p_{o,e}/p_{b}:
where C equals 0.67 and is independent of g. This same relation has been derived by Young^{10} 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 disturbances^{1} (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, yields^{1}:
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 socalled PrandtlMeyer 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 PrandtlMeyer flows on an argon plasma to get a better understanding of the behaviour of an expanding plasma.
RESLTLTS
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 gas^{11}. 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 (M_{1}) and the maximum Mach wave of 4.1 (M_{2}) the plasma accelerates. In accordance with gas dynamics, when Mach number M_{2} 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 M_{2} wave lines intersect each other compressively. If we neglect bending of the Mach wave lines in the preshock
region, we can obtain an estimation of the preshock region length. For an argon plasma flowing out of a 4 mm diameter straight cascaded arc we estimated a preshock 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.
CONCLU SIONS
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 PrandtlMeyer 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 PrandtlMeyer 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.
ACKNOWLEDGEMENT
We thank A. Leroux, J.A.M. van der Mullen, and M.C.M. van de Sanden for their support.
REFERENCES
 Oosthuizen P.H., and W.E. Carscallen, Compressible Fluid Flow, McGrawHill 1997.
 S. Schreier, Compressible Flow, Wiley 1982.
 E. Becker, Gasdynamik, B.G. Teubner Verlagsgesellschaft 1965.
 Kroesen G.M.W., D.C. Schram, and J.C.M. de Haas, Plasma Chem. & Plasma Proc., Vol. 10, No. 4 (1990) 531551.
 M.J. de Graaf, R.P. Dahiya, F.J. de Hoog, M.J.F. van de Sande, and D.C. Schram, J. Phys. (Paris), Colloq. 51 (1990) CS  387.
 R.F.G. Meulenbroeks, A.J. van beek, A.J.G. van Helvoort, M.C.M. van de Sanden and D.C. Schram, Phys. Rev. E49 (1994) 4397.
 Kroesen G.M.W., D.C. Schram, A.T.M. Wilbers, and G.J. Meeusen, Contrib. Plasma Phys. Vol. 31 No. 1 (1991) 2742.
 M.C.M. van de Sanden, thesis, Eindhoven University of Technology (1991).
 H. Ashkenas, and F. S. Sherman, Proc. Rarefied Gasdynamics 4, ed. J.H. de Leeuw (Academic Press, New York, 1966).
 W.S. Young, The Physics of Fluids, Vol. 18, No. 1 l, November 1975.
 K.T.A.L. Burm, W.J. Goedheer, and D.C. Schram, to be published.
NUMERICAL MODELLING OF ELECTRODE PLASMA GENERATION
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
INTRODUCTION
There is a wide spectrum of arc applications, for example in the field of electric circuit breakers, electric arc gas heaters, spacevehicle reentry 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 arcelectrode 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 prerequisite 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 nonequilibrium 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, multispecies, two temperature NavierStokes equations were used in the model together with some kinetic theory equations and Maxwell's equations.
NUMERICAL SCHEME
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 convectiondiffusionionization operator splitting scheme which has previously been used for reacting gas flows^{8}, with extra operations for the electromagnetic effects. The NavierStokes 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, (F_{v}, G_{v}) 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 onedimensional 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.
MODEL PROBLEM
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 N_{2}. 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.
REFERENCES
 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. 229235, 1993.
 X. Zhou, J. Heberlein, E. Pfender, "Theoretical study of factors influencing arc erosion of cathode" , IEEE Transactions On Components, Packaging and Manufacturing Technology, Part A, vol. 17, no. 1, pp. 107112, 1994.
 Y. Nakagawa, Y. Yoshioka, "Theoretical calculation of the process of contact arc erosion using a one dimensional contact model", IEEE Transactions On Components, Hybrids and Manufacturing Technology, vol. 1, no. l, pp. 99102, 1978.
 S. N. Kharin, "Mathematical model of arc erosion in electric contacts", in l6th International Conference On Electrical Contact, (Loughborough, England), pp. 205209, 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. 490493, 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. 5460, 1998.
 J. J. Gonzalez, A. Gleizes, P. Proulx, M. Boulos, "Mathematical modelling of a freeburning arc in the presence of metal vapour", Journal of Applied Physics, vol: 74, no. 5, pp. 30653070, 1993.
 S. R. Amaratunga, A numerical study into surface catalytic effects in nonequilibrium reacting viscous laminar hypersonic flow. PhD thesis, Department of Aeronautics & Astronautics, Southampton University, 1998.
VACUUM SYSTEM FOR EXPERIMENTS ON INTERACTION OF WEAKLY IONIZED HIGHLY DISSOCIATED HYDROGEN PLASMA WITH SOLID SURFACES
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.
CONSTRUCTION DETAILS
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 CHARACTERIZATION
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).
H RECOMBINATION ON SOLID SURFACES
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.
DISCHARGE CLEANING
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.
NONLINEAR CONVECTIVE HEAT TRANSFER IN A TRANSITIONAL PLASMA PLUME
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 laminarturbulent 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 laminarturbulent 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 selfsustained, 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 (EckertWeise) 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 lowdimensional 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 TaylorCouette flow or RayleighBenard 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.
NUMERICAL SIMULATION OF MULTICOMPONENT INDUCTIVE PLASMA FLOWS UNDER CHEMICAL NONEQUILIBRIUM
Vanden Abeele, G. Degrez, P. Barbante, J.P. Mellado González
von Karman Institute for Fluid Dynamics SteenwegopWaterloo 72, 1640 St. GenesiusRode, Belgium
INTRODUCTION
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 nonpolluted 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 reentry space vehicles. To properly simulate reentry flight conditions, inductive plasmas need to be operated at pressures below 0.1 atm, where thermal and chemical nonequilibrium 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 multicomponent inductive plasmas (e.g. air) under chemical nonequilibrium. To the authors' knowledge, continuum models of argon inductive plasmas under non equilibrium have been presented by Mostaghimi et al.^{4} (1987), by Semin^{5} (1991) and by Benoy^{6} (1993). Unfortunately, these models can not be easily extended to more general multicomponent mixtures.
Whereas argon plasmas can be modeled by a straightforward threecomponent formalism, a full multicomponent formalism (e.g. multicomponent diffusion model, ...) is required to simulate e.g. air plasmas. Moreover, the evaluation of the thermodynamic and transport properties of a multicomponent 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 semiimplicit 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.
PHYSICOCHEMICAL MODELING OF MULTICOMPONENT PLASMAS
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 Arrheniustype source terms.^{7} The plasma thermodynamic properties are determined through statistical mechanics and the plasma transport properties are computed with the wellknown method of Chapman and Enskog.^{8}
Multicomponent species diffusive fluxes are obtained from the full StefanMaxwell equations^{9} by means of a straightforward iterative procedure.^{10} The electron concentration is obtained from the electron species continuity equation, rather than by explicitly imposing quasineutrality. Provided the global and species continuity equations are discretized with care, it is shown that quasineutrality automatically holds. An elegant algorithm, in which no distinction needs to be made between electrons and heavy particles, is thus derived.
DISCRETIZATION AND ITERATIVE SOLUTION METHOD
The torch is modeled by a fully axisymmetric configuration. To this end, the outer inductor is represented by a series of parallel currentcarrying 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 pressurestabilized 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 uptodate workstations.
PRELIMINARY RESULTS AND CONCLUSION
The performance of the model is evaluated by calculating an atmospheric nitrogen plasma flow in the VKI minitorch.^{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 gridconverged. The equilibrium solution is first computed and then used as an initial guess for the nonequilibrium model. Both the equilibrium and nonequilibrium 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 nonequilibrium effects will be brought into the code and calculations will be performed for lower pressure levels.
Figure 1: Computed temperature field in the VKI minitorch (6 kW, 27 MHz, 1 atm)
 ^{1} Boulos, M. I., The inductively coupled radio frequency plasma. Pure & Appl. Chem., 57(9), pp. 13211352, 1985.
 ^{2} Kolesnikov, A. F., Aerothermodynamic simulation in sub and supersonic highenthalpy 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 reentry simulation. ESA SP426, ESTEC, Noordwijk, the Netherlands, 1999.
 ^{4} Mostaghimi, J., Proulx, P., Boulos, M. I., A twotemperature model of the inductively coupled radio frequency plasma. J. Appl. Phys., 61(5), pp. 17531760, 1987.
 ^{5} Semin, V. A., Theory of nonequilibrium inductive high frequency discharge in a gas flow. Fluid Dynamics (translated from Russian), 2), pp. 282288, 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 nonequilibrium. TP2867, 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., Selfconsistent StefanMaxwell relations for multicomponent ambipolar diffusion in twotemperature plasma mixtures. TN196, von Karman Institute, St. GenesiusRode, Belgium, 1999.
 ^{10} Sutton, K., Gnoffo, P. A., Multicomponent diffusion with application to computational aerothermodynamics. TP 982575, AIAA, Albuquerque, New Mexico, 1998.
 ^{11} Vanden Abeele, D., Degrez, G., n efficient model for inductive plasma calculations. TP 982825, AIAA, Albuquerque, New Mexico, 1998.
RESONANCE IN A TRANSITIONAL PLASMA PLUME
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 arcrestricting 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 selfsustained (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 organpipe 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 nonlinear 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).
A LIF STUDY ON THE EXPANSION BEHAVIOUR OF A PLASMA BEAM GENERATED FROM A MIXTURE OF Ar AND H_{2}
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 ArH_{2} mixture, spatially resolved densities, temperatures and velocities of ground state atomic hydrogen are obtained by applying twophoton 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.
1 INTRODUCTION
When a cascaded arc^{l} created plasma is expanded into a vacuum vessel, a versatile high quality particle beam is obtained. Such an expanding plasma beam has many applications^{2} 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 H_{2} 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 twophoton excitation laser induced fluorescence process^{3,4} (TALIF). H is excited with two 205.14 nm photons from the 1s^{2}S ground state to the 3d^{2}D and 3s^{2}S states. The excitation is monitored by detection of the fluorescence yield on the Balmera line at 656.3 nm.
Figure 1 shows a typical spectral scan of the twophoton transition. Integration of the line profile allows the determination of the relative H density. In order to obtain absolute number density the LIF setup has to be calibrated. This is accomplished via a titration with N0^{2} in a flow tube reactor^{5}. 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 setup
A simplified scheme of the experimental setup 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 H_{2} is used. The UV laser beam generation has been extensively described. A tunable 50 Hz NdYAG pumped dye laser delivers radiation around 615 nm. The output of the dyelaser is frequencytripled using nonlinear 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 Balmera line are collected with a photomultiplier tube. The delivered signal is then processed using a computer.
The laser frequency is calibrated by simultaneous recording of the absorption spectrum of molecular iodine^{6,7}.
3 Results and discussions
From the adiabatic supersonic expansion theory^{8,9}, a value of 4000 m.s^{1} is obtained for the velocity of an ArH 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 HankineHugoniot^{10} 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, HankineHugoniot 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 path^{11} 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.
Acknowledgments
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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