Density Evolution of Atoms and Atomic Radicals in Plasma
Expansions
R. Engeln∗ , S. Mazouffre† , P. Vankan∗ and D.C. Schram∗
Department of Applied Physics, Centre for Plasma Physics and Radiation Technology (CPS), Eindhoven
University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
†
Laboratoire d’Aérothermique, CNRS, 1C avenue de la Recherche Scientifique, 45071 Orléans cedex 2, France
∗
Abstract. The evolution of density, temperature and velocity of argon, hydrogen and nitrogen atoms in expanding plasma
has been studied extensively by laser spectroscopic means. Both temperature and velocity evolution in the first part of
the supersonic expansion can be described using the adiabatic expansion theory developed for the expansion of a neutral
gas. For the argon atoms the density behavior is also in accordance with this theory. However, in front of the stationary
shock, it is observed that the background argon gas invades the supersonic part of the plasma jet. For atomic hydrogen and
nitrogen radicals, the density clearly deviates from the expected 1/z 2 behavior. The hydrogen and nitrogen radicals escape
the supersonic domain of the plasma jet. The reason for this outward diffusion process is the large partial pressure difference
between the plasma jet and the background. This large difference is induced by the efficient wall association of the atomic
species.
1. INTRODUCTION
Understanding the transport of atoms and atomic radicals in a plasma expansion, is of interest from a fundamental
point of view as well as from a more technological point of view. A plasma expansion is a very general physical
phenomenon which covers a broad range of dimensions, ranging from astrophysical objects [1] to small laser spots
[2]. In comparison with the expansion of a neutral gas, plasma expansion is a more complex phenomenon. For
instance, different kind of particles are present (neutrals, ions, electrons and photons), current and electric fields
can be generated, and the flow is often not isentropic. From a technological perspective, the understanding of the
efficient formation of atomic radicals, which are of relevance for industrial applications like e.g. deposition of thin
films [3, 4, 5], surface modification [6] and plasma assisted catalysis [7], is of major importance.
In order to clearly understand the dynamics of such a plasma jet, neutral Ar atoms and H and N radicals have
been probed in such a way that the plasma flow is not disturbed. The local argon atom density is monitored by
means of UV Rayleigh scattering whereas the Ar velocity and temperature are measured by means of Laser Induced
Fluorescence (LIF). The detection of ground-state hydrogen and nitrogen atoms is more cumbersome due to the large
energy gap between the electronic ground state and the first excited states. Therefore, hydrogen and nitrogen atoms are
spatially probed by means of Two-Photon Absorption Laser Induced Fluorescence (TALIF). By applying this method
for different positions in the expansion, the H and N distribution in the plasma jet in terms of density, temperature,
and velocity has been completely mapped. In this contribution, we review our results on the transport of argon atoms,
and ground-state hydrogen and nitrogen atoms in terms of density in the expansion of a thermal plasma generated by
a DC wall stabilized arc plasma source. The results obtained from the study of such a plasma jet may be generalized
to other kind of plasma expansion with very different dimensions, e.g. solar outbursts and laser spots.
2. EXPERIMENTAL
Spectroscopic techniques like (Two-photon Absorption) Laser Induced Fluorescence ((TA)LIF), Coherent Anti-Stokes
Raman Scattering (CARS) [8] and Rayleigh scattering have been used to study transport properties of atoms, atomic
radicals and molecules in thermal plasma expansion. The thermal plasma is created in a cascaded arc [9] that typically
CP663, Rarefied Gas Dynamics: 23rd International Symposium, edited by A. D. Ketsdever and E. P. Muntz
© 2003 American Institute of Physics 0-7354-0124-1/03/$20.00
FIGURE 1.
Schematic view of the TALIF and Rayleigh scattering setup.
operates at 50 A dc current and with a cathode-anode voltage of about 100 V. The arc consists of 4 to 6 water cooled
copper plates with a center hole of 4 mm diameter. The three cathodes are placed concentrically around the channel and
the last plate acts as anode for the discharge. Typically a flow of 3 standard liters per minute (slm) is applied through
the arc. The plasma source and the TALIF and Rayleigh scattering excitation and detection scheme, are schematically
drawn in Fig. 1. The TALIF technique allows for the spatially resolved determination of density, temperature and
velocity of e.g. ground state hydrogen and nitrogen atoms. Rayleigh scattering is used to determine the total heavy
particle density. The UV laser beam originates from a Nd:YAG laser pumped pulsed dye laser, which is tripled in
frequency. In this way tunable narrow band (about 0.1 cm−1 ) UV light between 200 and 220 nm is produced. In case
an argon plasma is studied in terms of velocity and temperature, a single mode cw diode laser is used that emits light
around 810 nm. The cascaded arc can be moved with respect to the excitation and detection area. In this way the
plasma jet can be mapped without re-adjusting the alignment of the excitation and detection branch.
3. PLASMA EXPANSION
3.1. Argon case
In the case of an expanding argon plasma, it has been demonstrated by means of Rayleigh scattering [8, 10, 11]
and Doppler shifted LIF spectroscopy [12] that the expansion of neutral argon atoms in terms of velocity, temperature
and density can be well understood in terms of an adiabatic supersonic expansion of an ideal gas [13] with a slightly
lower adiabatic exponent, i.e. 1.4 in stead of 5/3. This difference is due to the ionization degree and difference in heat
conduction of the argon plasma as compared to neutral argon gas.
If one assumes that the particles in the jet originate from a point source and flow along straight stream lines, the
theoretical density development is written as follows:
n(z) = n0
1
.
1 + z2 /z2re f
(1)
Here, zre f is a scaling length which is determined by the properties in the early expansion and by the source nozzle
geometry (it is of the order of the diameter of the source outlet). In the supersonic domain, a rarefaction effect due
to an increase in beam diameter, causes the density to decrease with z−2 , after a distance equal to a few times the
nozzle diameter (see Fig. 2). As can be seen in Fig. 2, the density behavior is independent of background pressure, as
is to be expected. Further downstream the expanding plasma collides with the standing background gas which leads
to the formation of a stationary shock wave of which thickness and position depend on the background pressure [14].
Throughout the shock front, the density rises whereas the axial velocity component decreases. This arises from the
FIGURE 2. Ar atom density evolution in a supersonically expanding argon-hydrogen plasma for two different background
pressures (stagnation pressure in the arc is 0.6 atm.). The solid line represents a fit through the data points that represent the
supersonic part of the expansion and using Eq. (1).
conservation of the forward flux. The density jump is connected to the Mach number ahead of the shock wave (M ≈ 3)
through the Rankine-Hugoniot relations [15]. Behind the shock front, i.e. in the subsonic domain, the plasma flows
at constant pressure. Thus the density rises slowly because the temperature decreases due to heat transfer towards
the vessel wall. A closer look at the velocity distribution function (VDF) of the argon atoms around the stationary
shock, shows a clear departure from a Gaussian distribution function [12]. We have shown that these VDFs can be
decomposed into two Gaussian VDFs: one is determined by the conditions in the supersonic part of the jet (high
velocity, ’low’ temperature), and one by the conditions at the end of the shock in the subsonic domain (low velocity,
’high’ temperature). The contents of the ’fast’ distribution decreases in going through the stationary shock from the
supersonic to the subsonic region, while the contents of the ’slow’ distribution increases in that direction. We ascribe
the ’slow’ component to background gas that invades the expanding plasma jet in the overexpanded region upstream
from the stationary shock front. Measurements of the radial velocity distribution in front of the stationary shock show
clearly that part of the argon atom density of the argon atoms has a velocity component into the direction of the center
of the jet.
Because of the large set of data on the supersonically expanding thermal argon plasma, this system is ideally suited
to validate computational approaches to model plasma expansion. In [16] two computational approaches have been
compared, i.e. continuum fluid dynamics (CFD) and direct simulation Monte Carlo (DSMC). For CFD calculations
the commercially available code FLUENT [17] has been utilized, while for the DSMC method the standard procedure
developed by Bird [18] has been applied.
3.2. Atomic hydrogen case
Plasma expansion of atomic hydrogen is of particular interest. Such a light radical plays an important role in the field
of nuclear fusion, e.g. Tokamak plasmas [19] and manufacturing techniques like processing and deposition plasmas.
Furthermore, H is one of the main components of both stellar and interstellar matter. In [20], we have shown that the
transport of H radicals, contrary to that of argon neutrals, can not be entirely described in terms of the well-established
free jet flow picture. Hydrogen atoms exhibit a very specific behaviour.
Hydrogen atoms are excited with two 205 nm photons from the 1s2 S ground state to the 3d2 D and 3s2 S states.
The laser beam intensity is low enough to induce any parasitic effect such as stimulated emission, production of
H+ , and dissociation of H2 molecules. The excitation is then monitored by detection of the resulting fluorescence
on the Balmer-α (Hα ) line at 656 nm using a gated photo-multiplier tube (PMT). A narrow band interference filter
(∆λ = 10 nm) is used to isolate the Hα line from the plasma emission. A slit mask is used to define the detection volume
FIGURE 3. H atom density evolution in a supersonically expanding hydrogen plasma (the stagnation pressure in the plasma
source is about 0.14 atm.). The two lines show the 1/zβ dependence, with β ≈ 2.6 at P = 16 Pa and β ≈ 2.2 at P = 42 Pa.
(< 1 mm3 ) which dimensions are smaller than any gradient scale length. The PMT signal is recorded by means of
an oscilloscope connected to a computer. The dye-laser frequency is calibrated by the simultaneous recording of the
absorption spectrum of molecular iodine. From a spectral scan over the two-photon transition, the local H atom density,
temperature, and velocity along the laser beam are measured. Absolute number densities are obtained by calibrating
the TALIF setup by means of a titration reaction with NO2 in a flow tube reactor [21].
In the argon case, a density increase and velocity decrease is observed at the stationary shock front. This means that
the forward flux is conserved, a basic constraint to adiabatic expansions [13]. Contrary to the argon case, the hydrogen
atom axial density profile does not show an increase at the stationary shock front (see Fig. 3), while the profile of the
drift velocity shows a clear decrease. This means that the forward flux of H atoms is not conserved in the shock region.
This anomalous H atom shock pattern has been reported in [11, 20]. It is postulated that strong density gradients
between the core of the jet and its surroundings, due to a low H concentration in the background gas, are responsible
for an outward diffusion of H atoms. We have called this phenomenon the radical de-focusing effect [20]. The efficient
association at the wall of hydrogen ground-state atoms leading to molecular hydrogen, is responsible for the very low
atomic hydrogen background density [22]. One could argue that H atoms recombine in volume during the expansion
process to form molecular hydrogen, which would also lead to a non-conservation of the axial H flux. However, under
our experimental conditions (pressures below 100 Pa), the rates of these three-body reactions are much too low to lead
to any significant recombination during the residence time.
Furthermore, as already mentioned in [23], the steepness of the density decay within the supersonic domain depends
on pback , which means that H particles exiting the cascaded arc receive information about the standing ambient gas.
This proofs that a shock wave structure does not form a totally closed system but it can be permeable to some particles.
As shown in Fig. 3, the H axial density profile ahead of the shock wave can be described by a slightly modified point
source expansion law. At several nozzle diameters downstream from the exit of the arc, the density drop can be
described with 1/zβ ; β becomes closer to 2 at higher pressures [11], meaning that H atoms are better confined inside
the supersonic jet. In other words, it becomes more difficult for H to cross the barrel shock wave at high p back , since
the local mean free path decreases. This decrease explains why the H density in the ambient gas depends on p back , as
can be seen in Fig. 3.
In [23, 24] the VDF’s in the stationary shock in a pure hydrogen expanding plasma have been studied. Like in
the argon case, the distribution functions can be decomposed into two Maxwellian distributions. The fast component
corresponds to the unhampered supersonic distribution, while the slow component corresponds to the conditions in the
shock region. This results from collisions of hydrogen atoms in the jet with H2 molecules penetrating the jet from the
surroundings.
FIGURE 4. N atom density evolution in a supersonically expanding nitrogen plasma at two different background pressures (the
stagnation pressure in the plasma source is 0.44 atm.).
3.3. Atomic nitrogen case
Nitrogen and nitrogen-containing plasmas are already used for a variety of applications. In the field of surface
treatments, such plasmas are widely employed for modifying specific surface properties, e.g. wetability or hardness,
of metals and polymers (see the list of references in [25]). In the astronautics area, nitrogen plasma jets are used to study
energy transfer to the surface of a space vehicle that occurs during the entry stage in the Earth’s atmosphere [26, 27]. An
entirely new domain of applications is nowadays emerging. Because of their wide bandgap and strong chemical bond,
nitrogen containing semiconductors like GaN based alloys offer the promise of major improvements in performance
of opto-electronic devices. Applications such as blue-light emitting diodes [28], laser diodes and sensitive solar blind
photo-detectors are currently under development [29]. Moreover, a material like SiN appears to be very suitable as
anti-reflection coating for high conversion efficiency in solar cells [30].
In the nitrogen plasma case the cascaded arc channel has a diameter of 3 mm, in stead of 4 mm that has been used in
the argon and atomic hydrogen case. The operating standard conditions are: a 55 A direct current (dc), a cathode-anode
voltage of 120 V and a N2 gas flow of 1.5 slm. The stagnation pressure inside the arc is 0.44 atm. Nitrogen atoms are
excited with two 206.7 nm photons from the 2p 4 S3/2 ground-state to the 3p 4 S3/2 state [25, 31]. The excitation is
monitored by detection of the 742-747 nm infrared fluorescence radiation that results from the spontaneous emission
to the 3s 4 P manifold. The infrared radiation is directed towards a gated photomultiplier tube (Hamamatsu R928,
1.5 µ s opening time). The continuous background light emitted by the nitrogen plasma is strongly reduced by a 10 nm
FWHM interference filter centered at 742 nm. The current delivered by the detector is charge integrated and recorded
by means of an ADC connected to a computer. From a spectral scan over the two-photon transition, the local N( 4 S)
atom density, temperature and velocity are determined. Absolute number densities are obtained by calibrating the
N(4 S) atom fluorescence yield using a well defined amount of krypton gas [25, 32]. Krypton atom has a two-photon
excitation scheme very similar to that of nitrogen and the ratio of the two-photon absorption cross-section of Kr to
N(4 S) has been accurately measured [32].
The on-axis profile of the ground-state nitrogen atom density is shown in Fig. 4 for two different background
pressures. In the supersonic domain of the expansion and behind z = 4 mm, that corresponds to the distance it takes
for the jet to open, the N(4 S) density decreases quadratically with the axial position z regardless of the pressure. This
indicates that the drop in density along the jet centerline is a direct consequence of the increase in the jet diameter,
like in the argon case. The compression stage through the normal stationary shock wave is clearly visible in Fig. 4.
A compression ratio of 1.7 is found for both background pressures. Using the well-established Rankine-Hugoniot
relations [14, 33], a Mach number ahead of the shock wave of 1.4 is deduced from the N( 4 S) atom density jump.
This estimated Mach number is about three times less than the one directly obtained from the measurement of the
axial velocity [34] meaning that the compression effect is somehow attenuated. Furthermore the magnitude of the rise
in density across the shock wave does not match the drop in velocity. This disagreement confirms the fact, already
implied in the previous remark, that the N(4 S) atom forward flux is not conserved across the shock front. In the
subsonic domain the density decreases slowly, as can be seen in Fig. 4, whereas the neutral gas supersonic expansion
theory predicts a flow at constant static pressure beyond the shock wave [33]. In accordance with the perfect gas law
in the subsonic domain, the density should increase since the plasma flow cools down.
Ground-state nitrogen atoms can recombine in volume to form molecular nitrogen according to the following threeparticle reactions
N + N + N → N2 (A, B) + N k ≈ 1.4 × 10−44 m6 s−1
N + N + N2 → N2 (A, B) + N2 k ≈ 6.8 × 10−46 m6 s−1 .
The reaction rates, however, are too low to lead to any significant loss of N(4 S) atoms under our experimental
conditions (for a more complete review of nitrogen plasma kinetics see [35, 36, 37]). Therefore the observed losses
of atomic nitrogen in the course of the plasma expansion can only be explained by the existence of an escape path
for N(4 S) atoms. Like in the hydrogen case, the observed departure from the classical expansion picture in the case of
nitrogen atoms is understandable in terms of plasma-surface interactions. The too small density jump across the shock
wave as well as the decrease in N(4 S) partial static pressure in the subsonic domain both originate in recombination
of N(4 S) atoms at the vessel walls where they form nitrogen molecules. Nitrogen atoms, however, are better confined
inside the nitrogen plasma jet than H atoms in hydrogen containing plasma expansions. For instance, there is no
significant losses of N(4 S) in the supersonic domain. This gain in confinement results from the combination of several
factors. First, the momentum exchange cross-section of N-N2 collisions is slightly higher than the cross-section of
H-H2 collisions [38] which has consequences on the local mean free path. Second, the high mass of N atoms leads
to a low thermal speed in spite of a relatively high temperature in the jet. Third, the loss probability of N atoms on a
stainless steel surface is quite low for an atomic radical. Currently available values in literature vary from 7×10 −2 to
8×10−3 [39].
In the case of H atoms the reported loss coefficients values set around 0.2 [22, 40]. The low recombination
probability of N(4 S) on metallic surfaces is often explained in the following way [39]. The wall is first covered by
a layer of N atoms on top of which a layer of protective molecular nitrogen is quickly formed. The latter prevents
N atoms to reach the surface and therefore to recombine. Due to the combination of all these factors, the outward
diffusion flux of N(4 S) atoms stays limited and nitrogen atoms are relatively well transported towards the downstream
region.
Also for a pure nitrogen expanding plasma the VDF’s in the stationary shock wave have been measured [24]. Similar
results are obtained as in the hydrogen case. The VDF’s show that the nitrogen atoms before and after the shock are in
thermal equilibrium, while in the shock the VDF’s can be decomposed into two Maxwellian distributions.
4. CONCLUSIONS
In this paper we have reviewed our results on the density evolution in argon, hydrogen and nitrogen plasma of
respectively, argon metastables, atomic hydrogen and nitrogen radicals, obtained by laser spectroscopic means. The
argon case is also used to validate continuum fluid dynamics (CFD) and direct simulation Monte Carlo (DSMC) codes
for this kind of expansion. In several papers also the temperature and velocity of the gases have been reported.
In order to be able to fully exploit the possibilities of plasma expansion, studies of the transport properties and
kinetics of argon, atomic hydrogen and nitrogen have been performed over the last couple of years. A phenomenon
that had not been observed in cold gas expansions, i.e. the radical de-focussing effect, has been observed both in
hydrogen and nitrogen plasma expansion. This effect has large implications for plasma chemical processing, where
optimal production and minimal loss of atomic radicals is wanted. Due to the fact that the experiments are performed
at conditions at which mean free paths for collisions are in the order of the dimensions of the expanding plasma jet,
leads to an invasion of background gas before the stationary shock. This has been directly observed in an argon plasma
expansion via part of a density distribution of which the velocity is directed inwards. The same is probably true for
molecular hydrogen and nitrogen invading a H2 /N2 plasma jet. Work is in progress to exemplify this. Also, due to
large partial pressure differences for atomic radicals between the core of the plasma jet and the background, mainly
induced by surface association, the atomic radicals escape the supersonic part of the expansion.
ACKNOWLEDGMENTS
The authors would like to acknowledge the fruitful discussions with M.C.M. van de Sanden, the contributions of N.
Sadeghi to the Doppler shifted LIF experiments on argon, I.S.J. Bakker for the nitrogen measurements, and the skillful
technical assistance of M.J.F. van de Sande, J. Jansen, A.B.M. Hüsken, and H.M.M. de Jong. This work is part of the
research program of the Dutch Foundation of Fundamental Research on Matter (FOM). It is financially supported by
the Dutch Organization for Scientific Research (NOW) and the Euratom foundation.
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