22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Effect of gas discharge conditions on argon surface-wave-sustained plasma torch
kinetics
P. Marinova, M. Atanasova and E. Benova
St. Kliment Ohridski University of Sofia, Sofia, Bulgaria
Abstract: The main plasma parameters as electron energy distribution function, argon ions
density, excited argon atoms density and electron-neutral collision frequency are obtained
on the base of a self-consistent numerical model of argon surface-wave-sustained
discharge. Their dependence on the gas discharge conditions is also shown.
Keywords: plasma kinetics, atmospheric pressure plasma, plasma modelling
1. General
Surface-wave-sustained discharges (SWDs) have been
studied both theoretically and experimentally in the last
40 years. The wide interest in SWDs results from the
increasing number of applications they have found in
various fields, like technology [1], medicine [2, 3], etc.
That is due to their ability to work in wide range of
discharge conditions: frequencies from MHz to GHz, gas
pressure from mTorr to several atm, discharge radius
from µm to several cm, discharge length from mm to
several meter, working gas – rare, molecular gasses and
arbitrary mixtures. The latest applications demand the
plasma sources to be small, inexpensive and to have
sufficiently high concentration of charged particles and
chemically active species. Moreover applications like
medical plasmas need to be sustained in open air, and to
have considerably low gas temperature.
Adequate
solution to the above requirements is offered by the
atmospheric pressure SWDs.
However practical applications require detailed
knowledge of the discharge characteristics on the
discharge conditions, more precisely density profiles of
the plasma constituents – electrons, excited species and
ions as well as distribution of the electric field, and the
electron and gas temperature. Such knowledge can be
provided in economical and reliable way by a
self-consistent model.
2. Model
The model consists of two parts – electrodynamics of
the wave sustaining the discharge coupled to plasma
kinetics [4]. Basis of the model are Boltzmann’s
equation, particles balance equations and Maxwell’s
equations. The model is applied to plasma torch (plasma–
vacuum configuration at atmospheric pressure).
The plasma torch is sustained by travelling
electromagnetic wave excited by wave launcher situated
at one end of a plasma column. The wave propagates
along the plasma–dielectric interface and heats the
electrons. Absorbing the wave energy the electrons are
able to create and sustain plasma by collisions. Due to the
high pressure conditions it is necessary to account for the
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Fig. 1. Plasma torch at atmospheric pressure.
effect of interactions between electrons and heavy
particles on the wave propagation.
Therefore the
electron–neutral collision frequency (obtained from the
kinetic part of the model) is taken into account in the
expression for the plasma permittivity. Applying this
expression in the Maxwell’s equations, a complex
dispersion equation is obtained. Its solution gives
dependences of the wave propagation and attenuation
coefficients in inhomogeneous plasma column on the
wave length (wave number), usually presented through
phase and attenuation diagrams. The wave energy
balance equation solved together with the electron energy
balance equation provides a link between electrodynamics
and kinetics.
3. Results
In this work by means of the self-consistent model a
study on the effect of the configuration accounted via the
plasma radius R and the frequency f of the wave
sustaining the plasma on Argon SWD is made. All
plasma characteristics change along the column due to the
axial inhomogeneity of the plasma. The model allows to
obtain all plasma characteristics as a function of plasma
density. The plasma density changes along the plasma
column and it is axial inhomogeneous, the electron energy
distribution function, the electron–neutral collision
frequency for momentum transfer [5], the atomic and
molecular ions densities, the population of all excited
states, the gas temperature, the mean electron energy and
the mean power for electron-ion pair creating in the
discharge are in the scope of this study.
The discharge conditions considered in the study are:
plasma with radius 0.05 cm, 0.1 cm and 0.2 cm sustained
1
by surface wave of frequencies 2 GHz, 1.5 GHz, 1 GHz
and 0.5 GHz.
At atmospheric pressure complicated argon energy
level diagram should be considered and a lot of
elementary processes should be taken under
consideration. The following species are included in the
argon energy level diagram at atmospheric pressure
model: Ar, Ar(4s), Ar(4p), Ar(3d), Ar(5s), Ar(5p),
Ar(4d), Ar(6s), Ar 2 *, Ar+, Ar 2 +, and Ar 3 + (Fig. 2). All
these excited states are considered as blocks of levels with
effective energy:
m
uk = ∑ uk, j / m
j =1
Fig. 3. Electron energy distribution function for different
radius and wave frequency 1 GHz at plasma 3.1015 cm-3.
where u k,j is the energy of each level in the block k and m
is their number.
In all calculations the averaged
population is used.
Fig. 4. Electron energy distribution function for different
radius and wave frequency 1 GHz at plasma density
2.1011 cm-3.
Fig. 2. Argon energy levels diagram
A self-consistent modelling of SWDs requires the
knowledge of the EEDF, which determines the electron
transport parameters, the rates of elementary processes,
and several other key quantities such as the effective
electron-neutral collision frequency for momentum
transfer ν eff and the mean power θ. In argon plasmas the
EEDF usually strongly differs from Maxwellian at plasma
density bellow 1015 cm-3.
The EEDF obtained satisfies both the particle and
energy balance equations for electrons as well as the
balance equations for heavy particles considered.
At atmospheric pressure the EEDF is Maxwellian at
high plasma densities as it is shown in Fig. 3 for fixed
plasma density 3.1015 cm-3. At low plasma densities
(2.1011 cm-3, Fig. 4) it slightly deviates from the
Maxwellian one.
One can see from Fig. 5 that with wave frequency
increasing electron – the neutral collision frequency
increases at higher plasma density.
The observed
2
dependence is better defined at low wave frequency and
abates with the increasing of the wave frequency. The
effect of the plasma radius on the electron-neutral
collision frequency is shown on Fig. 6. The results
indicate insignificant influence of the plasma radius on
the investigated plasma parameter.
Fig. 5. Electron-neutral collision frequency as a function
of plasma density for different wave frequency and radius
0.05 cm.
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Fig. 6. Electron-neutral collision frequency as a function
of plasma density for different radius and wave frequency
1 GHz.
Fig. 8. Argon 4s excited state population as a function of
plasma density for different radius and wave frequency
1 GHz.
In Figs. 7 and 8 the behaviour of 4s excited state
population as function of plasma density is preserved. It
is observed that Argon excited states concentrations
increase with plasma density increasing. The Figs. 7 and
8 show that the influence of the wave frequency (Fig. 7)
on 4s population is insignificant while the effect of the
plasma radius (Fig. 8) is considerable. At low plasma
density the level population is higher at smaller plasma
radius while at high plasma density (above 1013 cm-3)
there is no effect of the radius. The observation made for
argon 4s excited state population is also valid for the other
electron energy levels included in the model 4p, 5s, 3d,
6s, 5p and 4d.
the wave frequency can be observed on Ar 2 + (Fig. 13) and
Ar 3 + densities.
Fig. 9. Ar 2 concentration as a function of plasma density
for different radius and wave frequency 1 GHz.
Fig. 7. Argon 4s excited state population as a function of
plasma density for different wave frequency and radius
0.05 cm.
This theoretical investigation also gives the argon ions
Ar+, Ar 2 + and Ar 3 + and argon molecule Ar 2 densities as a
function of the plasma density. The effect of the plasma
radius is significant for Ar 2 and Ar+ at low plasma
densities and it is presented in Fig. 9 and Fig. 10 while
they are not dependent on the wave frequency (Fig. 11
and Fig. 12). No influence of both the plasma radius and
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Fig. 10. Ar+ concentration as a function of plasma density
for different radius and wave frequency 1 GHz.
3
influence of the two parameters on the electron energy
distribution function, argon ions density, excited argon
atoms density and electron–neutral collision frequency
has been studied.
In the argon energy levels population the influence of
the wave frequency on the plasma characteristics is
insignificantly while the effect of the plasma radius is
considerable at low plasma densities. The opposite can be
observed for the electron neutral collision frequency:
strong influence on the wave frequency at high plasma
density and no dependence of plasma radius. The same
behaviour is observed for Ar 2 and Ar+.
Fig. 11. Ar 2 concentration as a function of plasma
density for different wave frequency and radius 0.05 cm.
5. References
[1] D. Mariotti and R.M. Sankaran. J. Phys. D: Appl.
Phys., 43, 323001 (2010)
[2] M. Vandamme, et al. Plasma Med., 1, 27 (2011)
[3] G. Fridman, et al. New J. Phys., 11, 115012 (2009)
[4] E. Benova and M. Pencheva. J. Phys.: Conf. Ser.,
207, 012023 (2010)
[5] E. Benova and T. Petrova. in: 30th ICPIG, August
28th – September 2nd 2011 (Belfast, Northern
Ireland, UK) C9-252 (2011)
Fig. 12. Ar+ concentration as a function of plasma density
for different wave frequency and radius 0.05 cm.
Fig. 13. Ar 2 + concentration as a function of plasma
density for different radius and wave frequency 1 GHz.
4. Conclusion
Argon plasma column at atmospheric pressure
sustained by travelling electromagnetic surface wave is
theoretically studied by means of a self-consistent model.
The kinetic part of the model gives the dependence of
the plasma characteristics on the plasma discharge
conditions: plasma radius and wave frequency. The
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