Download Determination of Argon metastable density from relative emission

Determination of Argon metastable density from relative emission intensity
measurements combined with optical emission cross section data
S. Adams1, J. Miles1, A. Laber1, V. Demidov2 J. Williamson3, B. Tolson3
1
Propulsion Directorate, Air Force Research Laboratory, Wright-Patterson AFB, OH, USA
2
UES Inc., Dayton, OH, USA
3
Innovative Scientific Solutions Inc., Dayton, OH, USA
Abstract: Measurements of relative intensities of violet spectral lines within an argon pulsed
discharge were applied to a model of excitation rates from the Ar ground and metastable states
using previously published electron impact optical cross sections which yield the absolute argon metastable concentrations within the discharge for a known electric field.
Keywords: argon, metastable, spectroscopy, model
1. Introduction
The plasma diagnostic technique of optical emission
spectroscopy can yield a variety of information depending
on the resolution of measurement and the extent of supporting data that exists on the fundamental optical properties of the species of interest. On the most basic level, a
simple knowledge of the spectral location of strong transition lines can yield information on the identity of plasma species and changing line intensities with time may
indicate temporal changes in the density of the species.
More advanced plasma diagnostics can be achieved when
optical emission measurements are combined with available electron-impact cross sections, which can potentially
yield many useful plasma parameters such as electron
density, electron temperature, and gas temperature as well
as absolute species concentration. In recent years, a
considerable amount of data has been compiled for electron excitation of rare-gas atoms including Argon [1]. In
particular for Ar, optical cross-sections have been measured for electron excitation from both the ground state
and metastable states [2], representing direct and stepwise
electron impact excitation respectively. Here, it is
shown that simple measurements of specific relative
spectral intensities under certain conditions allow calculations of absolute Ar metastable concentrations.
2. Theory and Model
The ground state of Ar has an electron configuration
which is a closed shell with a total angular momentum
value of J=0. The first excited state is a configuration consisting of four levels with J=1,0,1 and 2
(which are designated the 1s2, 1s3, 1s4, and 1s5 levels in
Paschen’s notation). The J=1 levels (1s2 and 1s4) are
short lived due to the dipole allowed transition to the
ground state, but the J=0 and J=2 levels (1s3 and 1s5)
are considered triplet spin state with dipole forbidden
transitions to the singlet ground state and are thus considered metastable states, with long radiative lifetimes.
Comprehensive data has been previously compiled of
electron excitation cross sections from the ground state
and from the 1s3 and 1s5 metastable states of Ar into a
limited number of excited states including the 2p and the
3p configurations [2,3]. This study focuses on modeling
excitation into the ten levels of the 3p configuration from
both the ground and metastable states and interpreting the
resulting optical emission in the violet spectral region.
Of particular utility to this analysis is the fact that the
electron excitation pattern from the singlet ground state
and the triplet metastable states is quite different between
the various 10 levels of the 3p state (3p1..3p10). The result of this pattern is that the emission spectrum of 3p-1s
transitions will display a unique intensity distribution depending on whether the 3p state is generated by direct
electron excitation from the ground state, or stepwise excitation from one of the 1s metastable states [4]. An
energy level diagram for Ar is shown in Fig. 1 which illustrates how this dual excitation phenomenon affects, for
example, two particular emission lines in the violet, at
419.8 nm and 420 nm from the 3p5 and 3p9 levels respec-
Fig. 1 Direct and stepwise excitation and emission in Ar
tively. Fig. 1 displays the direct electron excitation from
the ground state to the 3p manifold, which results in the
population of both the 3p5 and 3p9 levels and emission at
both 419.8 nm and 420 nm. The relative intensity of
these emission lines due to direct electron excitation can
be determined for a known electron energy distribution
function, but in many cases the 420 nm/419.8 nm ratio is
approximately equal.
Also illustrated in Fig.1 is stepwise excitation which
occurs readily from the 1s5 metastable state to the 3p9
state, and in all cases results in a much stronger 420 nm
emission compared to 419.8 nm. Thus, the relative
amount of direct excitation and stepwise excitation occurring within an Ar discharge will strongly affect the 420
nm/419.8 nm emission ratio, along with the rest of the
violet spectral line intensity distribution [5].
The available optical cross section data allow the entire violet emission spectrum to be predicted quite accurately for a known electron energy distribution function.
In many Ar plasma situations it is found that the spectrum
in the violet region contains significant contributions from
both direct and stepwise excitation. This study has
shown that a model combining the 3p excitation cross
sections from both the ground state and metastable states
can also accurately predict spectral distributions with
contributions from both direct and stepwise excitation.
3. Experiment
For this study, a direct current (dc) pulsed discharge
was used to generate the Ar plasma. The motivation for
using the pulsed discharge was to create an environment
with variable Ar metastable density, where the optical
emission spectra could be easily and accurately analyzed
as a function of metastable density. The Ar metastable
density within the flowing pulsed discharge is assumed to
be very low in the first few μs of the pulse, but then is
assumed to build over time during the discharge. By
collecting the optical emission spectra within small gated
time periods, the resulting spectra reflected the metastable
density during each respective period. For an Ar pulsed
dc discharge, emission spectra from very early in the
pulse would be expected to show less evidence of stepwise electron impact excitation compared to later times.
The pulsed discharge tube was made of quartz, 5 cm in
diameter and 1 meter in length with hollow aluminum
electrodes and generated a flowing Ar discharge at 5
mTorr. The duration of the pulsed excitation field was
100 μs at a frequency of 10 Hz. The 5 mTorr discharge
pressure matched the target Ar pressure for the published
optical cross section data, so these optical cross sections
could be applied without pressure correction to model our
discharge spectral intensity distributions. The relatively
long 1 meter tube length was used for the 5 mTorr discharge to match the pressure-distance (pd) product corresponding to the minimum breakdown voltage in the Ar
Paschen curve.
For the optical detection in this experiment, light was
collected and focused into a fiber-optic coupled 0.5 m
Acton 500i spectrometer. The spectrometer output was
imaged by an Andor intensified CCD (ICCD) camera,
which provided spectral analyses in the range of 410 nm
to 430 nm with a gated temporal width of 0.1 μs. The
E/N of the discharge in the emission region, where E is
the electric field and N is the concentration of neutral
particles, was calculated by measuring the potential difference between two electric probes spanning the optical
detection region.
4. Results and Discussion
The optical emission in the 410 nm to 430 nm range
from the Ar dc discharge included several Ar (3p→1s)
transitions along with several emissions lines from Ar+
excited states. To model the relative intensities of these
emission lines, rates were calculated for direct and stepwise electron impact excitation as well as electron impact
ionization to Ar+*, all leading to 410-430 nm emission.
The expression relating the optical emission intensities to
the excitation rates is
.
where Iij(λ) is the emission intensity of the Ar(3pi→1sj)
transition, ng and nm are the ground and metastable state
densities, kijd and kijs are the direct and stepwise excitation
rates in cm3/s leading to Ar(3pi→1sj) emission at wavelength λij. The direct and stepwise electron impact excitation rates, kijd and kijs , can be found by
inf
k ij = ∫ σ ij (ε )
0
2ε
f (ε )dε
m
where σij is the optical cross section, m is the electron
mass, ε is the electron energy, and f(ε) is the normalized
Maxwell-Boltzmann electron energy distribution function
(EEDF) . For this study, published data sets were applied in the model for σijd(ε) and σijs(ε) representing the
optical cross sections for direct and stepwise electron impact excitation from ground state and metastable Ar respectively and resulting in Ar (3pi→1sj) emission [1].
The function f(ε) was calculated for Ar using the numerical Boltzmann solver, BOLSIG, for a given E/N. To
include the Ar ion emission lines in the model, the ionization rate kyzion was calculated in the same fashion as the
neutral excitation rates above, but with the electron impact ionization leading to each Ar+(y→z) emission line at
wavelength λyz in the 410 nm to 430 nm range. Published data sets for the optical cross sections σyzion(ε) were
used in the model [1].
The model was applied to fit experimental optical
emission spectral data taken at various times within the Ar
pulsed dc discharge. With the E/N measured experimentally, the only adjustable parameter in the fit was the
ratio of densities of Ar 1s metastables to ground state
neutral Ar atoms (nm/ng). Fig. 2 shows the experimental
optical emission spectrum (solid line) taken early in the
discharge, 1 μs into the pulse, where the electric field is
relatively high during gas breakdown. As seen in this
case, the model provided a reasonable fit to the experimental optical emission data with a measured E/N of
1500 Td and the nm/ng ratio set to 0.0%. Since we assumed the metastable density to be negligible this early in
the discharge, the good fit with nm/ng = 0.0 is a positive
confirmation of our modeling accuracy. Note the two
closely spaced lines near 420 nm, in which the ratio of the
420 nm to the 419.8 nm line is less than 1 with a value of
approximately 0.7.
Fig. 2 Spectrum and fit at 1 μs into the Ar pulse discharge.
Fig. 3 shows the experimental data and modeled fit for
the emission later in the discharge, 50 μs into the pulse,
when the metastable concentration was expected to be
more significant. At 50 μs into the pulse, the electric
field had decreased and stabilized compared to early in
the pulse and E/N was measured to be 650 Td. The best
fit of the spectrum occurred with a metastable ratio of
nm/ng = 1.0%, which corresponded to a metastable density
of 1.6x1012 cm-3. Note that the ratio of the 420 nm to the
419.8 nm line is now greater than 1, with a value of approximately 1.7. Additional spectra taken from 50 μs to
100 μs into the pulse seemed relatively consistent which
indicated that the metastable concentration had reached
equilibrium by 50 μs into the discharge.
Fig. 3 Spectrum and fit at 50 μs into the Ar pulse discharge
At 100 μs into the discharge, the applied pulse was
ending and the electric field was decaying rapidly so that
the E/N was difficult to measure. We assumed, though,
that nm/ng had not changed significantly from the equilibrium concentration, and we used the model to fit the
spectral data at the end of the pulse by allowing the E/N
to vary. Fig. 4 shows the experimental data and modeled
fit for the emission 100 μs into the pulse, when the metastable ratio was assumed to still be nm/ng = 0.010. An
E/N value of 220 Td provided the best fit to the experimental data. In this case, the ratio of the 420 nm line
intensity to the 419.8 nm line was approximately 3, which
was much greater than in the other cases.
Fig. 4 Spectrum and fit during pulsed discharge decay.
The model was further used to calculate the 420 nm to
419.8 nm intensity ratio for a larger range of E/N and
nm/ng values using the cross section data for 5 mTorr.
The plot in Fig. 5 shows the results of this calculation.
With this plot, given a measured E/N and a measured 420
nm to 419.8 nm intensity ratio, the ratio of the metastable
to ground state density of Ar, and thus the absolute metastable concentration, could be easily predicted. The
accuracy of a prediction in this plot depends in which
region of the chart the parameters coincided, as some regions are more sensitive to the variation of parameters.
Fig. 5 Plot of emission intensity ratio vs nm/ng for varying E/N.
5. Summary
Information on absolute Ar metastable concentrations
has been derived from measurements of relative intensities in the violet emission spectrum. The different patterns
of excitation rates from the Ar ground and metastable
states allow the emission rates due to the excitation from
the various levels to be combined and generate a predicted spectrum. This diagnostic technique was applied
to a pulsed dc Ar discharge where the E/N was measured
or assumed and the resulting fit of the relative emission
intensities provided a calculation of the absolute number
density of Ar metastables. The generalized model was
presented as a plot where the 420 nm to 419.8 nm line
intensity ratio was predicted for a given E/N and metastable concentration using published electron impact cross
sections for 5 mTorr of Ar.
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