Download line ratio electron temperature diagnostic in helicon plasma

LINE RATIO ELECTRON TEMPERATURE
DIAGNOSTIC IN HELICON PLASMA
R.F. Boivin, J. L. Kline, E. E. Scime
Department of Physics
West Virginia University
Poster presented at the 43 APS-DPP,
Long Beach, California,
October 2001
ABSTRACT
Electron temperature measurements in helicon plasmas are difficult. The
presence of intense RF fields in the plasma complicates the interpretation of
Langmuir probe measurements. Furthermore, the non-negligible ion temperature in
the plasma shortens considerably the lifetime of conventional Langmuir probes. A
spectroscopic technique based on the relative intensities of neutral helium lines is
used to measure the electron temperature in the HELIX (Hot hELicon eXperiment)
plasma. The link between measured line intensity ratio and plasma electron
temperature is complex and, a number of issues must be examined for the
diagnostic. We show that a line ratio diagnostic can be used to determine the
electron temperature in a helicon plasma source. For plasma densities lower than 8
x 1010 cm-3, the simple Steady State Corona model can be used with reasonable
accuracy. Addition of metastable contributions to the SSC model improves the
agreement between theory and experiment. This result is incompatible with the
presence of a large fraction of hot electron in the helicon source electron
distribution, even at low plasma density. For higher plasma densities a more
complex Collisional Radiative model is needed. The data indicates that excitation
transfer processes (and not metastables excitation contributions) are in fact the
LINE
dominant
secondary processes that invalidate the SSC model at densities above 1011
cm-3.
Plasma Physics Laboratory
PLASMA PARAMETERS
PARAMETER
HELIX (Helicon Source)
LEIA(Space Chamber)
_________________________________________________________________________________________
Driving Frequency
4 to 14 MHz
-----------
Chamber diameter
0.15 m
1.8 m
Chamber length
1.6 m
4.4 m
Plasma lifetime
Steady state
Steady state
Operating pressure
10-4 to 10-1 Torr
PLEIA ≈ .1 PHELIX
ne
1016 - 1019 m-3
1016 - 1019 m-3
Te
≈ 5 to 20 eV
≈ 5 to 20 eV
Ti
≈ 0.1 to 1 eV
≈ 0.1 to 1 eV
B
200 - 1300 G
5 - 100 G
ρe (e gyro r)
(.6 - 4.0) 10-4 m
(.075 - 1.5)10-2 m
Plasma Physics Laboratory
LINE INTENSITY FROM THE PLASMA
The plasma emits radiation that is collected by the spectrometer through the fiber optics interface.
The plasma emissivity εji (watt/volume • solid angle) at a specific wavelength λji corresponding to an
atomic transition from level j to level i, can be written as:
εji = (4π)-1 hνji Nj Aji
where hνji is the photon energy associated to the transition, Nj is the population of the emitting level
(cm-3), Aji is the Einstein coefficient for the transition. Assuming a uniform plasma, the photon count
rate Ip (λji) measured by the CCD camera at wavelength λji is given by:
Ip (λji) = (4π)-1 Nj Aji V Ω T (λji) η (λji)
where V is the plasma volume seen by the monochromator, Ω is the solid angle subtended by the
collection optics, T(λji) is the transmission factor of the detection system and, η(λji) is the CCD
camera quantum efficiency at wavelength λji. Thus, the ratio of the photonic count rate for two lines
(wavelength λji and λkl) is:
I p (λji ) Nj Aji T (λji ) η (λji) 1 Nj Aji
=
=
I p (λkl) Nk Akl T (λkl) η (λkl) FR Nk Akl
where the T(λ) η(λ) products are associated with the response of the detection system at a given
wavelength. Using an absolutely calibrated radiation source, a calibration of the detection system at
the two wavelengths is performed, yielding the relative calibration factor FR.
Plasma Physics Laboratory
STEADY STATE CORONA MODEL
The Steady Sate Corona (SSC) model can be used to predict the population of excited levels provided the
plasma condition satisfies the applicability criteria for the model. For this model the following conditions
must be valid: the electron velocity distribution can be described by a maxwellian; the ion and neutral
temperatures are less than or equal to the electron temperature; the plasma is optically thin to its own
radiation. We will assume that hot electrons represent at best a negligible fraction of the entire
distribution and that the distribution is essentially maxwellian. It is consistent with this model that only a
small fraction of the neutral or ion populations are in one of their possible excited states with respect to
the ground state. A balance between the rate of collisional excitation from the ground state and the rate of
spontaneous radiative decay determines the population densities of the excited levels. The population of
the level j (Nj ) is given under the SSC model by the expression:
ne No <σ v>oj = Nj Σi<j Aji
Where No is the population of the ground level population, ne is the electron density, Σi<j Aji is the total
transition probability from level j to all lower states, and <σ v>oj is the excitation rate coefficient for the
electron impact excitation of the level j from ground state. The excitation rates used in this paper are
taken from the Kato and Janev compilation. The line ratio expressed in terms of excitation rate
coefficients becomes:
RI (Te ) =
I p (λ ji )
I p (λkl )
=
1 < σv >oj Bji 1 Eji (Te )
=
FR < σv >ok Bkl FR Ekl (Te )
where Bji = Aji (Σi<j Aji )-1 is the “branching ratio” and, Eji(Te) is the emission rate coefficient (Eji(Te) = Bji <
σ v >oj ). In this model, the line intensity ratio function RI(Te) depends solely on the electron temperature in
the plasma. The SSC model is believed to be able to predict the electron temperature with reasonable
accuracy for electron densities up to 1011 cm-3.
Plasma Physics Laboratory
METASTABLE CONTRIBUTIONS
The SSC model assumed that line emission is the result of single collisions between electrons and
atoms in the ground state followed by direct radiative de-excitation. At higher densities, this assumption is
no longer valid since the occurrence of secondary processes involving collisions with excited or ionized
atoms becomes important. The secondary processes include: volume recombination; collisions between
excited atoms and ground state atoms; cascading redistribution effects; excitation transfer collisions;
excitation from metastables. We limit this discussion to low temperature, low to moderate density He
plasmas (Te ≤ 20 eV, ne ≤ 1 x 1013 cm-3) where several of these secondary processes can be neglected.
Actually, only the latter two processes are important for these plasma conditions. The excitation transfer
collisions effect will be important if the upper line level has neighboring level(s) with about the same energy.
Excitation transfer cross-sections are also larger when transitions between levels are optically allowed.
Finally, excitation contributions from the metastable levels can be important if the metastables are close to
the ground state (large metastable population) or if metastables are energetically close to the emitting excited
levels.
Fortunately, contributions from the metastable levels can be accurately evaluated using a Collisional
Radiative (CR) model to evaluate the population of these levels. These contributions can be integrated in the
line ratio expression by replacing the emission rate coefficients by an apparent or resulting emission rate
coefficient Eji*(Te, ne) and Ekl*(Te, ne) that include both direct (ground) and indirect (metastables) excitation:
*
1 Eji (Te , ne )
RI (Te , ne ) =
FR Ekl* (Te , ne )
This line intensity ratio function is essentially the SSC model corrected for metastable contributions. The
line ratio becomes a function of both electron temperature and plasma density. Excitation transfer
contributions cannot easily be incorporated into the SSC model.
Plasma Physics Laboratory
COLLISIONAL RADIATIVE MODEL
A Collisional Radiative (CR) model can also be used to predict the electron temperature. The CR
model doesn’t assume that bound excited populations originate exclusively from the ground state via
electron impact excitation. Secondary processes like excitation transfer, recombination and, ionization
involving all excited states are included in the computation. In order to use this model, the plasma must
satisfied the following conditions: the electron velocity distribution can be described by a Maxwellian; the
ionization process is by electron collision from any bound level and is partially balanced by three-body
recombination into any level; excitation transfer between any pair of bound level are induced by electron
collisions; radiation is emitted when a bound electron makes a spontaneous transition to a lower level or
when a free electron makes a collisionless transition into a bound level; the plasma is optically thin to its
own resonance radiation. With these assumptions, a set of equations describing the population of bound
levels Ni can be written as:
dNi /dt = ne Σj≠i Sji Nj + Σj>i Aji Nj - ne Σj≠i Sij Ni - Σj<i Aij Ni - ne Ii Ni = 0
The Sij (excitation/de-excitation rate coefficients) and Ii (ionization rate coefficients) are all functions of
Te and ne. The first term corresponds to the excitation or de-excitation of the electron population of all
levels j that end up at level i. The second term corresponds to the spontaneous de-excitation from higher
j levels to level i. The third term is associated with the excitation or de-excitation of level i. The fourth
term is the spontaneous de-excitation originating from level i. The last term is associated with the
ionization rate of the electron population of level i. A system of N (level number) coupled differential
equations must be solved simultaneously to obtain the population of a given level. For the He atom, the
second and fourth terms on the right side of this equation can be evaluated accurately since the Aij
coefficients are well known. However, the picture is quite different for the remaining terms. The
excitation cross-sections of short-lived excited state are poorly known. Theoretical calculations are often
used to fill the missing rate coefficients. Cross-sections obtained by different models can differ by one or
more orders of magnitude at low electron energy.
Plasma Physics Laboratory
HELIUM TRANSITIONS FOR DIAGNOSTICS
The line ratio of the selected transitions must depend as much as possible on Te and as little as possible
on ne. The radiation must also escape from the plasma without being re-absorbed (the plasma must be
optically thin). These transitions must be in the detection and sensitivity range of the spectrometer.
Transitions originating from a level with principal quantum number n > 5 will not be considered since
the electron population of these higher levels becomes smaller with increasing n, resulting in weak
transitions.
Transitions ending at either the ground state 11S or the metastable levels 21S and 23S will not be
considered since the plasma is not optically thin with respect to these transitions (resulting intensities are
strongly affected by re-absorption).
There are two reasons to avoid D → P transitions. First, excitation transfer cross-sections for allowed
transitions are much larger than for non-allowed transitions. Second, the excitation transfer is inversely
proportional to the energy difference between levels and strongly dependent on plasma density. For
example, the energy difference between the 31P and 31D levels is only .013 eV while the corresponding
quantity between the 33P and 33D levels .066 eV. Thus, these transitions will be more sensitive to
plasma density than electron temperature.
Line ratios using S → P transitions are better suited to measure electron temperature. The contributions
from the metastable 21S and 23S states due to excitation transfer are small since these S-S transitions are
forbidden and the resulting cross-section are small. Also, for a given n level, the energy of the S levels is
significantly different than the energy of the other P, D or F levels. Thus, excitation transfer crosssections between S and any of these P, D or F levels are also small compared to cross-sections involving
only P, D, and F levels.
Plasma Physics Laboratory
E (eV)
He GROTRIAN DIAGRAM
1S
25
24
1P
1D
(Singlet)
5
4
3S
5
4
438.8
443.8
492.2
504.8
23
1F
3
501.6
667.8
728.1
3P
3D
3F
(Triplet)
Ionization 24.580 eV
402.6
412.0
447.2
471.3
3
587.6
706.5
22
2
2058.1
21
2
388.9
M
2
1082.9
M: Metastable States
20
58.4
0
1
Ground State
WVU Plasma Physics Laboratory
2
M
Helium Energy Levels
_________________________________________
Level
Energy (eV) Level Energy (eV)
_________________________________________
21S
20.610
23S
19.814
1
2P
21.212
23P
20.958
31S
22.914
33S
22.712
31P
23.081
33P
23.001
31D
23.068
33D
23.067
41S
23.667
43S
23.588
41P
23.736
43P
23.730
41D
23.730
43D
23.730
41F
23.731
43F
23.731
51S
24.005
53S
23.965
51P
24.039
53P
24.022
51D
24.036
53D
24.036
51F
24.037
53F
24.037
_________________________________________
POSSIBLE TRANSITIONS FOR DIAGNOSTIC
________________________________________________________________
Transition
λ (nm)
Aji (x 108 s-1)
Bji
________________________________________________________________
51Sè21P
443.8
0.0330
0.482
41Sè21P
504.8
0.0675
0.596
31Sè21P
728.1
0.1829
1.000
53Sè23P
412.0
0.0444
0.475
43Sè23P
471.3
0.0955
0.596
33Sè23P
706.5
0.2790
1.000
________________________________________________________________
The 31S → 21P (728.1 nm) / 33→ 23P (706.5 nm) ratio. Both transitions are within the same spectral
region. These transitions are very intense since both originate from the n = 3 level. They have exactly
the same branching ratio. A CR model has been used previously to predict electron temperature from
this line ratio as a function of plasma density. Drawback(s): close proximity of the metastable levels.
The excitation contributions from the metastable levels will be the largest among the possible transition
pairs. This proximity will results in significant plasma re-absorption of the emission lines (next page).
The 41S → 21P (504.8 nm) / 43S → 23P (471.3 nm) ratio. These transitions are in the same spectral
region and have similar branching ratios. Their intensities are weaker than the preceding pair but still
easily detectable. Being energetically further apart from the metastables than the n = 3 transitions, they
are less affected by excitation transfer from these levels. Two different CR models have been used to
determine electron temperature from this line ratio as a function of plasma density.
The 51S → 21P (443.8 nm) / 53S → 23P (412.0 nm) ratio. These transitions are in the same spectral
region and have similar branching ratios. Originating from the n = 5 level they are minimally affected
by the metastable levels. Drawback(s): These transitions are weak when compared to the other pairs.
The small difference in energy between all the n = 5 levels is also conducive to large excitation transfer
rates between levels. No CR model has been used to predict temperature from this line ratio.
Plasma Physics Laboratory
OPTICAL ESCAPE FACTOR AND MEAN OPTICAL DEPTH
Line intensities associated with transitions are the result of spontaneous emission, stimulated emission
and absorption. A line is optically thin if both stimulated emission and absorption are negligible compare to
spontaneous emission. The 2 important parameters to quantify the opacity of the plasma are the Optical
Escape Factor (OEF) and the Mean Optical Depth (MOD). The OEF corresponds to the fraction of light
that can escape the plasma while the MOD is the exponential absorption coefficient associated with a given
transition. For a thin plasma OEF ≈ 1 while MOD ≤ 0.01. Assuming that for He transitions the dominant
broadening mechanism is Doppler broadening, the MOD τo and the OEF Λ(τo) are given by [Holstein]:
n1 g2 A21 λo r
3
τo = τ (νo ) =
8 g1 π 3/ 2 vth

2
3
n 
τo
τo
(−1) n+1τ o 
 τo
Λ(τ o ) = 1 −  −
+
⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅
2
3
2
!
4
3
!
n + 1 n! 



n1 is the lower level, g1 , g2 are the statistical weight of the lower and upper levels, A21 and λo are the
transition probability and central wavelength value, vth is the He thermal velocity and r is the plasma radius.
λ
τo
Λ
τo
Λ
τo
Λ
τo
Λ
(nm)
(ne = 1011 cm-3)
(ne = 1012 cm-3)
(ne = 1013 cm-3)
(ne = 1014 cm-3)
______________________________________________________________________________________________________________
412.0
1.85 e-3
0.9987
1.45 e-2
0.9898
3.00 e-2
0.9790
2.25 e-2
0.9841
443.8
1.79 e-6
1.0000
1.72 e-5
1.0000
1.72 e-4
0.9999
1.50 e-3
0.9989
471.3
2.00 e-3
0.9986
1.55 e-2
0.9890
3.20 e-2
0.9777
2.45 e-2
0.9825
504.8
1.90 e-6
1.0000
1.80 e-5
1.0000
1.80 e-4
0.9999
1.60 e-3
0.9989
706.5
6.65 e-2
0.9542
4.61 e-1
0.7285
8.45 e-1
0.5666
7.15 e-1
0.6158
728.1
4.55 e-5
1.0000
4.40 e-4
0.9997
4.40 e-3
0.9969
3.85 e-2
0.9733
For all singlet transitions, the OEF is essentially unity and the plasma is optically thin. Transitions from the
upper levels 53S and 43S (412.0 and 471.3 nm) can be considered as optically thin for plasmas with ne up to
1014 cm-3 (less than 2% of re-absorption in each case). The transition from the 33S level (706.5 nm) is
largely re-absorbed by the plasma (≈ 5% at 1011 cm-3, ≈ 43% at 1013 cm-3 and, ≈ 40% at 1014 cm-3). The
706.5 nm line intensity must be corrected for re-absorption. Since re-absorption is a function of the neutral
density profile and of the dominant broadening mechanism, the correction is non-trivial. If possible, the
line ratio diagnostic should not use this transition. It is important to observe that it is the combination of
large excited population (23P level) and high plasma density that is responsible for re-absorption.
Plasma Physics Laboratory
HELIX PLASMA SOURCE (UPPER VIEW)
11
Y
9
8
7
X
5
12
2
4
10
3
11
µ
1
6
1.8 m
1. Digital camera (near axial viewport)
2. Pumping station
3. Gas inlet
4. Plasma column
5. Fractional helix antenna
6. Magnetic field coils
7. Glass chamber section (right), SS chamber section (left)
8. Spectroscopy optics
9. Retractable RF compensated Langmuir probe
10. Microwave interferometer
11. 2-D LIF Injection and collection optics
12. Large space chamber
SPECTROMETER
Monochromator. 1.33 meter Czerny-Turner type scanning monochromator (range 185 to 1300 nm,
Holographic grating 1200 grooves/mm, F-number 11.6, dispersion 0.62 nm/mm, and with a maximum
resolution of 0.015 nm)
CCD Camera. Charged Coupled Device (CCD) imaging camera (wavelength range 200 to 1100 nm,
acquisition time from 10-2 s to several minutes, binning capability, 5.35 nm bandwidth, and a quantum
efficiency between 0.2 and 0.55 over the sensitivity range). The CCD camera is operated under a
dynamic background subtraction mode which eliminates background noise from the signal.
Light Collection unit. The light collection system used a 25 mm collimator lens mated to a 50 µ grade
silica fiber optics cable with matching numerical aperture. The light collection unit is located 0.35 m
downstream from the end of the antenna. The detection area defined by a light collection system at the
center of the plasma chamber is 0.07 cm2. A micro-positioning system can be used to move the
detection optics to obtain a radial scan of the plasma column.
Calibration. An absolutely calibrated light source is used to calibrate the response of the spectrometer
at different wavelengths (relative calibration).
Uncertainty. For any HELIX plasma conditions, photon count fluctuations represent 1% of the total
integrated intensity except at low plasma densities (ne < 3 x 1010 cm-3) where they can reach up to 5%.
The resulting uncertainty (including counting fluctuations, re-absorption effects and calibration
contributions) on the line ratio measurements are about ± 8 % at low plasma densities, and less than or
equal to ± 3.4 % for the rest of the density range covered in this poster.
Plasma Physics Laboratory
RF COMPENSATED LANGMUIR PROBE
Two modifications have been made to a standard Langmuir probe (L. P.). The first is the addition of a
floating electrode. The electrode is exposed to the plasma potential fluctuations and is connected to the L. P.
tip via a large capacitor. This helps to lower the sheath impedance and forces L. P. tip to follow the plasma
potential oscillations; thereby reducing the distortion in the trace. The second modification is a chain of RF
chokes. These are placed after the probe tip, but before the current is measured. The chokes increase the
impedance of the circuit at the RF frequency. The L. P. is connected to a high impedance source meter that
sweeps the voltage and records the collection current. After a number of sweeps, the data is averaged and
recorded by a computer.
A (typical) series of L. P. measurements performed under the same plasma condition (400 watts, 6.6 x 10-3
Torr, 1 kGauss, 9 MHz) is shown below. These measurements were taken within a span of 20 minutes which
is much longer than the time needed to make a line ratio measurement (≈ 2 minutes). The probe measures an
average electron temperature of 9.28 eV. Overall, electron temperature fluctuations are in the order of ≈ 2 %.
The absolute uncertainty on the electron temperature is estimated to be ≈ ± 15 %. The probe measures a peak
density of 3.2 x 1011 cm-3. The electron density fluctuations are within ± 5 %. A microwave interferometer is
used to calibrate the L. P. (see Earl Scime Poster). The absolute uncertainty is within ± 15 %.
0.006
0.005
Te = 9.224 eV
0.004
0.006
Te = 9.278eV
0.005
11
0.005
11
-3
ne = 3.30 x 10 cm
11
-3
ne = 3.31 x 10 cm
0.004
0.005
Te = 9.356 eV
Te = 9.289 eV
0.004
-3
11
ne = 3.08 x 10 cm
0.004
-3
ne = 3.17 x 10 cm
0.003
0.003
0.003
0.003
0.002
0.002
0.001
0.001
0
0
-0.001
-0.001
0.002
0.002
0.001
0.001
0
0
-0.001
-0.002
-0.002
-50
-40
-30
-20
-10
0
Biasing Voltage
(Volts)
10
20
30
-0.001
-0.002
-50
-40
-30
-20
-10
0
Biasing Voltage
(Volts)
10
20
30
-0.002
-50
-40
-30
-20
-10
0
Biasing Voltage
(Volts)
10
20
30
-50
-40
-30
-20
-10
0
Biasing Voltage
(Volts)
10
20
30
Probe Scan (Half Profile)
11
-3
)
3.5 10
Plasma Density (cm
3.0 10
2.5 10
18
11
Plasma Conditions:
1 kGauss
6.6 mTorr
400 Watts
16
11
14
11
12
2.0 10
11
10
1.5 10
11
8
1.0 10
5.0 10
11
6
10
Plasma Column Center
4
0.0
-40
-30
-20
-10
0
Position in Plasma Column (mm)
Plasma Physics Laboratory
10
Electron Temperature (eV)
4.0 10
> 90% of the line emission originates
from the inner plasma core
1.2
Exp Points
SSC Model
Error bars
1
0.8
All Points
0.6
Line Ratio ( Ι
/Ι
)
504.8 471.3
0.4
0.2
0
1.2
n < 8 x 10
1
10
e
cm
-3
0.8
0.6
0.4
0.2
0
1.2
n > 8 x 10
1
e
10
cm
-3
0.8
0.6
0.4
0.2
0
0
5
10
15
20
Electron Temperature (eV)
Plasma Physics Laboratory
25
30
Integrated line intensities at T = 10 eV
e
10
6
Line Intensity (Counts)
Same slope
Different slopes
Red: Triplet line emission (471.3 nm)
10
10
5
Blue: Singlet line emission (504.8 nm)
4
Highly correlated line intensities
==> Important ground state contributions
Triplet line intensity scales as n (c o re)
e
1000
10
10
10
11
10
-3
P lasma Core Density (cm )
Plasma Physics Laboratory
12
10 eV Line Ratio ( Ι
504.8
/Ι
471.3
)
0.8
Steady State Corona Model
0.7
Steady State Corona Model +
Metastables Contributions
0.6
Experimental values
0.5
Brosda Collisional Radiative Model
0.4
0.3
Sasaki et al. Collisional Radiative Model
0.2
0.1
0
10
10
10
11
10
12
10
-3
Plasma Density (cm )
Plasma Physics Laboratory
13
Scalable Line Ratio Function
0.8
10 eV Line Ratio Function Fit (from exp. data)
0.6
Line Ratio ( Ι
504.8
/Ι
471.3
)
0.7
12 eV Line Ratio Values (Plasma T = 12 eV)
e
0.5
0.4
0.3
7 eV Line Ratio Values (Plasma T = 7eV)
e
0.2
10
10
10
11
10
12
10
-3
Plasma Density (cm )
Plasma Physics Laboratory
13
CONCLUSION
We have shown that a line ratio diagnostic can be used to determine the electron
temperature in a helicon plasma source. A careful selection of the transitions is crucial to
ensure the validity of the diagnostic. For plasma densities lower than 8 x 1010 cm-3, the
simple Steady State Corona model can be used with reasonable accuracy. Addition of
metastable contributions to the SSC model improves the agreement between theory and
experiment. This agreement is incompatible with the presence of a large fraction of
hot electrons in the helicon source electron distribution, even at low plasma density. For
higher plasma densities a more complex Collisional Radiative model is needed. To our
knowledge, this is the first time that a precise density demarcation value has been
identified for the selection of the different models. The agreement between models and
experimental ratios is reasonably good. We show that excitation transfer processes (and
not metastables excitation contributions) are in fact the dominant secondary processes
that invalidate the SSC model at densities above 1011 cm-3. Finally, a scalable line ratio
function can be used to predict electron temperature for plasma with density ranging from
107 to 1012 cm-3. This range could be extended further (up to 1013 cm-3) by increasing the
rf power beyond the maximum value used in these experiments (1 Kwatt).
Part of this poster is included in a publication from Physic of Plasma (Dec 2001):
Electron Temperature Measurement by a Helium Line Intensity Ratio Method in Helicon
Plasmas.
Plasma Physics Laboratory