PSFC/JA-10-8
The Ar17+ Ly2/Ly1 Ratio in
Alcator C-Mod Tokamak Plasmas
Rice, J.E., Reinke, M.L., Ashbourn, J.M.A.1,
Ince-Cushman, A.C. 2, Podpaly, Y.A., Gu, M.F.3,
Bitter, M.4, Hill, K. 4, Rachlew, E. 5
1
Mathematical Institute, University of Oxford, Oxford, UK
2
current address: McKinsey and Co., New York, NY
3
formerly of LLNL, Livermore, CA
4
Princeton Plasma Physics Laboratory
5
KTH, Stockholm, Sweden
May 2010
Plasma Science and Fusion Center
Massachusetts Institute of Technology
Cambridge MA 02139 USA
This work was supported by the U.S. Department of Energy, Grant No. DE-FC0299ER54512. Reproduction, translation, publication, use and disposal, in whole or in part,
by or for the United States government is permitted.
The Ar17+ Lyα2 /Lyα1 Ratio in Alcator C-Mod Tokamak Plasmas
J.E. Rice† , M.L. Reinke† , J.M.A. Ashbourn‡ , A.C. Ince-Cushman†♭ , Y.A. Podpaly† ,
M.F. Gu♯ , M. Bitter♮ , K. Hill♮ and E. Rachlew∗
†
Plasma Science and Fusion Center, MIT, Cambridge, MA, USA
‡
Mathematical Institute, University of Oxford, Oxford, England
♭
current address: McKinsey and Co., New York, NY, USA
♯
♮
formerly of LLNL, Livermore, CA, USA
Princeton Plasma Physics Laboratory, Princeton, NJ, USA
∗
KTH, Stockholm, Sweden
Abstract
Spectra of hydrogen-like Ar17+ have been obtained from Alcator C-Mod tokamak
plasmas using a spatially imaging high resolution x-ray spectrometer system. The ratio
of Lyα2 (1S1/2 - 2P1/2 ) to Lyα1 (1S1/2 - 2P3/2 ) was found to be ∼ 0.52 regardless of
plasma parameters, which is somewhat greater than the ratio of the statistical weights
of the upper levels, 1/2. This difference is partially due to the effects of electron and
ion collisional excitation of fine structure sub-levels. For the observations presented
here, electron densities were in the range from 3×1019 /m3 to 4×1020 /m3 with electron
and ion temperatures between 1 and 4 keV. Experimental results are compared to calculations from COLRAD, a collisional-radiative modeling code, with good agreement
shown.
1
ion
Al
Cl
Ar
Ti
Cr
Ni
exp. ratio
0.50-0.55
0.53-0.58
0.54(?)
0.50-0.56
0.56
0.57(?)
calc. ratio
0.53-0.55
0.51
0.51
0.51
0.56
device
COMPASS-D
JET
Alcator C
JT-60U
FT
JET
Ref.
[8]
[9]
[4]
[7, 14]
[6, 14]
[5, 14]
Table 1: Measured and calculated Lyα doublet ratios for different elements and tokamak devices.
I. Introduction
Following the development of high resolution x-ray spectrometers, detailed spectra
from hydgrogen-like ions in tokamak plasmas became available [1, 2, 3, 4, 5, 6, 7],
and the Lyα doublet components (Lyα1 : 1s 1 S 12 - 2p 2 P 32 and Lyα2 : 1s 1 S 12 - 2p 2 P 12 )
were easily resolved. The earliest investigations [1, 2, 3, 4] were concerned mainly
with satellite identifications and modeling, including precise wavelength determinations. Subsequent studies [5, 6, 7, 8, 9] have addressed the ratio of Lyα2 to Lyα1 ,
which is typically found to be slightly larger than the ratio of the statistical weights
of the upper levels (1/2). Table I summarizes observations of different hydrogen-like
ions from several tokamaks, including the experimental and calculated Lyα ratios, and
spans atomic number from 13 to 28, obtained over a large range of operating conditions. For the Ni point, the experimental ratio was stated to be 0.6, but examination of
the published spectrum suggests a ratio of 0.57. In general, the calculated ratios are a
little smaller than the observations. There seems to be no systematic dependence on
atomic number, electron density or the ratio of the ionization potential to the electron
temperature, which ranges from 0.3 to 1.1. The deviation from 1/2 has been attributed
partially to electron and ion collisions in fine structure sub-levels [10, 11, 12].
In this paper, details of the observed Ar17+ x-ray spectra from Alcator C-Mod are
described in Section III after an outline of the code modeling is given in Section II,
and observed parameter scalings of the Ly α doublet ratio, along with calculations, are
presented in Section IV.
II. Code Description
The effects of electron and ion collisions in fine structure sub-levels have been incorporated into the COLRAD code [13, 14, 15]. COLRAD uses a collisional-radiative
model which includes the following processes to determine the excited level populations for hydrogen-like ions present as a small admixture in a high-temperature plasma:
i) excitation and de-excitation by electron impact, ii) ionization by electron impact, iii)
excitation and de-excitation by heavy charged particle impact, iv) spontaneous radiative
de-excitation, v) radiative recombination, vi) three-body recombination, vii) magnetic
2
dipole radiative de-excitation of the 2S 12 state, and viii) two-photon decay of the 2S 12
state. The n=2 sublevel diagram for Ar17+ is shown in Fig. 1. The contribution from
Ar17+
-8880
-8890
2P3/2
103 cm-1
-8900
-8910
-8920
-8930
2S1/2
-8940
-8950
0
2P1/2
1
2
3
4
5
Figure 1: The n=2 sublevel energy diagram for Ar 17+ . The 1S1/2 ground state energy
is -35699.78x103 cm−1 [16].
the magnetic dipole transition, 2S 12 → 1S 12 , is included in the values for the Lymanalpha intensity ratios as this cannot be resolved experimentally from the 2P 12 → 1S 12
transition. The levels with principal quantum number n = 2, 3 and 4 are resolved into
their fine-structure (n, l, j) components, whereas the levels with n ≥ 5 are treated as
unresolved. COLRAD does not calculate the contribution to the intensity ratio from
dielectronic satellite lines originating from doubly excited helium-like ions. COLRAD
allows for the input of an ion temperature distinct from the electron temperature into
the collisional-radiative model. Other effects such as polarization from non-thermal
electrons and optical thickness have been considered and ruled out for JT-60U observations [7].
III. Observed Spectra
3
The observations presented here were from the Alcator C-Mod tokamak [17], a
compact (major radius R ∼ 0.67 m, minor radius a ∼ 0.21 m), high magnetic field (B
≤ 8 T) device with molybdenum plasma-facing components. Electron densities have
been obtained in the range from 2×1019 /m3 to 1×1021 /m3 with electron temperatures
between 1 and 9 keV [18]. Discharges were seeded with argon injected through a
piezo-electric valve with non-perturbing concentrations typically 10−4 ne . X-ray spectra of H-like Ar17+ were recorded with a high throughput, high resolution imaging
Johann type spectrometer [19]. Time histories of relevant plasma parameters for a typical C-Mod discharge are shown in Fig. 2. 3.5 MW of radio frequency power (80 MHz)
3.0
ne
(1020/m3)
2.5
2.0
1.5
Zeff
1.0
0.5
0.0
0.0
0.5
1.0
1.5
(keV)
3
2.0
Te
2
1
0
Ti
0.0
0.5
1.0
1.5
int (arb)
800
2.0
Ar17+
600
400
200
Mo32+
0
0.0
0.5
1.0
t (s)
1.5
2.0
Figure 2: Time histories of the average electron density and Zeff (top frame), central
electron and ion temperatures (middle frame), and argon and molybdenum brightnesses
(bottom frame) for a 5.4 T deuterium H-mode discharge. Also shown in the bottom
frame is the argon gas pulse waveform.
were delivered between 0.6 and 1.5 s, which enabled the plasma to enter a high energy
confinement operational regime (H-mode [20]), in this case with an electron density
of 2.8×1020 /m3 and central electron and ion temperatures of 2.6 keV and 2.5 keV, respectively. For the range of electron temperatures presented here, the Ar17+ emissivity
profiles are centrally peaked. Z eff (≡ Σni Zi 2 /Σni Zi ), a global measure of the plasma
4
impurity content (and an indicator of the majority ion density relative to the electron
density), was ∼1.8. All spectra have been averaged over sawtooth oscillations, which
are apparent in the electron temperature waveform. Spectra are all integrated along a
line of sight through the plasma core. The x-ray spectrum in the range from 3725 to
3775 mÅ, for the steady state portion of a discharge with n e = 0.7x1020 /m3 and Te =
2230 eV, is shown in Fig. 3. The spectrum is dominated by the Lyα doublet [16, 3, 4]
1000
800
intensity (arb)
LyD1
Ar17+
600
LyD2
400
200
Mo32+
T
J
0
3730
3740
3750
3760
wavelength (mA)
3770
Figure 3: The x-ray spectrum of the Ar 17+ Lyα doublet and associated satellites (dots),
and a synthetic spectrum (solid curve).
(1s 1 S 12 - 2p 2 P 32 at 3731.10 mÅ and 1s 1 S 12 - 2p 2 P 12 at 3736.52 mÅ). Also apparent are several n=2 dielectronic satellite lines [21, 3, 4], the brightest of which are J
(1s2p 1 P1 - 2p2 1 D2 at 3771.79 mÅ) and T (1s2s 1 S0 - 2s2p 1 P1 at 3755.26 mÅ).
The solid curve shown is a synthetic spectrum. For the Ly α doublet, a simple population model [22] including only electron impact excitation out of the ground state
was considered, so the line intensities are in the ratio of the oscillator strengths, which
is exactly 1/2. The synthetic spectrum is normalized to Lyα1 and underestimates the
relative intensity of Lyα2 , while there is good agreement for the relative intensity of
the satellites. For the satellites, wavelengths and dielectronic recombination rates from
the Flexible Atomic Code [23] were used; for the spectator electrons, the levels n=2 to
5
n=7 have been included. Wavelengths and satellite intensity factors have been benchmarked against earlier calculations for n=2 [21] and n=3 [24] satellites, and the results
are in good qualitative agreement. An expanded view of the synthetic spectrum in the
range from 3725 to 3745 mÅ, highlighting the higher n satellites in the vicinity of the
doublet, is shown in Fig. 4. The contribution from these satellites to the Lyα doublet
intensities at this electron temperature is minimal, less than 1% for even the brightest
individual line. In the bottom frame of Fig. 4 is shown the composite spectrum for
inten. (arb)
1000.0
Ar17+
100.0
10.0
1.0
0.1
3725
3730
3735
3740
3745
satellite composite
25
inten. (arb)
20
15
3
10
4
5
5
0
3725
6
2
7
3730
3735
3740
wavelength (mA)
3745
Figure 4: A synthetic spectrum of the Lyα doublet, with individual n=2 (dotted), n=3
(purple short dash), n=4 (green dash-dot), n=5 (red dash-dot-dot-dot), n=6 (mustard
long dash) and n=7 (solid) satellites (top frame). In the bottom frame is shown the
satellite composites for each n, including the combined total.
each n level and the total composite of all satellites. The total number of individual
lines for each n level is: n=2, 15 lines; n=3, 51 lines; n=4, 56 lines; n=5, 42 lines; n=6,
30 lines; n=7, 25 lines. With increasing n, the satellite spectra converge in wavelength
and relative intensity to a feature resembling the Ly α doublet since with high enough n
the perturbation to the n=2 level becomes minimal. Regardless of electron temperature,
the total composite satellite contribution to the Lyα doublet line ratio is roughly in the
same ratio as the Lyα doublet itself, so has a negligible effect on the inferred ratio.
6
Another issue for the proper determination of the doublet ratio is the presence of a
molybdenum line at 3739.8 mÅ [25], which is evident in Fig. 3. An example of a spectrum dominated by this 2p-4d transition in neon-like Mo32+ (including its satellites)
is shown in Fig. 5. Care must be taken when the molybdenum intensity is significant
1•105
2p-4d
intensity (arb)
8•104
Mo32+
6•104
4•104
2•104
Ar17+
0
3730
3740
3750
3760
wavelength (mA)
3770
Figure 5: The spectrum in the vicinity of the Mo32+ 2p-4d transition.
compared to the argon intensity. To be on the safe side, any spectra where the Mo intensity is greater than the Ar intensity have not been included in the following scalings.
In all cases this Mo line has been included in the fits. For the spectrum of Fig. 3, the
measured Lyα doublet line ratio is 0.524±.006, which is larger than 1/2. The best three
line fit to the spectrum of Fig. 3 is shown in Fig. 6.
IV. Scalings and Modeling
The line ratio Lyα2 /Lyα1 has been determined over a large range of plasma parameters with electron density from 3×1019 /m3 to 4×1020 /m3 , electron temperature
between 800 and 4200 eV, ion temperature from 1 to 3 keV, magnetic field between 2.7
and 8.0 T, and with deuterium and helium majority ions. A database of observations
7
1000
800
intensity (arb)
LyD1
600
LyD2
400
200
Mo32+
0
3730
3735
wavelength (mA)
3740
Figure 6: The observed spectrum in Fig. 3 (dots), synthetic spectrum (solid) and the
best three line fit (dashed).
8
from the steady state portion of over 200 individual discharges has been assembled.
Shown in Fig. 7 is the Lyα doublet ratio as a function of average electron density for
three discharge types: deuterium H-mode, and deuterium and helium low confinement
mode (L-mode) plasmas (H-mode plasmas have better energy and particle confinement
than L-mode discharges and generally have higher density, with the profile shapes different mainly at the plasma periphery.). There is almost no variation in the ratio with
electron density and the values fall between 0.515 and 0.535 with an average of 0.524,
which is statistically significantly greater than 1/2. There is also no dependence on
working gas or confinement mode.
0.55
LyD2/LyD1
0.54
0.53
0.52
0.51
0.50
0
1
2
ne (1020/m3)
3
4
Figure 7: The Lyα doublet ratio as a function of average electron density represented
as follows: asterisks- deuterium H-mode, dots- deuterium L-mode, squares- helium
L-mode, triangles- COLRAD calculations.
The Lyα doublet ratio as a function of central electron temperature is shown in
Fig. 8. Similar to the scaling with electron density, there is very little variation with
temperature.
COLRAD calculations have been performed for selected discharge conditions and
are also shown in Figs. 7 and 8. These calculated values are all between 0.52 and 0.53,
which is in good agreement with the observed values.
9
0.55
LyD2/LyD1
0.54
0.53
0.52
0.51
0.50
0
1000
2000
3000
Te (eV)
4000
5000
Figure 8: The Lyα doublet ratio as a function of central electron temperature, with the
same symbol representations as in Fig. 7.
10
V. Summary
The Ar17+ Lyα doublet ratio has been determined from Alcator C-Mod tokamak
plasmas under a wide range of operating conditions. The average value of this ratio
is 0.524 with no dependence on electron density (from 0.3 to 4.0 x 1020 /m3 ) or electron temperature (from 1 to 4 keV). Good agreement has been found with collisionalradiative modeling using the COLRAD code. Nearby high n satellite lines have been
modeled using the Flexible Atomic Code, and the contribution of high n satellites to
the Lyα doublet ratio is minimal.
VI. Acknowledgements
The authors thank Jerry Hughes for providing electron density and temperature
profiles, Jim Irby for electron density measurements, Amanda Hubbard for electron
temperatures, Catherine Fiore for ion temperatures, Earl Marmar for Z eff measurements and the Alcator C-Mod operations and ICRF groups for expert running of the
tokamak. Work at MIT was supported by by DoE Contract No. DE-FC02-99ER54512.
References
[1] M. Bitter et al., Phys. Rev. A 29 (1984) 661.
[2] E. Källne et al., J. Phys. B 17 (1984) L115.
[3] E. Källne et al., Phys. Scr. 31 (1985) 551.
[4] E.S. Marmar et al., Phys. Rev. A 33 (1986) 774.
[5] F. Bombarda et al., Phys. Rev. A 37 (1988) 504.
[6] R. Bartiromo et al., Phys. Rev. A 40 (1989) 7387.
[7] H. Kubo et al., Phys. Rev. A 46 (1992) 7877.
[8] J.M.A. Ashbourn et al., Phys. Rev. E 65 (2002) 066410.
[9] J.M.A. Ashbourn et al., Phys. Rev. E 71 (2005) 017401.
[10] V.P. Shevelko et al., J. Phys. B 9 (1976) 2859.
[11] N.N. Ljepojevic, J. Phys. B 17 (1984) 3057.
[12] G.J. Tallents, J. Phys. B 17 (1984) 3677.
[13] N.N. Ljepojevic et al., Comput. Phys. Commun. 44 (1987) 157.
[14] J.M.A. Ashbourn et al., Phys. Rev. A 52 (1995) 4966.
[15] J.M.A. Ashbourn, Phys. Rev. E 59 (1999) 6198.
11
[16] G.W. Erickson, J. Phys. Chem. Ref. Data 6 (1977) 831.
[17] E.S. Marmar et al., Fusion Sci. Technol. 51 (2007) 261.
[18] N.P. Basse et al., Fusion Sci. Technol. 51 (2007) 476.
[19] A. Ince-Cushman et al., Rev. Sci. Instrum. 79 (2008) 10E302.
[20] M. Greenwald et al., Fusion Sci. Technol. 51 (2007) 266.
[21] L.A. Vainshtein and U.I. Safronova, At. Data Nucl. Data Tables 21 (1978) 49.
[22] R. Mewe, Astron. Astrophys. 20 (1972) 215.
[23] M.F. Gu, Astrophys. J. 582 (2003) 1241.
[24] L.A. Vainshtein and U.I. Safronova, At. Data Nucl. Data Tables 25 (1980) 317.
[25] J.E. Rice et al., Phys Rev A 51 (1995) 3551.
12