Improved absolute calibration of core Thomson scattering(ts) diagnostics on Alctor C-Mod Yunxing Ma, J.W.Hughes, A.Hubbard MIT Plasma Science and Fusion Center Presented at 2008 APS DPP Conference Dallas, Nov 19
Abstract The Thomson scattering (TS) diagnostics on Alcator C-Mod have been upgraded to provide measurements with improved radial spatial resolution of 1cm in the range of r/a<0.6. To accurately obtain electron densities (ne), we absolutely calibrate TS using two independent methods. First, we backfill the vessel with deuterium or hydrogen gas at room temperature and measure the anti-stokes Raman scattering from the TS Nd:YAG lasers. Second, we take advantage of the fact that measurements of second-order harmonic electron cyclotron emission (ECE) from plasma are cutoff at certain electron densities and radial locations in a known magnetic geometry. These cutoffs allow us to cross-calibrate simultaneous TS ne measurements with ECE diagnostics, in specially designed low-field, high-density discharges. Results from both techniques are analyzed and used to produce reasonable ne profiles for plasma discharges. The reliability of each technique is assessed, and discrepancies between the two techniques are discussed. The ultimate goal is to refine the gas calibration technique such that dedicated discharges are not necessary for TS calibration.
Motivation Absolute calibration is essential to give meaningful ne measurements Benefit the transport studies which require accurate measurements of electron density gradient (core peaking, ITB, etc.) Contribution to particle transport studies on Alcator C-Mod (with improved 1cm (0.06a) radial resolution)
TS on Alcator C-Mod [1,2] 2 Nd YAG laser 30Hz,1.3J,8nm pulse Collection fibers (Configuration as of 2003) Scattering volume Cooke triplet F/7, f=30.8cm To polychromators C-mod Vessel
Upgraded 16-channel C-Mod core TS Layout of Optical fibers Scattering geometry in C-Mod Tokamak Radial mapping of TS measured ne profile in an ITB plasma discharge 1070628019 1.3s ITB
Method One Cross calibration with ECE cutoff ECE (electron-cyclotron emission) diagnostics measure frequencies at 2 nd harmonics, has right hand cutoff at [2] 2 2 2ω ce ω pe Choose the magnetic field to place ECE radial cutoff locations close to TS locations Raise electron density to achieve cutoff conditions Derive a correction of absolute calibration factor to scale up or down each TS measured ne to match the ECE cutoff value on the corresponding location This technique has been successfully applied on Alcator C-mod [2]. Line integrated TS profile is well within 10% of measurements from interferometer chords.
Typical ECE cutoff signal traces -4 B_tor 1080311022-4.5-5 -5.5 0 0.5 1 1.5 2 0.3 Raw ECE Channel 1 3.09928E+20 0.2 0.1 0 0 0.9 0.5 1 ECE Ch. 1 Radius (m) 1080311022 1.5 2 0.8 cutoffs 0.7 0 0.5 1 0.12 Raw ECE Channel 7 1.90076E+20 1.5 2 0.1 0.08 0.060 0.5 1 1.5 2 0.9 ECE Ch. 7 Radius (m) 1080311022 0.8 0.7 0 0.5 1 3e+20 nl_01, nl_04 1080311022 1.5 2 2e+20 1e+20 0 0 0.5 1 1.5 2 t(s) Toroidal magnetic Field (center) Cutoff density for this channel ECE cutoff signals in the core are stronger and cleaner than near the edge Global electron density
Fitted TS density profile from ECE cross calibration Radial locations Chan R 1 0.741 2 0.807 3 0.785 4 0.764 5 0.717 6 0.693 7 0.808 8 0.829
Method Two Gas calibration A standard and widely used method to calibrate TS on Tokamaks. [3,4,5,6] Filling the machine with gas (H2 or D2) and detect the rotational Raman scattering (RRS) lines (J=2 0,J=3 1) from Nd:YAG lasers Keeping the temperature of gas constant, taking measurements at various pressures (hence densities). Determine optical efficiency by relating measured signals to Raman cross sections Making TS calibration self-contained (doesn t depend on other diagnostics for absolute calibration)
Derivation of TS density factor TS response during plasma discharges: TS TS pl S = ne e ( Lσ 90Ω ) e(, ) ( ) las stsη Yf S λ T dc eyn λ dλ L---vertical length of scattering volume Ωs ---radiation solid angle Ts---transmission efficiency η---quantum efficiency Se---Salpeter TS shape factor [11] TS σ 90 TS response to RRS in gas: S = ngelas( LΩsTs ) Yf Σy ( ) dc n k k The TS density factor: ---90 deg TS cross section= η λ σ Ram pl Ram Ram A= σ ( LΩ Tη) = σ S / ne Yf Σy ( λ ) σ TS TS Ram pl Ram Ram 90 s s 90 g las dc n k 90 k 90 2 r e
Absolute calibration factor The Absolute calibration factors are defined as 1 24, A = 9.657 10 ΣY f y ( ) / RT pl i j Ram Ram TS i k i, j dc, ij n k 90, k i g 90 λ σ σ Detector subscript: i polychromator channel, j---spectral channel y --- normalized spectral response for a given λ detector channel to DC light n (instrument function) pl f dc --ratio of APD response of fast varying laser pulse to slowing varying DC signal Y ---relative integral response for spectral channels in a given polychromator to a steady and uniform light source R ---Raman response ratio to unit laser energy (next slide) Tg ---Controlled gas temperature in the machine, at 307K (34C) σ ----90 degree scattering cross section. TS denotes Thomson, Ram for Raman scattering.subscript k for different Raman lines (slide 13) ---wavelength of scattered Raman light (slide13) λ
R is Raman response ratio to unit laser energy Ram R = S / E [ J] P[ torr] is the slope of the linear fitting, as shown below. S Ram is the Raman scattering signals las g H2(9993A) H2(10247A) D2(2 lines) Y axis--- Raman signal/laser energy[j] X axis--- gas pressure [torr] Uncertainty of fitted slopes: D2~6% H2(9993A)~20% H2(10242A)~25%
RRS cross sections and position of Raman lines Gas J=2 0 J=3 1 Wavelength (A) σ90(10^-33cm^2) Wavelength (A) σ90(10^-33cm^2) H2 10242 5.4868 9993 5.894 D2 10438 14.978 10309 6.0167 Plot of Y*yn, i=4 *calibration done In 2002, etc. --refer to appendix for more information
Calculated density factor channel H2(9993A) H2(10242A) H2(wgt. Ave.) D2 Wgt. ave. all ECE co 1 6.006(22%) 7.188(32.1%) 6.299(11.4%) 6.321(12.9%) 6.313(10.5/9.5%) 6.98 2 6.461(19.6%) 7.344(29.1%) 6.669(10.9%) 5.012(12.2%) 5.413(9.8/9.8%)* 6.00 3 5.300(19.2%) 6.465(28.6%) 5.571(8.9%) 5.372(12.1%) 5.442(9.7/7.1%) 5.86 4 10.44(32.8%) 11.50(27.9%) 11.01(23.4%) 8.746(12.1%) 9.127(10.5/8.6%) 9.99 5 4.73(18.1%) 6.092(26.4%) 5.033(7.5%) 5.941(12.2%) 5.551(9.5/10.4%) 5.67 6 6.38(29.7%) 8.917(29.1%) 7.270(15.3%) 5.113(12.0%) 5.413(10.5/0.8%) 6.23 7 6.32(21.3%) 7.194(27.1%) 6.601(11.0%) 5.631(11.8%) 5.887(9.7/5.2%) 6.21 8 6.08(21.3%) 7.533(25.8%) 6.530(10.8%) 5.111(11.9%) 5.454(9.7/9.6%) 6.03 * 6.313(10.5/9.5%)---value(fractional error/percentage off from ECE c.o.)
Preliminary fitted density profiles Radial locations 1 0.736 2 0.799 3 0.778 4 0.758 5 0.695 6 0.713 7 0.811 8 0.831
Conclusions ECE cutoff cross calibration is a reliable calibration technique for core TS on Alcator C- Mod. But there are deficiencies for edge channels. Preliminary calculated weight averaged gas calibration factors agree with ECE cutoff results within 12%. The density profile fitted from weight averaged (over H2 and D2 data) density factors are relatively low compared with that from ECE cutoffs (~10%). However the relative shape is kept. Also why is there a big discrepancy between the factors calculated from H2(9993A) and H2(10242A) (or D2) is so far unable to be resolved. (possibilities discussed on next slide)
Major sources of error (1) difference between theoretical calculated cross sections and the real values during experiments. Usually it s estimated as 10% [7].The theoretical prediction is insufficient to accurately determine the calibration factors. (2) error from the linear fit of Raman response ratio. This value for D2 is about 6%, H2 10242A about 25%, and H2 9993A about 20% (3) the measurements of Yi,j for each spectral channel. (5~10%) (4) Vessel temperature: in lack of bulk temperature measurements, this is assumed +/- 5C (or more, maybe). This uncertainty will change the value of Raman cross section about 1%, and the value of density factor by less than 2%. (5) Laser energy measurements. (estimated as 5%) (6) Value of polychromator instrument function at Raman lines (less than 2%)
Proposed remedies for reducing uncertainties in calibration Accurately on-bench measuring the integral pl response (Yi,j) and relative gain ratio ( f dc )for each detector In-lab measuring Raman cross sections of H2 and D2 gases in a vacuum chamber simulating the environment in C-Mod machine On-site simultaneous measuring Raman cross sections and calibrating TS (to propose) Taking more shots at more pressures to make the linear fit of Raman response ratios more precise Operating polychromators at lower temperature for stronger gain in order to reduce the errors from linear fitting of Raman response ratios
Appendix: Calculation of RRS cross section (1) F(J) is the thermal population of rotational energy level J [8] gn the statistical weight factor. B0 --- rotational constant for homenuclear molecules, a good approximation for Q [8](I nuclear spin) (2) σ Ram zz Ram σ90 = FJ ( ) σzz = for J J-2 anti-stokes lines [8] is the Raman shifted wavelength, is the anisotropy of polarizibility of ground vib-rotaional state. (interpolated from [9],[10] for 1064nm) γ 00 Ram F J Q g J J J hcb k T 1 ( ) = N(2 + 1)exp( ( + 1) 0 / B ) Q= I + k T hcb 2 (2 1) B / 2 4 56 π JJ ( 1) 4 15 λk (2J+ 1)(2J 1) λ k 0 γ 2 00
Appendix: List of calculation results Gas * B0 a I b c λ(a) F d γ00 σzz σ90 gn σ90r e H2 60.85 0.5 10242 0.128 3.113 4.262 5.487 1 4.601 9993 0.097 3.113 6.041 5.894 3 4.721 D2 30.44 1 10438 0.404 3.012 3.706 14.98 6 13.86 10309 0.120 3.012 5.008 6.016 3 5.44 Transition: 2 0 3 1 laser wavelength 1064nm *: at 307K (34C) a: http://cccbdb.nist.gov/default.htm b: in 10[-25]cm[3] c: in 10[-32]cm[2] d: in 10[-33]cm[2] e: in 10[-33]cm[2]. Calculated by Röhr [7]. Laser wavelength 1059nm, temperature at 20C
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