Hubbard, A.E.

Hughes, J.W.

Johnson, D.

Marmar, E.S.

Mossessian, D.A.

Simon, D.

DSpace@MIT

PSFC/JA-00-23High Resolution Edge Thomson ScatteringMeasurements on the Alcator C-Mod TokamakJ. W. Hughes, D. A. Mossessian, A. E. Hubbard,E. S. Marmar, D. Johnson†, D. Simon†August 2000Plasma Science and Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139†Plasma Physics LaboratoryPrinceton UniversityPrinceton, New Jersey 08544Submitted to Review of Scientific Instruments. (Presented as a poster at the13th Topical Conference on High Temperature Plasma Diagnostics, Tucson,Arizona, June 18–22, 2000.)This work was supported in part by the U.S. Department of Energy Con-tract No. DE-FC02-99ER54512. Reproduction, translation, publication, useand disposal, in whole or in part, by or for the United States government ispermitted.AbstractA high resolution Thomson scattering diagnostic is in operation on the AlcatorC-Mod tokamak, measuring radial proﬁles of electron temperature and densityat the plasma edge. Photons are scattered from an Nd-YAG laser beam pulsedat 30 Hz (1.3-J, 8-ns pulse), and are measured by a ﬁlter polychromator withfour spectral channels. The polychromator measures Te in the range of 15–800 eV and ne of 0.3–3×1020 m−3. Twenty scattering volumes are locatedabout the last closed ﬂux surface, spaced for a nominal resolution of 1.3 mmin midplane radial coordinates. High resolution is essential for measuring edgeTe and ne proﬁles on C-Mod, since these quantities exhibit gradient scalelengths as small as 2 mm in H-mode. The steep proﬁles at the H-mode edgeare ﬁt to a parameterized pedestal function for ease of analysis. Measuredproﬁles are compared with edge proﬁles from electron cyclotron emission andvisible continuum diagnostics.I. INTRODUCTIONIn tokamak fusion experiments, the formation of a transport barrier at theplasma edge is observed upon transition from the low conﬁnement mode (L-mode) to the high conﬁnement mode (H-mode).1 The barrier is characterizedby a pronounced steepening in the radial proﬁles of both electron density (ne)and electron temperature (Te). This region is commonly called the pedestalregion, due to the typical shape of the edge proﬁles. Because factors like coreplasma conﬁnement and edge stability are known to be sensitive to conditionsin the pedestal region, accurate and well-resolved pedestal measurements aredesirable.The Alcator C-Mod tokamak2 (R = 0.67 m, a = 0.22 m) has an H-modepedestal region less than 1 cm in width. Within this or a lesser distance,plasma ne can fall from more than 1020 m−3 to below 1019 m−3. Likewise, Tecan drop from several hundred eV to less than 10 eV. Measurements of theseparameters in the pedestal region must therefore be made with high spatialresolution. A Thomson scattering (TS) diagnostic with 1.3 mm nominal radialresolution has been implemented on Alcator C-Mod, in order to characterizethe Te and ne pedestals in H-mode.II. INSTRUMENT DESCRIPTIONThe edge TS diagnostic uses a Continuum PowerLight 9030 Nd:YAG laserwith 1.5 J pulse energy, 10 ns pulse duration, and a repetition rate of 30 Hz.The beam is steered through a vertical port of the tokamak and maintained ata major radius of 0.69 m. Scattered light is focused onto collection ﬁber opticsby an f/7 Cooke triplet with a demagniﬁcation of 1:2.3 Twenty collection ﬁbers1 Scattering volumesFibers toPolychromatorLCFS78-81Cooke tripletNd:YAGFigure 1: Alcator C-Mod cross-section and layout of TS collection optics. The Cooketriplet is f/7 with a demagnification of 1:2. 1-mm diameter collection fibers are mounted inthe image plane. Scattering locations are clustered about the LCFS at the upper plasmaedge.measuring 1.2 mm in diameter are positioned so that they image scatteringvolumes at the upper edge of the plasma, as shown in Fig. 1. Ray tracingcalculations indicate an imaged spot size of 1 mm for scattering locations30 cm above the optical axis. Misalignment of the beam with respect to thecollection ﬁbers can be corrected by changing voltages on three independentpiezoelectric mounts, which adjust the beam steering mirrors. To evaluatemisalignment, two alignment ﬁbers are arranged on either side of the ﬁberwith the innermost plasma view. With optimal alignment, over 95% of theobserved signal falls in the central channel. Beam misalignment is detected asexcess signal in either alignment ﬁber.The ﬁbers transmit light to an imaging ﬁlter polychromator,4 which has25 spatial channels in four spectral bands. The layout of the polychromatoris presented in Fig. 2. The polychromator input lens focuses light from the2Figure 2: Layout of four-channel polychromator; plan and side views. The detectorsmeasure TS in four bandpasses, with good rejection of the laser line.collection ﬁbers onto the ﬁrst of a series of four concave mirrors. Each of thesemirrors acts as a ﬁeld element, imaging the ﬁber spots onto a successive circularconcave mirror. Each circular mirror has a multilayer dielectric ﬁlter coatingthat transmits light in a particular bandpass. The light that is reﬂected fromeach of these bandpass ﬁlters is focused onto the next ﬁeld mirror in the series,or, in the case of the fourth ﬁlter, onto a dump. The ﬁlters are designed tohave very high rejection of the laser line (λ = 1064 nm), and the ﬁeld mirrorsare coated with a narrow pass dielectric ﬁlter that transmits the laser line. Theresult is a high degree of stray light attenuation. A blocking ﬁlter is placed onthe polychromator input lens in order to reject background light outside therange of the four bandpasses.Light transmitted through each bandpass ﬁlter is focused onto a 25-elementavalanche photodiode (APD) array. Each array element is 300× 250 µm, andthere is 50 µm of dead space between elements. The focus and alignment3of the image spots on the APDs is optimized by backlighting the collectionﬁbers and adjusting the APD positions until the cross-talk between adjacentAPDs is minimized. Because the focus and alignment are sensitive to smallchanges in position, thermal expansions and contractions within the positioncontrol mechanism must be minimized. In addition, APD response is highlysensitive to temperature. Thus, the polychromator is enclosed in thermalinsulation, while automatically regulated heaters maintain a constant internaltemperature of 32◦C.The APD signals have a both pulse contributions from TS and slowly vary-ing contributions from plasma background light. The plasma background sig-nal is isolated and subtracted from the total signal by the detector circuitry,which is described in Ref. 4. Because both the slow and pulse signals con-tribute to the noise in the TS measurements, both signals are sampled anddigitized. A fraction of the Nd:YAG beam leaking through a steering mirroratop the tokamak is used to trigger the sampling hardware. The diagnos-tic is controlled using standard CAMAC hardware driven by MDS-Plus dataacquisition software.5III. CALIBRATION AND DATA ANALYSISTo ﬁt Te and ne to the measured signals, we use the Thomson spectral formfactor, S(Te, θi, λ), with relativistic corrections, as given by Sheﬃeld.6 Here,θi is the scattering angle of the i-th spatial point. The expected response toThomson scattered light in the j-th spectral channel for the i-th spatial pointis then given byIi,j(ne, Te) = neE0(dσdΩ)TSAiCi,j∫ ∞0fj(λ)S(Te, θi, λ) dλ , (1)where E0 is the laser energy,(dσdΩ)TSis the diﬀerential cross section for TS, andthe fj(λ) are the normalized instrument functions of the spectral channels. Thecalibration factors, Ci,j, give the relative response of all the spectral channels,while the Ai are absolute sensitivity coeﬃcients for the spatial channels. Dataanalysis routines ﬁt experimentally measured signals to Eq. 1 with Te and neas ﬁtting parameters. We thus require a series of calibrations to obtain fj(λ),Ci,j, and Ai.To measure the fj(λ), we focus onto the APD arrays the output of ascannable monochromator with known spectral intensity. The spectral re-sponse of each APD array is measured and normalized to the monochromatoroutput. Fig. 3 shows the normalized instrument functions, along with S(Te, λ)at θi = 90◦, for two values of Te. The integral DC response of the individ-ual channels is measured by illuminating the collection ﬁbers with a source of4Figure 3: Edge TS polychromator instrument functions, fj. Spectral distributions ofThomson light at 10 and 300 eV (θ = 90◦) are also shown.known spectral brightness. The APD response to a fast pulse source in generaldiﬀers from the DC response, and so the relative responses to quickly varying(∼ 10 ns) and to slowly varying (> 1µs) signals are measured independently.This is done by directly illuminating the APD arrays with the output of a laserdiode, which is operated ﬁrst in short pulse mode, and second in long pulsemode. The results of the DC and pulsed calibrations are combined, yieldingthe Ci,j in Eq. 1.Knowing S(Te, θi, λ), fj(λ), and Ci,j enables us to measure Te at the i-thspatial location. In order to calculate ne from experimental TS signals, weobtain absolute sensitivity coeﬃcients, Ai, using Raman scattering (RS) inD2.7 Rotational anti-Stokes lines of known wavelength, λRSk , are measured inthe polychromator spectral channels. The Ai are computed from the RS signal,IRSi,j ; the laser energy, E0; the molecular density of the scattering gas, nD2 ; thediﬀerential cross sections for scattering into the k-th rotational line,(dσdΩ)RSk;5and the calibration terms Ci,j, fj(λRSk ). Several ﬁll pressures in the range of0–500 torr are used, and at least 1000 RS measurements are made at eachpressure, in order to minimize statistical uncertainty. Due to high rejection ofthe laser line, neither stray light nor Rayleigh scattering is measured.Based on the above calibrations, look-up tables of polychromator signalsare constructed as functions of Te. Experimental signals are ﬁt to these ta-bles using a non-linear least squares ﬁtting routine, and both Te and ne areobtained. By measuring the signals in the alignment channels and comparingwith that in the central channel, we can evaluate whether laser misalignmentoccurs, and correct ne measurements that would otherwise be underestimated.The scattering locations are mapped to the tokamak midplane along surfacesof constant magnetic ﬂux using results from the EFIT magnetics reconstruc-tion code.8 Assuming that Te and ne remain constant along ﬂux surfaces, thismapping gives midplane radial proﬁles of these quantities. The ﬁnite collectionﬁber diameter results in a minimum radial resolution of 1.3 mm. The Nd:YAGrepetition rate gives a temporal resolution of 33.3 ms.When edge proﬁles form pedestals, they are ﬁt to a parameterized function,f , on R′ = R−R0f , where R is midplane radius and R0f is the position of thepedestal center:f(R′) = bf +hf2[tanh(R′δf)+ 1]−mf (R′ + δf )H[−(R′ + δf)] (2)Here, bf is the pedestal baseline and hf is its height. The width is given by,∆f = 2δf . The Heaviside function, H[−(R′+δf)], allows one to account for theﬁnite radial slope, −mf , that exists inside the pedestal region. Pedestals arecharacterized using the parameters, hf , ∆f , and R0f , and also the maximumradial gradient, which is obtained according to |∇f |max = hf/∆f , and is locatedat R = R0f .IV. SUMMARY OF EXPERIMENTAL RESULTSWe measure Te from 15 to 800 eV at ne in the range of 0.3–2.5×1020 m−3.The dynamic range in both Te and ne allows complete coverage of AlcatorC-Mod edge proﬁles in H-mode, with uncertainties that are typically 5–20%.Proﬁles of Te and ne measured at time points before and after the H-modetransition are shown in Fig. 4 to illustrate the steepening in parameter gradi-ents that characterizes high conﬁnement.Once a plasma is in H-mode, parameter proﬁles generally are well ﬁt withthe pedestal function of Eq. 2. When the H-mode is fully developed, thedensity pedestal height, hn, is roughly 0.7 times the central plasma ne, andthe width, ∆n, typically ranges from 2 to 8 mm. The temperature pedestal6Figure 4: Edge profiles of Te and ne before and after L-H transition. Error bars on Te andne reflect estimated statistical uncertainties; also, ne error bars account for uncertainties inthe absolute calibration.7Figure 5: Comparison of TS and ECE Te profiles in L- and H-mode. Each ECE profilewas recorded during a 150-ms sweep of BΦ. The plotted TS profiles are averages over theduration of the sweep.exhibits a similar range of widths, but the height, hT , depends on the plasmaheating mechanism and conﬁnement characteristics. Temperature pedestalheights from 150 to 400 eV have been observed. Both the ne and Te pedestalsare located inside the LCFS. The Te pedestal is typically 1 mm inside the nepedestal.Edge Te proﬁles can also be obtained using electron cyclotron emission(ECE), as measured by a nine-channel grating polychromator. This diagnos-tic gives midplane Te at nine radial locations, corresponding to nine distinctmagnetic ﬁeld values. By sweeping the toroidal ﬁeld by 2–3% over a periodof 100–200 ms, we obtain a radial scan of the Te pedestal,9 the radial reso-lution of which is instrument-limited to 9 mm. In steady-state plasmas theTS temperatures during the sweep are time averaged and compared with theECE proﬁle. Due to uncertainties in both the location of these measurementsand the EFIT mapping of TS points to the midplane, the proﬁles exhibit avariable relative shift, usually 5–10 mm, that must be corrected. This shifthas been removed in Fig. 5, which compares proﬁles obtained in L-mode andH-mode plasmas. Agreement between ECE and TS is generally very goodin L-mode. In H-mode TS measurements give hT 10–20% larger than that8Figure 6: TS profiles are compared to visible emissivity measurements (solid curve) bycalculating bremsstrahlung emissivity profiles (circles) from Te and ne. The error envelopesgiven by the dashed and dotted lines reflect uncertainties in absolute calibration of eitherinstrument.from ECE, probably due to uncertainties in the fj(λ) and Ci,j described inSection II. The pedestal width measured with TS is routinely smaller than the9-mm resolution of ECE.Comparison also is made with measurements from a high-resolution visiblecontinuum array, which measures line-integrated plasma emissivity at 536 nmalong tangential chords. An Abel-inversion produces radial emissivity proﬁleswith 1 mm resolution. To compare these proﬁles with TS results, free-freebremsstrahlung emissivity is calculated from the Thomson Te and ne proﬁles,and the estimated value of Zeﬀ, usually between 1 and 2, at the plasma center.These proﬁles are compared in H-mode plasmas as in Fig. 6, again after relativeshifts are introduced. The measured emissivity proﬁle contains a signiﬁcantcomponent on and outside the LCFS that is not due to bremsstrahlung, and isthought to show a contribution from molecular deuterium. In addition, a bumpoccurring consistently at the top of the emissivity pedestal is thought to be anartifact of the inversion process. Ignoring these features, reasonable agreementexists between the measured and calculated emissivity pedestals. The widthsin general agree, while the amplitude of the measurement is consistently higher9than the height of the calculated pedestal. This discrepancy is consistentwith the expected uncertainties of 10–15% in the absolute calibrations of bothinstruments, as well as the uncertainty in Zeﬀ.V. CONCLUSIONThe edge TS diagnostic on Alcator C-Mod provides information on plasmaconditions near the LCFS. In this region the electron temperature and densityproﬁles have been measured with 1.3-mm radial resolution, and with 33.3-mstemporal resolution. Edge Te and ne proﬁles are obtained over a dynamicrange of 15–800 eV and 0.3–3.0×1020 m−3, respectively, allowing completecharacterization of H-mode pedestals, which can be as narrow as 2 mm. Sys-tematic errors of 10–20% may exist in the Te and ne measurements and arethe subject of ongoing evaluation. Within the bounds of measurement un-certainty, comparisons with midplane ECE and visible continuum diagnosticsshow reasonable agreement.VI. ACKNOWLEDGEMENTSWe would like to acknowledge the contributions to the edge Thomson scat-tering hardware provided by Princeton Scientiﬁc Instruments. This work issupported by DOE Coop. Agreement DE-FC02-99ER54512.10References1. ASDEX Team, Nucl. Fusion 29, 1959 (1989).2. I. H. Hutchinson, R. Boivin, F. Bombarda, P. Bonoli, S. Fairfax, C. Fiore,J. Goetz, S. Golovato, R. Granetz, M. Greenwald, S. Horne, A. Hubbard,J. Irby, B. LaBombard, B. Lipschultz, E. Marmar, G. McCracken, M.Porkolab, J. Rice, J. Snipes, Y. Takase, J. Terry, S. Wolfe, C. Chris-tensen, D. Garnier, M. Graf, T. Hsu, T. Luke, M. May, A. Niemczewski,G. Tinios, J. Schachter, and J. Urbahn, Phys. Plasmas 1, 1511 (1994).3. R. Watterson and K. Chen, Rev. Sci. Instrum. 61, 2867 (1990).4. D. Dimock, B. Grek, D. Johnson, B. LaBombard, B. Lipschultz, and G.McCracken, Rev. Sci. Instrum. 68, 700 (1997).5. J. A. Stillerman, T. W. Fredian, K. A. Klare, and G. Manduchi, Rev.Sci. Instrum. 68, 939 (1997).6. J. Sheﬃeld, Plasma Scattering of Electromagnetic Radiation, Academic,New York (1975).7. H. Ro¨hr, Phys. Lett. 81A, 451 (1981).8. L. L. Lao, H. St. John, R. D. Stambaugh, A. G. Kellman, and W. Pfeiﬀer,Nucl. Fusion 25, 1611 (1985).9. A. E. Hubbard, R. L. Boivin, R. S. Granetz, M. Greenwald, I. H. Hutch-inson, J. H. Irby, Y. In, J. Kesner, B. LaBombard, Y. Lin, J. E. Rice, T.Sunn Pedersen, J. A. Snipes, P. C. Stek, Y. Takase, S. M. Wolfe, and S.Wukitch, Phys. Plasmas 5, 1744 (1998).10. E. S. Marmar, et al., these Proceedings.11

High Resolution Edge Thomson Scattering Measurements on the Alcator C-Mod Tokamak

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High Resolution Edge Thomson Scattering Measurements on the Alcator C-Mod Tokamak

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