PSFC/JA-14-83

Two-dimensional AXUV-based radiated power density diagnostics on NSTX-U

I.Faust1, L. Delgado-Aparicio2, R. E. Bell2, K. Tritz3, A. Diallo2,

S. P. Gerhardt2, B. LeBlanc2, T. A. Kozub2, R.R. Parker1, B. C. Stratton2

1MIT - Plasma Science and Fusion Center, Cambridge, MA, 02139, USA 2Princeton Plasma Physics Laboratory, Princeton, NJ, 08540, USA 3The Johns Hopkins University, Baltimore, MD, 21209, USA

November 2014

Plasma Science and Fusion Center Massachusetts Institute of Technology

Cambridge MA 02139 USA This work was performed under US DOE contracts DE-FC02-99ER54512 at MIT and DE-AC02-09CH11466 at PPPL. Reproduction, translation, publication, use and disposal, in whole or in part, by or for the United States government is permitted.

Two-dimensional AXUV-based radiated power density diagnostics on

NSTX-Ua)

I.Faust1, L. Delgado-Aparicio2, R. E. Bell2, K. Tritz3, A. Diallo2, S. P. Gerhardt2, B. LeBlanc2, T. A. Kozub2, R.R. Parker1, B. C. Stratton21MIT - Plasma Science and Fusion Center, Cambridge, MA, 02139, USA2Princeton Plasma Physics Laboratory, Princeton, NJ, 08540, USA3The Johns Hopkins University, Baltimore, MD, 21209, USA

(Dated: 25 June 2014)

A new set of radiated-power-density diagnostics for the NSTX-U tokamak have been designed to measure thetwo-dimensional poloidal structure of the total photon emissivity profile in order to perform power balance,impurity transport and MHD studies. Multiple AXUV-diode based pinhole cameras will be installed in thesame toroidal angle at various poloidal locations. The local emissivity will be obtained from several types oftomographic reconstructions. The layout and response expected for the new radially viewing poloidal arrayswill be shown for different impurity concentrations to characterize the diagnostic sensitivity. The radiatedpower profile inverted from the array data will also be used for estimates of power losses during transitionsfrom various divertor configurations in NSTX-U. The effect of in-out and top/bottom asymmetries in thecore radiation from high-Z impurities will be addressed.

I. INTRODUCTION

Measurements of total radiated power (Prad) are im-portant for determining global power balance, diagnos-ing magnetohydrodynamic (MHD) behavior and under-standing impurity dynamics in tokamak plasmas. Char-acterizing the nature of this emission is of utmost impor-tance for the NSTX-U tokamak, requiring the use of spe-cially designed bolometer cameras. A new, 2-dimensionalset of pinhole cameras were developed to tomographicallyreconstruct the radiated power on a single poloidal plane.The system consists of three cameras utilizing photodi-odes to image the plasma from separate positions.It is important to understand the systematic errors

from converting measured chord brightnesses to the to-mographic poloidal emissivity profile. This underlies thevalidity and sensitivity of the reconstruction to changes inthe camera measurements. The highly shaped nature ofNSTX-U plasmas requires validation of inversion meth-ods. Testing tomographic methods on model emissivityprofiles provide a priori measure of the sensitivity ex-pected on the implemented NSTX-U diagnostic.

II. DIAGNOSTIC OVERVIEW

The wide spectral width necessary for bolometers (.1nm−1000 nm) requires the use of pinhole-based optics.Pinhole cameras have been used extensively for radio-metric measurement on tokamaks, both for bolometryand soft X-ray tomography using linear diode arrays1.

a)*Contributed paper published as part of the Proceedings of the20th Topical Conference on High-Temperature Plasma Diagnostics,Atlanta, Georgia, June, 2014.

Multiple measurements along a common axis are usedto measure the meridonal plane in a fan-beam geometry.These images are used in tandem with other measure-ments or symmetries to reconstruct the tokamak plasma.A new set of 3 pinhole cameras based on these principleshave been designed to resolve of the characteristics of thetotal photonic emissivity of expected NSTX-U plasmason a single poloidal plane.

Each camera is designed utilizing one AXUV20 diodearray composed of 20 vacuum-ultraviolet measuring sil-

FIG. 1. Chord geometry and plasma equilibrium for syntheticdischarge, point of chord tangency to plasma center plottedin red.

2

icon diodes. The diodes provide fast time response, ro-bustness in tokamak environments and wide spectral sen-sitivity. Unlike an ideal bolometer, the spectral sensitiv-ity of the diode array is variable versus photon energy.For the tested emissivities it is assumed that all emissioncomes from the region where sensitivity R ∼ .275 A/W,which is typical of high temperature regions.The camera placements were chosen to determine pro-

files of low angular order (m < 2) structure, with op-timization toward specific Fourier harmonic componentsassociated with impurity asymmetries and MHD modes.The first and second cameras are placed on the low-fieldside (LFS) above and below the midplane viewing hor-izontally at downward and upward angles respectively.The offset from the midplane improves the characteri-zation of in-out asymmetries expected in NSTX-U dis-charges (i.e. improved cos θ resolution). However, thestrong shaping typical to ST plasmas limited the cameravertical offsets, insuring the reconstruction of the plasmaelongation (cos 2θ component). The third camera viewsvertically from the top of NSTX-U into the center stackand lower divertor. Together the three cameras give ac-curate resolution of the cosine m = 0, 1, 2 and sine m = 1modes.Each camera aperture was fully constrained for maxi-

mal throughput while preserving resolution. The rectan-gular pinhole size simultaneously limited the chord viewsto the center stack while also minimizing chord overlapin the same array. The known etendue and responsi-tivity provides absolute measure of expected current foreach diode for a known plasma emissivity profile. Theheight of NSTX-U vessel required a smaller aperture onthe third vertical viewing array to preserve resolution forthe smaller fan-beam.

III. SYNTHETIC DIAGNOSTIC

Model total photon emissivities were generated toscope necessary transimpedance gains while also test-ing the efficacy of tomographic schemes. The emissivi-ties were calculated using known cooling rates coupledwith experimental impurity and electron temperatureand density radial profiles.2 The profiles are based offof previous experimental NSTX data placed within theNSTX-U vessel geometry with a Prad of 0.5 MW, consist-ing mainly of C and Fe emission. The radiated power wasmapped poloidally utilizing a plasma equilibrium (gener-ated using the EFIT code3) for two cases. The first modelincluding a rotation-induced asymmetry and the seconda stationary control.The two model emissivities were converted into mea-

sured brightness profiles through the camera geometry.Two methods were utilized for generating the brightnessin order to validate the pinhole optimization. The firstmethod integrated the principal beam through emissiv-ity distribution. The second subdivided the pinhole anddiode into sub-surfaces and connected a chord from ev-

0.5 1.0 1.5R [m]

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

Z[m

]

a)

0.5 1.0 1.5

b)

0

15

30

45

60

75

90

105

120

kWm−3

FIG. 2. Model emissivities with (a) and without (b) asym-metry due to rotation (shot 138767).

ery sub-pinhole to every sub-diode. Over 10000 chordsper diode were traced through the plasma, providing ameasure of finite-aperture effects on the brightness. Eachof the finite-etendue beams were integrated through theradiated power and totalled. This provided a more ac-curate representation of the emission, especially as eachchord intercepts the conic surfaces of the NSTX-U vessel.

Results showed that the finite-aperture effects causeda less than 2% variation from the ideal principal beamrepresentation of the chord. In cases where there is sub-stantial gradients in emission perpendicular to the prin-cipal ray, the differences were substantially larger. Thiswas mainly seen in chords viewing near the edge of the

FIG. 3. Expected diode currents on the three cameras forthe two model emissivites generated with and without finite-aperture effects

3

0.5 1.0 1.5R [m]

−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5Z[m

]a)

0.5 1.0 1.5

b)

0

15

30

45

60

75

90

105

120

kWm−3

FIG. 4. Flux-Fourier tomographic reconstructions with rota-tion (a) and without rotation (b)

plasma, understating the necessity of measuring the edgeplasma accurately for bolometry. The importance of fineradial resolution is shown fundamentally in the capabil-ity for the inversion routines in recovering the dominantand radially-thin edge emission zone.

IV. TOMOGRAPHIC RECONSTRUCTION

The finite-aperture generated brightnesses were usedto test tomographic reconstruction of the total radi-ated power. Representations of the chord integrationwere parametrized into sets of polar and polar-like ba-sis functions4,5. First, the emissivity was assumed tobe a function of magnetic flux (using EFIT3) with flux-surface variation decomposed by an angular Fourier de-composition. While soft X-ray core emission is not fluxdependent6, significant edge emission is expected to fol-low the flux expansion typical of the edge plasma. Sec-ondly, Bessel-Fourier polar tomography5,7,8 was used totest its efficacy for flux-independent reconstruction.The matrix for inversion was assembled by iterating

the principal beam of each chord through the vessel andfinding the square-root magnetic flux (

√Ψ) value at each

position. The length of the step size was added fraction-ally to the nearest

√Ψ points where the emission was to

be determined. Angular harmonic dependencies followeda similar procedure but were also multiplied by the valueof the harmonic at the flux-mapped point. The ill-posedmatrix was sensitive to high-spatial frequency variationin

√Ψ necessitating the use of second-order Tikhonov

regularization9. This was done as inversions using sin-gular value decomposition (SVD) could not be used togenerate physically relevant solutions. For Bessel-Fourierreconstruction, the parameters of the matrix were calcu-

lated by a modified form of equation (9) in [10]

fml(p) = (J

m+1(x

ml)− J

m−1(x

ml))·∫ cos−1 p

0

cos(mθ) sin(xml(cos θ − p))dθ (1)

Additional zero-brightness chords were created at min-imum p which existed outside the vessel and distributedequally in angle. This was done to improve the angularvalidity of the tomographic reconstruction.The flux-Fourier method could only qualitatively re-

produce the significant edge radiated power and rotationinduced asymmetry. However, quantitative agreementwas found for the flat core emission. Bessel-Fourier re-constructions were distorted by the dominant the edgeemission. In principle the elongation of the radiatedpower can determined using 3 cameras, but the structureof the edge emission is composed of higher Fourier har-monics. Bessel-Fourier tomography is poorly suited forreconstruction in this case due to significant edge emis-sion and plasma shaping.

V. CONCLUSIONS

A design study for a bolometric 2-dimensional poloidaltomography system for NSTX-U was completed. Thethree AXUV-based pinhole cameras were optimallyplaced to tomographically reconstruct the total radiatedpower profile on a model equilibrium. A 3-dimensionalcamera model was used to minimize finite-aperture ef-fects and determine expected diode signals.Flux-Fourier and Bessel-Fourier methods were used to

recreate model radiated power profiles. It was found thatthe significant edge emission prevented the use of Bessel-Fourier methods to properly model the emissivity. Flux-Fourier tomography could resolve the edge emission andcore asymmetry, but was limited in radial resolution.This work was performed under US DOE contracts

DE-FC02-99ER54512 at MIT and DE-AC02-09CH11466at PPPL.

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