DIII–D - INFO - Home documents/2010_09_16_shafer.pdfM.W. ORNL Seminar, Sept. 2010 Slide 3 Outline • Background: RMPs & Measurements – Edge Visible Measurements in L-mode & Ohmic,

NATIONAL FUSION FACILITYS A N D I E G O

DIII–D

Design of a Soft X-Ray System on DIII-D for Imaging Magnetic Topology in the Pedestal Region

M.W. Shafer1, D.J. Battaglia2, E.A. Unterberg1, T.E. Evans3, J. Canik1, J. Harris1, S. Ohdachi4, R. Maingi1, D.L. Hillis1

1ORNL 2ORISE/ORNL 3GA 4NIFS

Presented at ORNL September 16, 2010


DIII–DM.W. ORNL Seminar, Sept. 2010 Slide 2

Soft X-Ray Imaging System (SXRIS): Designed to Examine Islands in the Pedestal Region •  Motivation: What role do Resonant Magnetic Perturbations

(RMPs) play inside the pedestal? –  Understanding essential for ELM control. –  Plasma response / screening not well understood. –  Island measurements are needed.

•  Approach: Tangential Pinhole-based SXR imaging system in the X-Point region –  Designed for stationary islands via external fields.

•  Flux expansion at X-point increases island sizes.

–  Benefits of SXR Imaging: •  Suitable for higher temperature emission (T > 1keV). •  filter lower energy emission. We can “peel” away outer layers edge

contamination. •  High spatial resolution, if image can be inverted properly.

•  This work assesses diagnostic feasibility. –  Data extraction, analysis, signal-to-noise, resolution



Outline

•  Background: RMPs & Measurements

–  Edge Visible Measurements in L-mode & Ohmic, SXR in Core

•  Synthetic diagnostic model

–  Design goals & modeled diagnostic

–  3D SXR emissivity model used

•  Image analysis methods

–  Focus: Image inversion of line-integrated view

–  Metric needed for assessment, 1st: sensitivity to noise

•  Diagnostic layout, signal-to-noise and resolution

–  SNR ~ 10 @ ~ 1 cm resolution

Emphasis



Outline











Emphasis



ELM Control Concept: RMP → Edge Stochasticity → Increase Transport →↓∇pped → ELM Stabilization

Expectation based on quasilinear transport theory:

stochastic layer reduces peak ∇p and shifts it inward

•  Experimental data has outward shifted ∇p peak rather than inward

Theory Experiment



Two Sets of Non-Axisymmetric Coils on DIII-D Produce RMPs

–  The 4-turn C-coil and single-turn upper/lower I-coil can be configured for n=3 RMP experiments or n=1 field-error correction



H-Mode: Measurements of 3D PWI Field Structure Match Vacuum Prediction

•  Connection length calculation matches particle flux measurements

•  Internal structure (inside pedestal) has not been verified

–  Are fields shielded?

Schmitz et al. PPCF (2008).

Wall Interaction

Top of Pedestal ~1 keV



L-Mode & Ohmic: Edge Visible Imaging Agrees with Vacuum Modeling

•  Ohmic & L-Mode magnetic islands images agree with vacuum field modeling –  Better validity for vacuum field modeling –  What about diverted H-mode plasmas?

•  Visible diagnostics restricted to LCFS-PSI region

CIII Image

Inner Wall

Poincaré Plot

TEXTOR Tore Supra

Visible light

TRIPND

Schmitz et al. RMP Workshop (2008)

Evans et al. PoP (2002)



Proof of Principle: Working LHD SXR system Motivates Design

•  Pinhole/Foil with Fiber image guide to fast camera

–  Higher resolution w/ tangential viewing, opposed to chord fans.

•  Analysis uses tomographic inversion with regularization techniques

Ohdachi, et al, Plasma Science Tech. (2006).



Outline











Emphasis



Vacuum Field Modeling used to Identify Critical Island Structures

•  TRIP3D: vacuum field line tracing with error fields & 3D coils.

•  Island structure to be tested in outer region, 0.85 < ψn < 0.95. –  Island size varies ~20 cm to 1 cm –  Divertor region chosen for flux

expansion

•  Test Scenarios: –  0.75 < ψn < 0.85:

•  Remnant islands (8/3, 7/3, etc.)

–  0.85 < ψn < 0.95: •  Highly stochastic •  Large island (e.g. 3/1, 4/1) test

possible.

n=3 TRIP3D

50 cm 1 2

R (m)

-1

0

1

Z (m

)1.2 1.3 1.4 1.5 1.6

R (m)

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

Z (m

)

7/3

8/3

9/3

10/3

10/3

0.75

0.95

0.95

n = 3 surfaces n range = 0.75 - 0.95

132731 @ 2750, phi = 0



SXRIS Modeling Uses Realistic Geometry

•  Tangential viewing difficult given port and TF coil constraints

1.0 1.5 2.0 2.5R (m)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Z (m

)

132731:2750

top down

-3 -2 -1 0 1 2 3(m)

-3

-2

-1

0

1

2

3

(m) 50.47o

Rtan = 1.40000 mRpin = 2.20000Zpin = -0.820000Ztilt = -2.00000o

DP-T = 1.69706DS-P = 0.200000

~ 50 cm



3D “Phantom” Modeling Used to Evaluate SXR Emission & Validated with NSTX SXR Data

Te(R,Z,ϕ) & ne(R,Z,ϕ)

Zeff (R,Zϕ) Thom.S.

Te(R) ne(R)

Model

NSTX L-mode 900 kA 3 mm pinhole

20 kHz fps 7.6 μm Be filter

Battaglia, et al., Rev. Sci. Instrum. (2010) - accepted

Comparison of CCD Image and Model

(same scale)

Modeling Flowchart:

EMC3

Field-line Following e.g., TRIP3D

ψN(R,Z,ϕ) CHIANTI SXR model

115840

Chordal Line-Integration

(R,Z,ϕ) ε

X-ray filter

Imaging Optics Specifications

2D ’Phantom’ Image

3D Emissivity Synth. Diagnostic



TRIP3D and Profiles Mapped to Common Grid to Give 3D Effects

•  Assumption: –  χ|| >> χ⊥ –  Radial transport coefficients

given by profiles

•  Te(R) and ne(R) mapped to ψn,start from TRIP3D –  200 revolutions



RMP OFF

1.2 1.4 1.6 1.8 2.0 2.2R (m)

-1.2

-1.0

-0.8

-0.6

-0.4

Z (m

)

RMP ON

1.2 1.4 1.6 1.8 2.0 2.2R (m)

-1.2

-1.0

-0.8

-0.6

-0.4

Z (m

)

1.52.0

R (m)-1.0-0.5

Z (m)

0

5

10

1.52.0

R (m)-1.0-0.5

Z (m)

0

5

10

Emis

sivi

ty (a

.u.)

Emis

sivi

ty (a

.u.)

Single Emissivity Slice w/ & w/o RMP Show Island Structure

•  I-coil w/ n=3 RMP Includes error fields, other mode structure –  Reference case (no n=3) contains n=1 components, 3/1, 4/1.

SXR Emissivity

Flat Emissivity Islands



Integrated Image Obscures 3D Effects

•  Only gross structure, i.e. separatrix, is visible –  Striations in X-point region

RMP OFF

0 50 100 150 200 250Pixels

0

50

100

150

200

250

Pixe

ls

RMP ON

0 50 100 150 200 250Pixels

0

50

100

150

200

250

Pixe

ls

Simulated Camera Image



Outline











Emphasis



•  Image Inversion –  Convert line-integrated image to 2D emissivity slice –  Difficult given limited access view –  Testing Advanced Methods: Phillips-Tikhonov

•  3D Equilibria Comparison & Constraint –  HINT2, SIESTA can model the plasma response. –  V3FIT + synthetic diagnostic could constrain 3D equilibrium

•  Forward Modeling –  Iteration of modeled emissivity compared to data –  Difficult given complicated island structure and ergodization

3 Approaches to Data Analysis



Inversions Need Geometry Assumptions, Advanced Methods for Ill-Posed Problem •  Geometric Transform Matrix, L, maps 2D emissivity field, E,

to intensity measurement, S (ie, line-integrated image); e is measurement noise.

–  Geometric transform, L, constructed by assuming emission symmetry:

•  Toroidal symmetric •  Constant along field lines

•  Inversion of L is ill-posed problem; Phillips-Tikhonov (PT) regularization approximates inversion with Linear operation –  Minimize:

–  Linear Operation: ,

•  γ ~ weighting factor, M – constant, C = Laplacian Operator

€

S = L

E + e

€

γ CE 2+ S −LE 2 /M

€

ˆ E γ( ) = LTL + MγCTC( )−1LT S

Iwama et al., Appl. Phys. Lett (1989), Ohdachi et al., Plasma Sci. & Tech. (2006).



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PT Method Shows Promise for Image Inversion

•  Linear operator uses ϒ, to control smoothness vs. detail/noise:

Inversions:

Geometric Transform, L Source, E Image, S = L*E

€

ˆ E γ( ) = LTL + MγCTC( )−1LT S

€

ˆ E

€

ˆ E

€

ˆ E

€

γIncreasing

Coarse grid (64 x 64) used for fast computation



Inversion Matches Well to Source

•  Model data set shows strong flattened region at 7/3 –  Structure @ 8/3 –  Stochastic outside

•  Effects of islands clearly matched in Inversion –  7/3 ~ 5 cm easily

resolved.

Source

1.1 1.2 1.3 1.4 1.5 1.6 1.7

R (m)

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

Z (

m)

7/3

8/3

9/3

10/3

Equilibrium

1.1 1.2 1.3 1.4 1.5 1.6 1.7

R (m)

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

Z (

m)

7/3

8/3

9/3

10/3

Inversion

1.1 1.2 1.3 1.4 1.5 1.6 1.7

R (m)

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

Z (

m)

7/3

8/3

9/3

10/3

0.8 0.9 1.0 1.1

r (m)

0

1

2

3

4

SX

R E

mis

. (x

10

12 p

h. cm

-3s

-1)

0.75 0.80 0.85 0.90 0.95Psi_n

7/3 8/3 9/3 10/3

Eq.

Inv.

Source

€

ˆ E

€

E

€

Eeq



Inversion Being Characterized: Noise, Spatial Sensitivity

•  Set of metrics to be used, i.e. noise response, spatial sensitivity –  Vary levels and determine island characteristics

•  Use synthetic phantoms as input; 2 desired for study: A.  TRIP3D generated B.  Single island chain

Inversion Metric Level Phantom

Type Goodness of

fit Island Characteristics (width, phase, etc.)

Noise 0% 5%

10%

A B

??;??;?? ??;??;??

?? ?? ??

Spatial Sensitivity

0.3 cm 0.8 cm 1,3. cm

A B

??;??;?? ??;??;??

?? ?? ??

Work-Flow Matrix (example)



Inversion Matches Despite Addition of Noise

•  Random noise added to synthetic image at varying levels –  Largest effect of noise is outside imaged plasma –  Effect of noise can be reduced by use of smoothing/control

parameter in PT Linear Inversion Operator

Noise = 0.0 %

1.2 1.4 1.6R (m)

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

Z (m

)

7/3

8/3

9/3

9/3

10/3

10/3

= 1e-3

Noise = 2.0 %

1.2 1.4 1.6R (m)

7/3

8/3

9/3

9/3

10/3

10/3

= 1e-3

Noise = 5.0 %

1.2 1.4 1.6R (m)

7/3

8/3

9/3

9/3

10/3

10/3

= 1e-3

Noise = 10. %

1.2 1.4 1.6R (m)

7/3

8/3

9/3

9/3

10/3

10/3

= 1e-2€

ˆ E

€

ˆ E

€

ˆ E

€

ˆ E



0.8 0.9 1.0 1.1r (m)

0

1

2

3

4

SXR

Em

is. (

x1012

ph.

cm

-3s-1

)

0.8 0.9n

Noise = 0.0 %

Source

Eq.

= 1e-4 = 1e-3 = 1e-2 = 5e-1

7/3 8/3 9/3 10/3

0.8 0.9 1.0 1.1r (m)

0.8 0.9n

Noise = 2.0 %

Source

Eq.

= 1e-4 = 1e-3 = 1e-2 = 5e-1

7/3 8/3 9/3 10/3

0.8 0.9 1.0 1.1r (m)

0.8 0.9n

Noise = 5.0 %

Source

Eq.

= 1e-3 = 1e-2 = 5e-1

7/3 8/3 9/3 10/3

0.8 0.9 1.0 1.1r (m)

0.8 0.9n

Noise = 10. %

Source

Eq. = 1e-2 = 5e-1

7/3 8/3 9/3 10/3

Inversion Matches Despite Addition of Noise

•  Random noise added to synthetic image at varying levels –  Largest effect of noise is outside imaged plasma –  Effect of Noise is countered by use of smoothing/control

parameter in PT Linear Inversion Operator

•  Profile indicates higher smoothing helps recover from noise, but is limited.



ERMP

0 10 20 30 40 50 600

10

20

30

40

50

60EEQ

0 10 20 30 40 50 600

10

20

30

40

50

60

Inv(LRMP*ERMP) using LRMP

0 10 20 30 40 50 600

10

20

30

40

50

60Inv(LRMP*ERMP) using LEQ

0 10 20 30 40 50 600

10

20

30

40

50

60

Inversion Insensitive to Small Changes in Geometric Transform, L

Source, E w/ RMP Equilibrium w/o RMP

Inversion, w/ LRMP Inversion, w/ LEQ Equilibrium field lines used to construct L

Perturbed field lines used to construct L



3D Equilibria Can Introduce Plasma Response

Model Flow Chart 3D Equilibria

e.g., SIESTA/HINT2

ψN(R,Z,ϕ)

HINT2 vs Vacuum Field Connection Lengths •  3D equilibria modeling has shown large differences vs. vacuum field line following inside LCFS –  Important for

topology at top of H-mode pedestal

•  Leads to ability to constrain equilibria with SXR system

Wiegmann, Suzuki. et al.

Pedestal Inside

Pedestal Outside Pedestal

Te(R,Z,ϕ) & ne(R,Z,ϕ)

Zeff (R,Zϕ) Thom.S.

Te(R) ne(R)

EMC3

Field-line Following

ψN(R,Z,ϕ) CHIANTI SXR model

Chordal Line-Integration

X-ray filter

Imaging Optics Specifications

2D ’Phantom’ Image

3D Emissivity

Synth. Diagnostic

(R,Z,ϕ) ε



Outline











Emphasis



Concept for DIII-D SXR System Constrained by Port Structure & TF Coils

•  Relies on efficient scintillator with high resolution: CsI:Tl

•  Sensitivity: ~ 0.11 e-/ 1 kev X-ray –  Scintillator Efficiency, Light

Coupling Losses, Detector Efficiency

Tangency Plane

Pinhole

CsI:Tl Scintillator

Shafer, et al., Rev. Sci. Instrum. (2010) - accepted



SNR and Resolution Scans Made Based on Conservative Estimates of Governing Parameters

•  Operational Diagram: Flexible Pixel Size and Pinhole allow selection of SNR & Resolution –  1 mm pinhole with 128x128 pixels offers good performance

0.0 0.5 1.0 1.5 2.0 2.5Resolution (cm)

0.01

0.10

1.00

10.00

100.00SN

R

Dpin = 0.50 mm

Dpin = 0.75 mm

Dpin = 1.00 mm

Dpin = 1.25 mm

Dpin = 1.50 mm

64 x 64 = 1.17 mm eff. pixel128 x 128 = 0.59 mm eff. pixel256 x 256 = 0.29 mm eff. pixel512 x 512 = 0.15 mm eff. pixel1024 x 1024 = 0.07 mm eff. pixel

Target Area (based on TRIP3D estimates)

Integration Time Varies SNR (25 ms here)

CMOS noise specs. ND ~ 1e3 e-/s, NR~ 19e-

e.g. Vision Research Phantom v10

€

SNR = S / Nph + NR + ND



Summary: A New SXRIS Could Advance RMP/3D Physics

•  Experimental evidence for/against induced islands important for RMP theory and ITER

–  Target region: 0.75 < ψn < 0.98 to examine range of island phenomena (RMP, L-Mode, Rotation/Screening)

•  Modeling uses synthetic 3D emissivity & synthetic diagnostic

–  TRIP3D used to model emissivity so far

•  PT regularization utilized for inversion of images

–  Accurately reproduces source.

–  Full evaluation under way.

•  SNR ~ 10 at ~1 cm is achievable

–  Provides access to island structure.



Focus in the Next Year: Hardware Procurement and Software Refinement

•  Conceptual design made & Final design in-progress

–  Major Tasks:

•  Detailed engineering design for mating with machine in progress

•  Main component procurement

•  Further develop modular SXR analysis software

–  Develop SXR constraint on 3D equilibria (SEISTA & HINT2?)

–  Use 3D equilibria technique & Phillips-Tikhonov inversion on NSTX data

–  Envision portable software analysis for many machines for 3D studies

•  Working target to have hardware installed on DIII-D in Spring 2011

–  Vacuum equipment is initial focus

–  First data on DIII-D by Fall 2011

Documents

DIII–D - INFO - Home documents/2010_09_16_shafer.pdfM.W. ORNL Seminar, Sept. 2010 Slide 3 Outline • Background: RMPs & Measurements – Edge Visible Measurements in L-mode & Ohmic,