Sensitivity of EFITs to the Form of the MSE Fitting Function

Transcription

1 Sensitivity of EFITs to the Form of the MSE Fitting Function M.A. Makowski, S. Allen, R. Ellis, R. Geer, J. Jayakumar, J. Moller, B. Rice Poster RP1-020 DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 1

2 Issues and Motivation The form of the fitting function is found to have an effect on the measured pitch angles While relatively small ( ), the differences can influence: the location of the magnetic axis the magnitude of E r the boundary of the plasma DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 2

3 MSE Layout on DIII-D Toroidal Field Coils 360/0 Radial Array 30 Left Neutral Beam Tangential Array Edge Array B T Ω α 1 12 Dielectric Mirror v b Inner Wall 1.55 m 2.0 m 2.3 m DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct jy

4 Fitting Functions Differ Slightly in Form Currently use the tangent-slope form Sm = G tan[ 2( σ γ + ϕ) ] C m However, the tangent-offset form is better justified Sm = Gtan[ 2( γ + ϕ) ]+ G0 C m In the limit that σ = 1 and G 0 = 0, the two forms coincide DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 4

5 σ=1 is the Only Justified Value In the tangent-slope model, σ was introduced only to improve the fit. There is no other rationale for it When scans spanning ±180 rather than ±24 are used to determine σ, it s value is always found to be unity.(this can also be seen as a periodicity constraint) Modeling of the optical train also predicts σ = 1 DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 5

6 The Dielectric Mirror on the Edge Array Appears to Induce a Phase Shift between the S- and P-plane polarization components DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 6

7 The Value of σ Depends on the Scan Interval 3 Channel 5 Channel 18 6 S m, C m (Volts) S m C m S m C m σ = 1.00 ϕ s = ϕ c = γ polarizer (Degree) σ = 1.00 ϕ s = ϕ c = γ polarizer (Degree) 1 σ = 1.00 ϕ s = ϕ c = σ = 0.89 ϕ s = ϕ c = Sm, Cm (Volts) C m S m C m S m 3 4 DIII D NATIONAL FUSION FACILITY SAN DIEGO γ polarizer (Degree) aps01 mam 15-Oct γ polarizer (Degree) jy

8 Edge Array Poorly Fits Tangent-Slope Model 3 Tangent - Slope Fit 0.15 Channel 18 Channel 18 Tangent - Offset Fit γ fit - γ measured (Degree) γ fit - γ measure (Degree) RMS Error = f ts (γ polarizer ) RMS Error = G = χ 2 red = G = χ2 red = ϕ = ϕ = σ = G o = f to (γ polarizer ) γ polarizer (Degree) γ polarizer (Degree) DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct jy

9 All Channels are Consistent with the Tangent- Offset Model Edge array fits tangent-offset model significantly better than the tangent-slope model For the tangential and radial arrays, the calibration data fits the tangent-slope model with σ = 1, as well as the tangent-offset model with G 0 0. The value of the phase is the same for both fits. DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 9

10 Phase Shift Exists between Sin/Cos Signals for Edge Array Fitting the raw data to S = G sin[ 2( γ + ϕ )]+ G m s s s0 C = G cos[ 2( γ + ϕ )]+ G m c c c0 reveals ϕ s ϕ c for the edge array However, for the tangential and radial arrays, ϕ s ϕ c Edge phase shift is suspected to be caused by the dielectric mirror in this optical train DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 10

11 Phase Shift is Fit Well by Tangent-Offset For G s0 G c0 << 1 S G m ssin[ 2( γ + ϕs) ] = C G cos 2( γ + ϕ ) m c [ ] c Gs Gs = tan[ 2( γ + ϕc) ] cos[ 2( ϕs ϕs) ]+ sin 2 ϕs ϕs G G c This is the tangent-offset form with c ( ) [ ] DIII D NATIONAL FUSION FACILITY SAN DIEGO G G s = cos [ 2( ϕs ϕ )] c, G = Gtan[ 2( s )] 0 ϕ ϕc G c This reduces to the tangent-slope form when ϕ s = ϕ c and σ = 1 aps01 mam 15-Oct-01 11

12 Correction only Significant on Edge Array Difference in Gamma Between Tangent-Offset and Tangent-Slope Models γ (Degrees) Channel 6, Tangent-Offset Channel 6, Tangent-Slope Channel 17, Tangent-Offset Channel 17, Tangent-Slope γ tangent-offset - γ tangent-gamma (Degrees) Channel 6 Channel S m /C m (Dimensionless) S m /C m (Dimensionless) Tangent-offset and tangent-slope forms agree for tangential and radial arrays Forms differ for edge array by ±0.25 DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 12

13 Quality of Fit Improves with Number of Samples Coefficients not completely independent leading to apparently large errors Scan Range Step G ε(g) ϕ ε(ϕ) G 0 ε(g 0 ) (χ red ) ± ± ± ± ± ± ± ± ± Error is reduced as the range and number of sample points is increased Fit coefficients do not change as error is reduced DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 13

14 ϕ s, ϕ c (Degrees) DIII D NATIONAL FUSION FACILITY SAN DIEGO ϕ s and ϕ c Differ only on the Edge Array ϕ s ±24 Scan ϕ c ±24 Scan ϕ s ±180 Scan ϕ c ±180 Scan Tanngential Array Edge Array Channel Number aps01 mam 15-Oct Radial Array

15 Comparison of EFITs using Pitch Angles Computed with the Tangent-Slope Model (Curves in Black) and the Tangent-Offset Model (Curves in Magenta) DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 15

16 Ohmic, L-mode, Ip-ramp, No E r DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 16

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21 Typical Thrust 2 Shot with E r DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 17

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26 QDB/QH/EHO Shot with E r DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 18

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31 Thrust 7, Counter Injection, with E r DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 19

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36 RWM Shot with E r DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 20

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41 QH Mode, No E r DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 21

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46 Conclusions EFITs using the tangent-offset model consistently: Demonstrate considerably lower χ mse Predict lower E r (when present) Demonstrate similar or lower χ mag and χ psi Predict small differences in the location of the The magnetic axis (±1 cm) The plasma boundary (±1 cm) than those using the tangent-slope model DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 22

47 Conclusions (Con t) Only the calibration coefficients for the edge array are modified Elimination of the systematic error introduced by the tangent-slope model is most evident in the reduction in E r DIII D NATIONAL FUSION FACILITY SAN DIEGO aps01 mam 15-Oct-01 23