Error Estimation and Parameter Dependence of the Calculation of the - PowerPoint PPT Presentation

Error Estimation and Parameter Dependence of the Calculation of the Fast Ion Distribution Function, Temperature and Density Using Data From the KF1 High Energy NPA on JET Christian Schlatter, Duccio Testa, Marco Cecconello, Marko Santala, Andrea Murari C.Schlatter et al. TFD meeting 18-Dec-2003

Introduction : KF 1 KF1 LINE OF SIGHT NEUTRAL BEAM INJECTION • High energy NPA, neutral flux measurement of hydrogen and helium isotopes up to 4 MeV • Vertical line of sight, oct.4, R = 3.07 m • Measurement of fast ion ACTIVE f iFAST (E), T iFAST ⊥ and n iFAST CX VOLUME R=3.07m

discharge #61260 • pT-fusion expt • H-minority heating, 1 st harmonic • B T =3.4 T, • I p = 1.8 MA, • T e = 7 keV, • n e = 3·10 -19 m -3 , • W DIA = 2.5 MJ

Flux and its error bars Poisson’s distribution problem with calibration factor on ch.1 and ch.7

Fast ion distribution function f i (E) • N(E) = ( Ω S) · ∆ E · µ (E) · γ (E) · P υ (E) · f i (E) • N(E): neutral count rate • f i (E): fast ion distribution function • P υ (E): neutralization probability γ (E): plasma transparency (re-ionization probability) • ∆ E: energy width of the detector • µ (E): detection efficiency • • ( Ω S): étendue of the detector

Neutralization probability P υ (E) • I mpurity I nduced N eutralization model (IIN) A.A.Korotkov et al., NF 37 (1997) 35. • system of steady-state ion density balance equations for bare , [H]- and [He]- like impurities. • RR with electrons, CX with impurities, thermal deuterium and NBI atoms. ∑ συ ⋅ n • P υ (E) = q q / CX RR q q • Input parameters: impurity (He, Be, C) density ratios and confinement times, T i , n e , n D,thermal , Z eff

f i (E): Input parameter dependence

Fast ion perpendicular temperature T i ⊥ • Distribution function of ICRF heated ions ( Stix, NF 15 (1975) 737 ) ⎛− ⎞ E E ⎜ ⎟ ∝ ( ) exp f i E ⎜ ⎟ ⎝ ⎠ T T ⊥ ⊥ • inferred temperature ∂ ( ) 1 f E = − i ln ∂ E T E ⊥ • Central perpendicular temperature ( ) McClements et al, NF 37 (1997) 4 ⎛ + ⎞ * ( ) T E ≅ ⎜ ⎟ ⊥ ( 0 ) * 1 T T E ⎜ ⎟ ⊥ ⊥ ⎝ ⎠ 2 * E

T i (E,input parameter) Except for τ Be , τ He = 0 s, all other parameter modify T i (E) by < 10 %

n i (E): Input parameter dependence What is the parameter impact on the fast ion density?

Fast ion density n i E 1 max ( ) ∫ = ⋅ fast n f E dE • NPA: − i i E E max min E min • Spectroscopy: H n α = ∝ = α H , n n + + + + D e H D T n n n α α α H D T α = fast � 1.5·10 18 m -3 n n − α i e 1 • Fast particle energy measurement (NF33(1993)7) a ⎡ ⎤ 1 4 ( ) ( ) ( ) ∫ = π ⋅ κ ⋅ ⋅ + ⋅ = − fast 2 4 W R r r n r T T dr W W ⎢ ⎥ ⊥ 0 || fast i DIA MHD ⎣ ⎦ 2 3 0 Gaussian density and temperature profiles: � 1.2·10 18 m -3

Scan of τ Be r Γ = − + ' Dn Vn Z Z Z a n τ = Z τ Be = 2 sec Γ Z div Z ⇒ τ ≈ 1 s Z 37 ( 1997 ) 35 NF τ He [s] T(0) [keV] ∆ T(0)/T(0) [%] n i fast [m -3 ] ∆ n i fast /n i fast [%] 0.00 47379.2 1630.9 5.3E+17 -76.8 0.05 1328.4 94.9 1.3E+18 -42.2 0.10 875.3 43.0 1.7E+18 -26.9 0.20 690.0 18.9 2.0E+18 -14.6 0.30 632.5 11.0 2.1E+18 -9.2 τ Be = 0 sec 0.40 604.4 7.1 2.2E+18 -6.2 0.50 587.9 4.8 2.2E+18 -4.3 1.00 554.8 0.0 2.3E+18 0.0 1.50 543.8 -1.6 2.3E+18 1.6 2.00 538.5 -2.4 2.3E+18 2.3

Impact on n i : scan of τ C 1,5s: + 30% τ C = 2 sec 0.5s: -40% 1E+19 -3 ] 1E+18 fast [m 1E+17 n i τ C = 1s � 2.3·10 18 m -3 1E+16 τ C = 0 sec 0 0.5 1 1.5 2 τ C [s] α− line measurements: 1.5 · 10 18 m −3 ± 30% 0s: -100% Magn. measurements: 1.2·10 18 m −3 ± 30%

What about the error bars? 2 • 2 2 ⎛ ∆ ⎞ ⎛ ∆ ⎞ ⎛ ∆ ⎞ 2 ∆ γ µ ⎛ ∆ ⎞ f P N ⎜ ⎟ ≈ + ⎜ ⎟ + ⎜ ⎟ + = υ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ γ µ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ f P N υ ∆ n + + + ≈ ≈ 2 2 2 2 0 . 45 0 . 15 0 . 1 0 . 05 50 % n • The main source of uncertainties is the [H] electron donor density in the plasma core • This can be improved by a better analysis of the input parameters ∆ ∆ σ • T ≈ ⋅ − ≈ ⊥ 3 CX 2 10 10 % T ⊥ σ T ⊥ CX Main source: calculated C 5 -ions CX-cross-section (20 %) • • NF 37 (1997) 35, NF 40 (2000) 975

Conclusion • Very reliable and robust perpendicular fast core ion temperature measurement • Typical “crude IIN model” fast particle density measurement has ~50% uncertainty – refined analysis can bring it down – measurement consistent with edge spectroscopy and fast ion energy from magnetics • Detectors need recalibration C.Schlatter et al. TFD meeting 18-Dec-2003