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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

• 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

fiFAST(E), TiFAST⊥ and niFAST

KF1 LINE OF SIGHT NEUTRAL BEAM INJECTION ACTIVE CX VOLUME R=3.07m

• pT-fusion expt
• H-minority

heating, 1st harmonic

• BT=3.4 T,
• Ip = 1.8 MA,
• Te = 7 keV,
• ne = 3·10-19 m-3,
• WDIA = 2.5 MJ

discharge #61260

Flux and its error bars

Poisson’s distribution problem with calibration factor

• n ch.1 and ch.7

Fast ion distribution function fi(E)

• N(E) = (ΩS) · ∆E · µ(E) · γ(E) · Pυ(E) · fi(E)
• N(E): neutral count rate
• fi(E): fast ion distribution function
• Pυ(E): neutralization probability
• γ(E): plasma transparency (re-ionization probability)
• ∆E: energy width of the detector
• µ(E): detection efficiency
• (ΩS): étendue of the detector

Neutralization probability Pυ(E)

• Impurity Induced Neutralization 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.

• Pυ(E) =
• Input parameters: impurity (He, Be, C) density ratios

and confinement times, Ti, ne, nD,thermal, Zeff

∑

⋅

q q RR CX

n

q q /

συ

fi(E): Input parameter dependence

Fast ion perpendicular temperature Ti⊥

• Distribution function of ICRF heated ions (Stix, NF

15 (1975) 737)

• inferred temperature
• Central perpendicular temperature

McClements et al, NF 37 (1997) 4

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛− ∝

⊥ ⊥

T E T E E fi exp ) (

⊥

− = ∂ ∂ T E E f E

i

1 ) ( ln

( ) ( )

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ≅

⊥ ⊥ ⊥

* 2 * 1 * ) ( E E T E T T

Ti(E,input parameter)

Except for τBe, τHe = 0 s, all other parameter modify Ti(E) by < 10 %

ni(E): Input parameter dependence

What is the parameter impact on the fast ion density?

Fast ion density ni

• NPA:
• Spectroscopy:
• Fast particle energy measurement (NF33(1993)7)

( )

∫

⋅ − =

max min

min max

1

E E i fast i

dE E f E E n

e fast i e D T D H H

n n n n n n n n T D H H α α α

α α α α

− = = + + ∝ + + = 1 ,

( ) ( ) ( )

MHD DIA fast i a fast

W W dr T T r n r r R W − = ⋅ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + ⋅ ⋅ ⋅ =

⊥

∫

3 4 2 1 4

|| 2

κ π

Gaussian density and temperature profiles: 1.2·1018 m-3 1.5·1018 m-3

Scan of τBe

τHe [s] T(0) [keV] ∆T(0)/T(0) [%] ni

fast [m-3] ∆ni fast/ni 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

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

35 ) 1997 ( 37 1

'

NF s div n Vn a r Dn

Z Z Z Z Z Z Z

≈ ⇒ Γ = + − = Γ τ τ

τBe = 0 sec τBe = 2 sec

Impact on ni: scan of τC

1E+16 1E+17 1E+18 1E+19 0.5 1 1.5 2 τC [s] ni

fast [m

• 3]

0s: -100% 0.5s: -40% 1,5s: + 30%

τC = 1s 2.3·1018 m-3 α−line measurements: 1.5·1018 m−3 ± 30%

• Magn. measurements: 1.2·10 18 m−3 ± 30%

τC = 0 sec τC = 2 sec

What about the error bars?

• 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
• Main source: calculated C5-ions CX-cross-section (20 %)
• NF 37 (1997) 35, NF 40 (2000) 975

n n N N P P f f ∆ ≈ ≈ + + + = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∆ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∆ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∆ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∆ ≈ ∆ % 50 05 . 1 . 15 . 45 .

2 2 2 2 2 2 2 2

µ µ γ γ

υ υ

% 10 10 2

3

≈ ∆ ⋅ ≈ ∆

⊥ − ⊥ ⊥

T T T

CX CX

σ σ

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