October 20 2008 Milano Core-Pedestal Energy Confinement. Empirical Scaling Laws and "stiff"...

October 20 2008 Milano

Core-Pedestal Energy Confinement. Empirical Scaling

Laws and "stiff" profiles.

A. Jacchia1, F. De Luca2

1Consiglio Nazionale delle Ricerche - Istituto di Fisica del Plasma EURATOM - ENEA - CNR Association, via R.Cozzi, 53 - 20125 Milano Italy

2Dipartimento di Fisica, Università degli Studi di Milano

via Celoria, 16 20133 Milano Italy

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.



Local transport

Local T, n.. profiles

Theory

Match profiles with Interpretative-Predictive

Codes

Empirical Scaling laws

Mean-integralquantities

Statistical analysis

Extrapolation toUnexplored regimes

?link?

Local heat transport & Empirical scaling





A two-term model of the confinement in Elmy H–modes



• J.G.Cordey et al "A two-term model of the confinement in Elmy H-modes" Nucl. Fusion 43 (2003) 670



• D.C. McDonald et al "Recent progress on the development and analysis of the ITPA global H-mode using the confinement databases" Nucl. Fusion 47(2007) 147-174



Pedestal Scalar Database V3.2 (March 2002) - Te~Ti

JET, ASDEX-U, D3D, JT60,CMOD,MAST, JFT2M





• Wcore= W- Wped is based on the assumption that the total energy can be expressed as sum of independent quantities.

• Profile stiffness (consistency) links core and boundary behaviour.

• ETG, ITG modes control i.e. the steepness of electron and ion temperature profiles.

Core-Pedestal relationship in the presence of stiff temperature profiles

€

R∇T /T



Stiffness in JET Te,i profiles QuickTime™ and aTIFF (LZW) decompressor


1

10

3 3.2 3.4 3.6 3.8

66433_Ti

OhmicL-modetype I H-modetype III H-mode

R [m]

1

10

3 3.2 3.4 3.6 3.8

66433_Te

OhmicL-modetype I H-modetypt III H-mode

R [m]




are needed to see this picture.Stiffness in FTU EC heated L-mode

0.1

1

0.2 0.4 0.6 0.8 1

Te 18282Te 18281Te 18290Te ohmic

Te

[keV]

ρ

FTU

0.76 MW0.4 MW0.39 MW0.43 MW 0.4 MW

• Te profiles stiff in the

region 0.2 <ρ < 0.6. ne~1020 & Te~Ti.

• All profiles show same in the ‘confinement’ region independently of where and how much power is injected.

€

R∇Te /Te



"Stiff energy"- minimal model

€

Hp :R

LT

= R1

T

dT

dr= −A , A constant over a, Te = Ti ,

a

R= ε and ρ =

r

a

under these assumptions T(ρ ) = Tped e−Aε (ρ−1) where Tped is T(ρ =1)

The total energy content W becomes :

W =12π 2 Ra 2 n(ρ )T(ρ )ρ0

1

∫ dρ and Wped =12π 2Ra2npedTped

Work out the integral....

W = Wpedn

nped

1+Aε

3+

(Aε)2

12+ .....

⎡

⎣ ⎢

⎤

⎦ ⎥ ⇒

nped

n

W

Wped

−1 =Aε

3

W = f (A,Wped ,nped

n,ε)





0

2

4

0 2

JET

JT60

D3D

AUG

W ped

[MJ]

0

2

4

6

8

10

12

0 2 4

JET

JT60

D3D

AUG

W ped

[MJ]

W vs Wped of the Pedestal database QuickTime™ and aTIFF (LZW) decompressor


€

W = Wpedn

nped

1+Aε

3

⎡ ⎣ ⎢

⎤ ⎦ ⎥





QuickTime™ and aTIFF (Uncompressed) decompressor


-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Ip Bt P Meff n R eps k fq

WW

ped

Wcore

= W-Wped

• Regressing (OLS fitting) W, Wped and Wcore=W-Wped using the PSDBv3.2 assuming that W and Wped

are function of the global variables: I, R, P, n , B, k, , m, fq = q95/qcyl no differences within error bars in the scaling of W and Wcore = W-Wped are found because of the simple relationtionship between the two figures.



Thermal Conduction Model

Empirical Scaling of W, Wped &Wcore



€

W =1.7 ×10−2 I p1.39 BT

0.069P0.25M eff0.32 n0.04 R1.17ε−1.09k1.32 fq

0.65

Wped =1.0 ×10−3 I p1.47BT

0.07P0.41M eff0.84 n−0.005R1.05ε−1.31k1.63 fq

1.38

Wcore = 9.0 ×10−3 I p1.32BT

0.42P0.15M eff0.1 n0.09R1.39ε−1.24k1.64 fq

0.33



Stiffness does not mean unmodifiable T profilesan example from Asdex-Upgrade H-modes

1000

3000

5000

7000

9000

0 0.2 0.4 0.6 0.8ρ

t

Ti [ ]eV

3000

5000

7000

9000

AU shot #17219

5 MW NBI

5 MW NBI + 2 MW ECH

5 MW NBI + 2 MW ICH

Te

[eV]

If ICH heating does not modify R/LT = A hence confinement time degradation (vs P) physics is located in the pedestal; ECH heating modifies R/LT=A and core confinement drops.



0.09

0.11

0.13

0.15

4 5 6 7 8

ASDEX-Upgrade shot #17219

[ ]P MW

NBI

+NBI ICH

+NBI ECH

€

W = f (A,Wped ,nped

n,ε)





R/Lw scaling - statistical approach withthermal conduction model on PDB

€

nped

n

W

Wped

−1 =Aε

3+ .... A =

R

Lw

€

nped

n

W

Wped

−1 =1.4 I p1.15 BT

−0.07P−0.4 M eff−0.29 n0.06R−1.25ε−0.98k−2.8 fq

5.9







-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


Wped

nped

/nmean

W/Wped

-1





R/Lw scaling with thermal conduction modelon PDB data with no systematic error in Wped

€

nped

n

W

Wped

−1 =Aε

3+ .... A =

R

Lw

€

nped

n

W

Wped

−1 = −0.6 I p0.63 BT

−0.1P−0.7M eff0.86 n0.26R−0.08ε−1.0k−3.0 fq

3.67





No Errore sistematico



-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


nped

/nmean

W/Wped

-1

Wped



Conclusions• Statistical approach to core confinement is possible and

needed but profile stiffness must be accounted for.• An improved model for the "stiff energy" is possible

but this requires a more complex DB.• DB should contain ETG - ITG relevant plasma

parameters such for instance Te,i at ρ~0.5.• Global confinement and local heat transport studies

must be compared and common features understood to gain insight in prime principle physics.





Published results…



Mathfit-Wpedcalcolato.m



Offset due to systematic errors in Wped?



€

Wdia = Wpedn

nped

1+Aε

3+

(Aε)2

12+ .....

⎡

⎣ ⎢

⎤

⎦ ⎥





Energy Confinement timetime evolution

• At t=3 s ECH on • Energy confinement

time drops from

0=140 ms to

1=103 ms

• Scaling of not consistent with P-0.6

0.1

0.15

4 106

6 106

8 106

2.8 3 3.2 3.4 3.6 3.8

17219tau_tot P_TOT

time

0

1

June 2007

W(t) modelling

• Hand fit Wmhd solvingd/dt W= (P0+P1)-W/0 t<3.045 s

d/dt W= (P0+P1)-W/1 t>3.045 s

• Quite fast switch of 45 ms after the ECH switch on (less than 20 ms).

• Threshold in Te/Ti? Rotation? Not enough time resolution..

7 105

7.5 105

2.8 3 3.2 3.4 3.6 3.8

17219

Wmhd

1 = 0.103 s

0 = 0.140 s

time

Δ = 45.0 t ms0 = 0.14 s

τ1 = 0.103 s

P0 = 5 MW P

1 = 1.6 MW

June 2007

2.5 more MW of NBI added at t=5.5s in shot 17221

• NBI heating induces confinement time degradation.

• No change in Te/Ti

• Change in less sharp.• Scaling of consistent

with P-0.6.

0.1

0.15

4 106

6 106

8 106

5 5.2 5.4 5.6 5.8 6

17221tau_tot P_TOT

time

0

2

0

1

2

6 105

7 105

8 105

9 105

1 106

5 5.25 5.5 5.75 6

17221

Te/Ti rho~0.6 Wmhd

timeJune 2007

W/Wped Scaling should give critical gradient length of the

core

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2


Wcore

= W-Wped

W/Wped

- 1 (no offset)

€

nped

n

W

Wped

−1 =Aε

3+ ....

€

nped

n

W

Wped

−1∝ I pα 1 BT

α 2Pα 3M effα 4 nα 5Rα 6εα 7kα 8 fq

α 9

October 20 2008 Milano Core-Pedestal Energy Confinement. Empirical Scaling Laws and "stiff"...

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Transcript of October 20 2008 Milano Core-Pedestal Energy Confinement. Empirical Scaling Laws and "stiff"...