testing paleoclassical predictions against measured diii-d … wednesday/smith ttf_… · national...

Testing Paleoclassical PredictionsAgainst Measured DIII-D Pedestal Profiles

bySterling SmithwithR.J. Groebner, H.E. St. John, T.H. Osborne, and J.D. Callen*

*University of Wisconsin - Madison

Presented atthe Transport Task Force MeetingSan Diego, CA

April 6, 2011

NATIONAL FUSION FACILITYDIII–D

043-11/SS/jy


Outline

1. Description of database ofexperimental measurements

2. Description of the Paleoclassicalpedestal model

3. Paleoclassical predictions for thewhole database

4. Specific input and Paleoclassicalprofiles

5. Summary

Pedestal Database Measurements Come from aVariety of DIII-D H-mode Shots

NATIONAL FUSION FACILITYDIII–D 043-11/SS/jy

• Scans– ρ* scan for comparison with JET– EPED scaling tests

• shape• q95• βp

– ITER demo discharges• baseline• hybrid• steady state

• Data sources– ne and Te come from Thomson scattering– Zeff comes from ne and CER determination of Carbon

density– Data averaged over ~ 80–99% phase of multiple ELM

cycles


ne and Te Data are Fit by Modified Tanhfz Data are Fit by Spline

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fit =ped − o�

2 [ (1 + z*slo)e z − e − z

e z + e − z ] + ped + o�2

0

Pedestal Height

O�set Symmetry

Width

Slope

z ≡ 2sym − ρ

widρT ≡ sym Te

ρD ≡ sym ne


ne Tanh Symmetry Point Occurs Further Out for theDatabase than the Te Symmetry Point

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Green lineindicates equality

Local fueling mayaccount for ρD > ρ T


Paleoclassical Diffusion, Proportional toNeoclassical Resistivity, is a Minimum Transport

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• The main thrust of paleoclassical theory is that as poloidalmagnetic flux diffuses outward, it carries with it particles andenergy, which can be characterized by a single diffusioncoefficient, Dη ≡ ηnc

⎜⎜ /μ0, where the resistivity is the parallelneoclassical resistivity

• In this study ηnc⎜⎜ is evaluated based on equations given in

UW-CPTC 09-6R

• Because paleoclassical processes are only the minimumtransport processes, they are only dominant in the steepgradient region of the pedestal where other processes are lessdominant

• To compare the paleoclassical model of the electron pedestalto experimental measurements, we will evaluate Eqs. (1) & (2)(see next slide) at the symmetry point of the Te tanh fit ρT


Paleoclassical Predictions in the Pedestal:ne and ∇Te

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Electron density profile in the pedestal 1

ne(ρ) ∼a2 neDηV ʹ/a2

a+ ∫

a

ρNedρ

a2 DηV ʹ/ ¯

¯

a2ρ

(1)

Electron temperature gradient 2

−dTe

dρPe − (3/2)NeTe

(3/2)(V ʹDηnea2/a2)(2)

1UW-CPTC 10-6 Eq. (29)2UW-CPTC 10-6 Eq. (35)

∼


Definitions of Terms

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Across the Whole Database, PaleoclassicalPredictions of ∇Te|ρT are Fairly Close to Experiment

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Paleoclassicalpredictions are inthe ballpark ofexperimentalgradients

The line indicatesequality

avg(∇T pce /∇T exp

e ) =1.1 ± 0.6

Input & outputprofiles given onensuing slides forlabelled shots

-5 0 5 10 15 20 25 30 35 40Paleoclassical Te |ρT [keV/m]

0

10

20

30

40

50

Expe

rimen

tal

T e| ρ

T[keV

/m]

133137

136097

131499

136186

136068

138431

−∇

−∇


Te Predictions for Whole Database ShowDependence on Edge Electron Heat Flow

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Experimental ∇Teand paleoclassicalpredictions of ∇Teseem to betracking differentlywith edge power

Best agreement formoderate electronpower flows

-10

0

10

20

30

40

50

60

−∇T e

(ke

V/m

)

0 1 2 3 4Electron heat flow (MW)

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

(∇Tp

ce

/∇

Texp

e)|ρ T

-1 0 1 2 3 4 5 6 7Ion heat flow (MW)

Te gradients vs edge conductive heat flowsExperimental Paleoclassical


Across the Whole Database, Predictions of ne ρTOvershoot Experimental Measurements

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a(ρ > ρ T ) → a(ρT)

The line indicatesequality

avg(npce /nexp

e ) = 2.3 ± 0.5

Input & outputprofiles given onensuing slides forlabelled shots

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8Paleoclassical ne|ρT ; ¯ ¯a(a) → a(ρT) (1020/m3)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Exp

erim

ent

aln

e| ρ

T(1

020/m

3 )

133137

136097

131499

136186

136068

138431


ne Predictions for Whole Database DependGreatly on a at Edge

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Definition of npce

depends on a(a)in constant ofintegration

a varies more thanphysicallyreasonableoutside ρn ≈ 0.985

PC/XP Ratio:

– 4.9 ± 2(edge a)

– 2.3 ± 0.5(symmetry a)

0 1 2 3 4 5 6 7 8

Paleoclassical ne|ρT (1020/m3)

Exp

erim

ent

al n

e|ρ

T (1

020 /

m3 )

0.0

0.1

0.2

0.3

0.4

0.5

0.6

133137

136097

131499

136186

136068

138431

npce : a(ρ > ρT) → a(ρT)

npce : a(ρ > ρT) → a

Equality


Input Profiles: Shot 131499, Low ∇Tepc

Suspicious that Edge Ion Heat Flow >> Elec. Flow

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Ion quantities shown ingreen

Vertical line is ρT

Scalar inputs:

Shot 133137 is similar

Bt0=-1.9TR0=1.7 medge_elec_cond_energy_flow = 0.26 MWedge_ion_cond_energy_flow = 3 MWedge_part_flow = 4.4 x 1021/s

0.00

0.45

0.90ne [10 20/m3]

0.00

1.05

2.10 Te [keV]

1

2

3 Ze [ ]

2.5

6.5

10.5 q [ ]

-0.5

0.0

0.5Q net

e [MW /m3]

0

4

8Sn [10 21/m3/s]

0.48

0.54

0.60 r [m]

1.6

1.7

1.8 R [m]

0.6

0.7

0.8ρ [m]

0.00

0.45

0.90Γ [10 20/m2/s]

0.60

0.75

0.90H [ ]

1.50

2.75

4.00ρ|2R2

0/R2 [ ]

0.90 0.95 1.00ρn

1.5

7.5

13.5ρ|2 [ ]

0.90 0.95 1.00ρn

1.1

1.4

1.7R20/R

2 [ ]


Paleoclassical Predictions: Shot 131499, Low ∇Tepc

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Eq. (1) is sensitive to a atthe edge

–

The local source term Neis not a large contributor


Values ρT:

•

nexpe |ρT

= 0.37 ± 0.023npc

e |ρT= 0.66 ± 0.15

∇T expe |ρT = 22 ± 2.4

∇T pce |ρT = –2.5 ± 0.55

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

n e(1

020/m

3 )

nexpe

npce

npce ; a(ρ >ρT) → a(ρT)

npce ; Ne → 0,

a(ρ >ρT) → ¯

¯¯

a(ρT)

0.90 0.92 0.94 0.96 0.98 1.00ρn

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

T e(k

eV

)

Texpe Tpc

e


Input Profiles: Shot 136186, High ∇Tepc

High q, Low s>

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Vertical line is ρ T

Scalar inputs:

Bt0= -2 TR0 = 1.7 medge_elec_cond_energy_flow = 2.5 MWedge_ion_cond_energy_flow = 5.3 MWedge_part_flow = 3.6 x 1021/s

0.00

0.45

0.90ne [1020/m 3]

0.00

1.05

2.10 Te [keV]

1

2

3 Zeff [ ]

2.5

6.5

10.5 q [ ]

-0.5

0.0

0.5Qnet

e [MW/m3]

0

4

8Sn [1021/ m3/ s]

0.48

0.54

0.60 r [m]

1.6

1.7

1.8 R [m]

0.6

0.7

0.8 ρ [m]

0.00

0.45

0.90Γ [1020/ m2/ s]

0.60

0.75

0.90H [ ]

1.50

2.75

4.00ρ|2R2

0/ R2 [ ]

0.90 0.95 1.00ρn

1.5

7.5

13.5ρ|2 [ ]

0.90 0.95 1.00ρn

1.1

1.4

1.7R2

0/ R2 [ ]


Paleo Predictions: Shot 136186, High ∇Tepc

Low s → more Anomalous Transport

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The local source term Nehas a larger effect


Values at :ρT

>

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

n e[1

020/

m3 ]

nexpe

npce

npce ; a(ρ > ρ T) → a(ρT)

npce ; Ne → 0,

a(ρ > ρ T) → a(ρT)

0.90 0.92 0.94 0.96 0.98 1.00ρn

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

T e[k

eV

]

Texpe Tpc

e

nexpe |ρT

= 0.23 ± 0.013

npce |ρT

= 0.47 ± 0.054

−∇Texpe |ρT

= 18 ± 1.2

−∇Tpce |ρT

= 37 ± 2.9


Input Profiles: Shot 136068, Low ne, BT0; Ti > TeLow Edge Energy Flows

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Scalar inputs:

Shot 136097 is similar

Bt0= -1 TR0=1.7 medge_elec_cond_energy_flow = 0.56 MWedge_ion_cond_energy_flow = 0.43 MWedge_part_flow = 0.95 x 1021/s

0.00

0.45

0.90ne [1020/m3]

0.00

1.05

2.10 Te [keV]

1

2

3 Zeff [ ]

2.5

6.5

10.5 q [ ]

-0.5

0.0

0.5Qnet

e [MW/m3]

0

4

8Sn [1021/m3/s]

0.48

0.54

0.60 r [m]

1.6

1.7

1.8 R [m]

0.6

0.7

0.8ρ [m]

0.00

0.45

0.90Γ [1020/m2/s]

0.60

0.75

0.90H [ ]

1.50

2.75

4.00ρ|2R2

0/R2 [ ]

0.90 0.95 1.00ρn

1.5

7.5

13.5ρ|2 [ ]

0.90 0.95 1.00ρn

1.1

1.4

1.7R2

0/R2 [ ]


Paleo Predictions: Shot 136068, Low neTe and ∇Te Well Matched

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Values at :ρT

nexpe |ρT

= 0.37 ± 0.023npce |ρT

= 0.66 ± 0.15– ∇Texpe |ρT

= 22 ± 2.4– ∇Tpce |ρT

= −2.5 ± 0.55

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

n e(1

020/

m3 )

nexpe

npce

npce ; a(ρ >ρ T) → a(ρT)

npce ; Ne → 0,

a(ρ >ρ T) → a(ρT)

0.90 0.92 0.94 0.96 0.98 1.00ρn

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

T e(k

eV

)

Texpe Tpc

e


Input Profiles: Shot 138431, High ne Low Zeff

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Scalar inputs:

Bt0= -2.1 TR0=1.7 m

3.1 MW

2.8 MW21/s

0.00

0.45

0.90ne [1020/ m3]

0.00

1.05

2.10 Te [keV]

1

2

3 Zeff [ ]

2.5

6.5

10.5 q [ ]

-0.5

0.0

0.5Qnet

e [MW/ m3]

0

4

8Sn [1021/ m3/s]

0.48

0.54

0.60 r [m]

1.6

1.7

1.8 R [m]

0.6

0.7

0.8 ρ [m]

0.00

0.45

0.90Γ [1020/ m2/ s]

0.60

0.75

0.90H [ ]

1.50

2.75

4.00ρ|2R2

0/ R2 [ ]

0.90 0.95 1.00ρn

1.5

7.5

13.5ρ|2 [ ]

0.90 0.95 1.00ρn

1.1

1.4

1.7R2

0/ R2 [ ]


Paleo Predictions: Shot 138431, High neTe and ∇Te well Matched

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Values at :ρT

nexpe |ρT

= 0.53 ± 0.024npc

e |ρT= 1.5 ± 0.26

∇T expe |ρT

= 15 ± 1.3∇T pc

e |ρT= 20 ± 2.3

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

n e[1

020/

m3 ]

nexpe

npce

npce ; a(ρ > ρT ) → a(ρT)

npce ; Ne → 0,

a(ρ > ρT) → a(ρT)

0.90 0.92 0.94 0.96 0.98 1.00ρn

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

T e[k

eV

]

Texpe Tpc

e

Summary

DIII-D pedestal group has collected a database of profiles

Paleoclassical predictions for ne and ∇Te have been comparedto the database of profiles evaluated at the Te symmetry point ρT

The ratio of paleoclassical prediction to experimentalmeasurement is closer for ∇Te than ne

npce correlates well with nexp

e

npce depends heavily on the edge parameters a, Dη; not so

much on Ne

∇T pce depends heavily on the edge electron conductive power

flow

Future: Couple paleoclassical with TGLF to obtain anomoloustransport at top of pedestal


043-11/SS/jy

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