testing paleoclassical predictions against measured diii-d … wednesday/smith ttf_… · national...
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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
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NATIONAL FUSION FACILITYDIII–D
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
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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
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NATIONAL FUSION FACILITYDIII–D
ne and Te Data are Fit by Modified Tanhfz Data are Fit by Spline
043-11/SS/jy
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
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NATIONAL FUSION FACILITYDIII–D
ne Tanh Symmetry Point Occurs Further Out for theDatabase than the Te Symmetry Point
043-11/SS/jy
Green lineindicates equality
Local fueling mayaccount for ρD > ρ T
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NATIONAL FUSION FACILITYDIII–D
Paleoclassical Diffusion, Proportional toNeoclassical Resistivity, is a Minimum Transport
043-11/SS/jy
• 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
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NATIONAL FUSION FACILITYDIII–D
Paleoclassical Predictions in the Pedestal:ne and ∇Te
043-11/SS/jy
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)
∼
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NATIONAL FUSION FACILITYDIII–D
Definitions of Terms
043-11/SS/jy
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NATIONAL FUSION FACILITYDIII–D
Across the Whole Database, PaleoclassicalPredictions of ∇Te|ρT are Fairly Close to Experiment
043-11/SS/jy
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
−∇
−∇
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NATIONAL FUSION FACILITYDIII–D
Te Predictions for Whole Database ShowDependence on Edge Electron Heat Flow
043-11/SS/jy
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
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NATIONAL FUSION FACILITYDIII–D
Across the Whole Database, Predictions of ne ρTOvershoot Experimental Measurements
043-11/SS/jy
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
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NATIONAL FUSION FACILITYDIII–D
ne Predictions for Whole Database DependGreatly on a at Edge
043-11/SS/jy
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
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NATIONAL FUSION FACILITYDIII–D
Input Profiles: Shot 131499, Low ∇Tepc
Suspicious that Edge Ion Heat Flow >> Elec. Flow
043-11/SS/jy
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 [ ]
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NATIONAL FUSION FACILITYDIII–D
Paleoclassical Predictions: Shot 131499, Low ∇Tepc
043-11/SS/jy
Eq. (1) is sensitive to a atthe edge
–
The local source term Neis not a large contributor
Vertical line is ρT
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
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NATIONAL FUSION FACILITYDIII–D
Input Profiles: Shot 136186, High ∇Tepc
High q, Low s>
043-11/SS/jy
Ion quantities shown ingreen
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 [ ]
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NATIONAL FUSION FACILITYDIII–D
Paleo Predictions: Shot 136186, High ∇Tepc
Low s → more Anomalous Transport
043-11/SS/jy
Eq. (1) is sensitive to a atthe edge
The local source term Nehas a larger effect
Vertical line is ρT
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
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NATIONAL FUSION FACILITYDIII–D
Input Profiles: Shot 136068, Low ne, BT0; Ti > TeLow Edge Energy Flows
043-11/SS/jy
Ion quantities shown ingreen
Vertical line is ρT
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 [ ]
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NATIONAL FUSION FACILITYDIII–D
Paleo Predictions: Shot 136068, Low neTe and ∇Te Well Matched
043-11/SS/jy
Eq. (1) is sensitive to a atthe edge
The local source term Neis not a large contributor
Vertical line is ρT
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
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NATIONAL FUSION FACILITYDIII–D
Input Profiles: Shot 138431, High ne Low Zeff
043-11/SS/jy
Ion quantities shown ingreen
Vertical line is ρT
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 [ ]
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NATIONAL FUSION FACILITYDIII–D
Paleo Predictions: Shot 138431, High neTe and ∇Te well Matched
043-11/SS/jy
Eq. (1) is sensitive to a atthe edge
The local source term Neis not a large contributor
Vertical line is ρT
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
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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
NATIONAL FUSION FACILITYDIII–D
043-11/SS/jy