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
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
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
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
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
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
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)
∼
NATIONAL FUSION FACILITYDIII–D
Definitions of Terms
043-11/SS/jy
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
−∇
−∇
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
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
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
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 [ ]
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
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 [ ]
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
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 [ ]
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
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 [ ]
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
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