j.e. kinsey* g.m. staebler, r.e. waltz lehigh university
TRANSCRIPT
byJ.E. Kinsey*
byJ.E. Kinsey*
G.M. Staebler, R.E. Waltz
* Lehigh University* Lehigh University
Presented at theSherwood Fusion Theory Conference
Rochester, NY
April 24, 2002
Renormalization of the GLF23Transport Model & Burning Plasma
Projections on a Universal Curve of Q versus Tped
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Main Points
! GLF23 transport model has been renormalized
! Predicted fusion gain Q sensitive to temperature profile stiffnessand assumed auxiliary heat power
! Global formula that fits GLF23 fusion projections is found
! Fusion power scales with pedestal beta, Pfus ∝∝∝∝ (ββββped)2
! Ignition possible for reasonable pedestal beta values that areexpected to be MHD stable
! Need to know the power scaling and width of H-mode pedestalpressure in order to predict fusion Q accurately
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
GLF23 Transport Model Based Upon TurbulenceSimulations Shows Agreement With Profiles Across
Various Confinement Regimes! Statistics computed core stored energy (subtracting pedestal region) using
exactly same model used for ITB simulations
* T , T , v predicted for ITBs
φe i0.010
0.10
1.0
10
0.01 0.1 1 10
L-modeH-modeITB (NCS, OS, ERS, AT)
GLF
23 P
redi
cted
Wth
(M
J)
Experimental Wth
(MJ)
σRMS
= 12.2%129 discharges DIII-D, TFTR, C-mod, JET L-, H-mode, ITB
core stored energy
* 72 DIII-D, 20 JET, 28 TFTR, 9 C-mod
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Recent Gyro-kinetic Simulations of ITG/ETG TurbulenceMotivates a Renormalization of the GLF23 Model
! For parameters used to normalizeGLF23, gyro-kinetic ITG modesimulations predict a factor of 4 lowersaturation level than gyro-fluidsimulations
! ETG mode simulations show thatelectron thermal transport levels aresignificantly larger than whenassuming a square root of the massratio scaling from ITG simulations
! GLF23 refit using a 50 shot H-modedatabase from DIII-D, C-mod, JETwhere normalizing coefficients for ITGand ETG modes were adjustedseparately to minimize rms error instored energy
σσσσori = 10% """" σσσσrenorm = 8.7%
0.01
0.1
1
10
0.01 0.1 1 10GLF
23 P
redi
cted
Wth
(M
J)Experimental W
th (MJ)
σRMS = 8.7%
50 H-mode shots
DIII-DJETC-mod
CITG=0.27 CETG=4.8 New fit
(CITG/ETG =1.0 in original GLF23)
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Renormed GLF23 Model Does Not Agree as Well WithL-mode Profile Database Compared to Original Model
! Statistics computed for core stored energy (subtracting pedestal region)! RMS error increased from σσσσ =17% to 22%),
! Agreement better for DIII-D (σσσσ =21%->16%), worse for TFTR (σσσσ =10.5%->28%)geometric effects and/or TEM physics ?
0.01
0.1
1
101
0.01 0.1 1 10
DIII-DTFTR
GLF
23 P
redi
cted
Wth
(M
J)
Experimental Wth
(MJ)
σR M S
= 16.6%
43 L-mode discharges
ori GLF230.01
0.1
1
101
0.01 0.1 1 10
Experimental Wth
(MJ)
σR M S
= 22.4%renorm GLF23
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Renormed GLF23 Model Shows Agreement WithGyro-kinetic ITG Simulations of Cyclone Test Case
! Ion heat diffusivity via ITG modecomputed using GYRO gyro-kinetic code w/ adiabaticelectrons for Cyclone test case(Waltz, Candy)
! Original model, normalized togyro-fluid simulations,overpredicts diffusivity by morethan a factor of 3 at experimentalR/LTi
! Renormed GLF23 model showsexcellent agreement over a rangeof R/LTi for Cyclone parameters
0.0
5.0
10
15
20
0 3 6 9 12 15
GYROori GLF23 renorm GLF23
χ i / (c
sρ s2
/a)
R/LTi
R/LT
Cyclone case
Benchmark
* Dimits, et al., Phys. Plasmas 7, 969 (2000)
*
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Burning Plasma Projections
! The GLF23 model has been uniformly applied to ITER-FEAT, FIRE,and IGNITOR and the fusion performance assessed# Renormed model used# Temperature profiles predicted while computing the effects of ExB shear
and Shafranov shift stabilization# Toroidal rotation velocity assumed to be zero# Density profiles, equilibrium, heating sources taken as inputs# Assumed same plasma shape, safety factor profile# Alpha heating, Ohmic heating, Bremsstrahlung, synchrotron radiation
self-consistently computed
! Fusion power predicted for a range of pedestal temperatures
! Both conventional H-mode (flat density, monotonic q-profile) and ATscenarios (density peaking, reversed shear) considered
! Densities in FIRE and IGNITOR scaled so pedestal ββββ same as in ITERto keep αααα-stabilization at pedestal fixed
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Burning Plasma Design Parameters
Physical Qty IGNITOR FIRE ITER-FEAT
R (m) 1.33 2.14 6.20a (m) 0.46 0.60 2.00κ 1.80 1.80 1.80δ 0.40 0.40 0.40B (T) 13.0 10.0 5.30I (MA) 12.0 7.70
4.815.0 1.0n (10 m ) 8.5
Z 1.20 1.40 1.50P (MW) 10.0 20.0 40.0
T
P
eff
Aux
e
20 -3_
n / ne G 0.50 0.70 0.85
n = I /(πa ) Greenwald density limitG
2
P
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Fusion Projections Using Renormed GLF23Somewhat More Optimistic Than Original Model
! Increase in ETG mode stiffnesssomewhat offsets decrease inITG/TEM mode stiffness leading to asmall increase in fusionperformance
! Stiffness is a measure of how fastthe transport increases once thecritical gradient is exceeded
Stiff ➔ large diffusivity
Profiles unresponsive to additional power
! Pfus = 5 Pα , Q= Pfus /Paux
! Required Tped for Q=10 reduced by11% from 4.4 keV to 3.9 keV
! Q scales approximately as (Tped)2
0
2
4
6
8
10
12
14
16
0 1 2 3 4 5
Renorm GLF23
Ori GLF23
Qfu
s
Tped
(keV)
ITER-FEAT
Tped
for Q=10
reduced by 11%
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Fusion Projections From Competing Drift Wave BasedModels Sensitive to Stiffness of Core Transport
! GLF23 (stiff) and Multi-mode (lessstiff) transport models predict verydifferent levels of performance
Q ∝ (Tped )1.8 : GLF23
Q ∝ (Tped )0.6 : MM
! Both drift-wave based models thatagree with experimental dataequally well
! Models agree at high Tped butdiffer significantly at low Tped
! Identifying the true stiffness of thecore transport needs to beresolved ! Carefully designedexperiments are needed
0
5
10
15
20
0 1 2 3 4 5
GLF23
ITER-FEAT
MM
Q
Tped
(keV)
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Comparing Fusion Gain Q Between Various ProposedBurning Plasma Devices Can Be Misleading
! Predicted fusion gain, Q=Pfus/Paux, is highly dependent on assumed Paux
! Compare 3 devices at same βped for a given nped by changing density
! Need better method for comparing performance between devices
0
5
10
15
20
25
30
35
0 1 2 3 4 5
ITER (n/nG=0.85)
FIRE (n/nG=0.52)
IGNITOR (n/nG=0.36)
Qfu
s
Tped
(keV)
Renorm GLF23 Z
eff=1.0
0
5
10
15
20
25
10 20 30 40 50
GLF23
MM
Qfu
s
Paux
(MW)
Q ∝ (Paux
)-0.5
Q ∝ (Paux
)-0.9
ITER
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Pedestal Temperature for Sustaining H-mode Ignition (ITER)
! For Paux=40MW and ne/nG=0.85,Q=10 obtained at Tped=3.9 keV
! Auxiliary power in ITER at Q=10can be turned off and H-modemaintained at same Tped
! Ignition possible at Tped > 3.2 keVwhere pedestal power is higherthan H->L power threshold(PLH/2=25 MW)
! Profiles collapse when radiationlimit approached at minimum Tped
! Need Tped=CPped ! Pped=Pα-Prad+Paux
0
100
200
300
400
500
1 1.5 2 2.5 3 3.5 4
Paux
= 40 MW
Paux
= 0 MW
Pfu
s (M
W)
Tped
(keV)
ITER
Q=10P
ped=93 MW
Rad. collapse P
ped= 0
Pped
= 48 MW
Pped
=37 MW
H-mode collapse P
ped= 0.5P
LH = 25 MW (?)
igni
ted
//////
//////
///
σ
_
P = 2.54 M B n R a-1 0.82 0.58 1.0 0.81
LH
JEK - Sherwood 2002NATIONAL FUSION FACILITY
S A N D I E G O
DIII–D
Pedestal Temperature for Sustaining H-mode Ignition (FIRE)
! For Paux=20MW and ne/nG=0.7,Q=10 obtained at Tped=4.15keV
! Ignition possible at Tped > 3.3 keVwhere pedestal power is higherthan H->L power threshold(PLH/2=11 MW)
! Fusion gain similar to ITER forne/nG=0.7
Pped=Pα-Prad+Paux
_
_
0
50
100
150
200
250
300
1 1.5 2 2.5 3 3.5 4 4.5 5
Paux
=40 MW
Paux
=0 MW
Pfu
s (M
W)
Tped
(keV)
FIRE
Q=10P
ped=47 MW
Rad. collapseP
ped=0
Pped
=23 MW
Pped
=18 MW
H-mode collapseP
ped=0.5P
LH=11 MW ?
//////
//////
/////
igni
ted
JEK - Sherwood 2002NATIONAL FUSION FACILITY
S A N D I E G O
DIII–D
GLF23 Predictions Follow a Universal Curve With aFit to the Fusion Power That is Device Independent
! Seek simple formula characterizingfusion performance that is general
! Take Pfus ∝ ni2VF(T) where
V = κ(!a)2(2!R) is the volume
! Pfus from GLF23 scales as (Tped)1.8
! Define fusion power fit to GLF23 runs
Pfus= Vβped
2[B2I/(aB)]
2(ni/ne)
2Cform
where Cform is a form factor withdilution, peaking and critical gradientcorrections
Nfit
Cform= K (ne/nped,e)1.5
exp[2(2.15+(1- ni /ne) +.75(1+ν
-0.25))/(R/a)]
exp[2(+.00275Pnet (R/a)1.5
/(βped
0
Tped
1.5))
2 ]
with K=6.7x10-5, Pnet= Paux + Pα , βped = βped / (I/aB),ν=<ne>R/Tped
2
N
_
0.0
0.5
1.0
1.5
2.0
1.5 2.0 2.5 3.0 3.5 4.0
ITERFIREIGNITOR
Pfu
s/Pfu
s-fit
Tped
(keV)
fixed κ =1.8, q =3.095 95
* Fit at reference parameters
N
* revised after Sherwood
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
MHD Stability Constraints On Normalized Pedestal Beta
! MHD stability computed using
ELITE code (P. Snyder, P1C08)
! Limits due to intermediate-n
peeling-ballooning mode
instabilities
! Assuming a pedestal width of 0.03
times the minor radius sets a limitof βped=0.7N
0.00 0.02 0.04 0.06 0.080.0
0.5
1.0
1.5
2.0
pedestal width/minor radius (∆/a)
Nor
mal
ized
Ped
esta
l βN
ped=
βped
/(I/
aB)
Normalized Pedestal Stability Limits
ITER-FEATFIREIGNITOR
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Pedestal Beta Requirements for Fusion Performance
Device β0.5P
ITER-FEAT
FIRE
IGNITOR
25 0.70
11 1.08
23 ? 0.48
Device I/(aB)
ITER-FEAT
FIRE
IGNITOR
0.881.42
42.21.29
73.81.86
*
** P (MW), T (keV), B (T), n (10 m ), R (m), a (m)
*** n = 0.85n95 e
_
pedLH Pped
93
49
26
Q
10
10
10
Paux
40
20
10
nped
Pped
25-46
11-23
23-12
Pfus
230-368
171-104
Q
∞
∞
112-185
P = 2.54 M B n R a-1 0.82 0.58 1.0 0.81
LH20 -3
‡
‡ β range for Q=∞ : min @ 0.5 P , max @ Q=10 β
†
† IGNITOR is a limiter device,P scaling unkown
LH
0.85
0.70
0.50
ne /nG_
N
∞
β
0.56-0.70
0.87-1.08
0.59-0.48
pedN
w/ Paux Ignition
LH
ped
N
ped
N
NATIONAL FUSION FACILITYS A N D I E G O
DIII–D JEK - Sherwood 2002
Summary
! Motivated by recent gyro-kinetic simulations, the GLF23 model has beenrenormalized using a 50 shot H-mode database# Agrees well with ITG simulations for Cyclone test case
# RMS error reduced somewhat for H-mode profile database
# Less stiff -> small increase in fusion Q using renormalized model
! Predicted fusion gain sensitive to temperature profile stiffness# we need carefully designed experiments to test stiffness in plasma core
Q ∝ (Tped )1.8 : GLF23 Q ∝ (Tped )0.6 : MM
! Global formula fitting GLF23 fusion predictions has been found
! Fusion power scales as (ββββped ) 2
! Ignition possible for reasonable pedestal beta values that have beenshown to be MHD stable (widths near 3% of minor radius)
! We need to know the power scaling and width of the H-mode pedestalbeta in order to predict the fusion Q accurately