J.E. Kinsey* G.M. Staebler, R.E. Waltz Lehigh University ...

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



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



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)



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



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)

*



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



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



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%



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)



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



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



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



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



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

J.E. Kinsey* G.M. Staebler, R.E. Waltz Lehigh University ...

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