core-pedestal constraints on divertor design

Core-Pedestal Constraints on Divertor Design

ByA.W. Leonard

Presented toIAEA-TM on Divertor ConceptsVienna, AustriaNov. 4-7, 2019

2 IAEA-TM Div. Concepts, Vienna Sept. 2015

Upstream (midplane) constraints critical to improved confidence in future divertor design

• Divertor design must simultaneously accommodate core plasma as well as divertor target constraints– Divertor: q⊥≤10 MWm-3, Te≤ 5 eV, no transients (ELMs)– Core: High confinement, High b, etc.

• Divertor dissipation nonlinearly dependent on upstream boundary conditions; q||, nsep, ⨍imp (radiator)

– 𝑻𝒅𝒊𝒗 ∝𝒒∥

⁄𝟏𝟎 𝟕

𝒏𝒔𝒆𝒑𝟐 𝑳∥⁄𝟒 𝟕

𝟏6𝒇𝒓𝒂𝒅 𝟐

𝟏6𝒇𝒎𝒐𝒎 𝟐 , 𝒏𝒅𝒊𝒗 ∝𝒏𝒔𝒆𝒑𝟑 𝑳∥

⁄𝟔 𝟕

𝒒∥⁄𝟖 𝟕

𝟏6𝒇𝒎𝒐𝒎 𝟑

𝟏6𝒇𝒓𝒂𝒅 𝟐 , 𝒇𝒓𝒂𝒅 ∝ 𝒏𝒆,𝒅𝒊𝒗𝟐 𝒇𝒛

• Required divertor volume 𝑳∥ , or even need for an advanced divertor configuration is dependent on prediction of upstream boundary conditions!

• For discussion:– What is the status of predictive capability for upstream constraints?– What work is most urgent to improve our predictive capability?


Pedestal physics a critical aspect for prediction of upstream constraints in future tokamaks• 𝒒∥ at divertor entrance (SOL lq)

– Will pedestal turbulence expand SOL beyond existing lq scaling?– Will MHD stability expand SOL lq and/or limit upstream density?

• Accessible values of ⁄𝒏𝒔𝒆𝒑 𝒏𝒑𝒆𝒅– How does the pedestal density gradient respond to a radial ion flux?– What will be the core fueling rate setting the radial ion flux?

• Tolerable upstream seeded (radiating) impurity density, 𝒏𝒊𝒎𝒑,𝒔𝒆𝒑– Maximum core 𝑛CDE; 𝑃HIE ≥ 𝑓𝑃LM , Core MHD (NTMs), Fuel dilution– Accessible ⁄𝑛CDE,HIE 𝑛CDE,EIN dependent on pedestal density profile

• Other factors to consider– Divertor detachment control requirements; X-point sensitivity– Geometry; Triangularity, Double vs. Single null


Pedestal turbulence may drive SOL width beyond existing scaling

• How do we validate these models in regimes in existing devices where the drift width still dominates?– Scaling of turbulence characteristics?

XGC Modeling BOUT++ Modeling

Critical scaling parameter: 𝑩𝒑 ⁄𝒂 𝝆𝒊 ?


MHD stability may be a limit for narrow heat flux width during detached conditions

• MHD stability limit reached for nsep ~0.5nGW derived (Eich NF 2018):– ITPA lq scaling– lne~lTe

– acrit~2.5• Other observations

– Pedestal pressure often degrades for nsep ≥ 0.5 nGW

– SOL width increases with high density and detachment

– SOL limits may also be correlated with collisionality 0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.5

1

1.5

2

2.5

3

nsep / nGW

αse

p

W−AUGJET−CJET−ILWW−AUG Pellets#34613,H98>0.75#34613,H98<0.75#34971,H98>0.75#34971,H98<0.75

JET/AUG ∇psep

Eich, NF 2018


DIII-D finds similar ∇psep saturation at high power and high density

• Separatrix pressure gradient saturates for nsep ≥ 0.4 nGW

• Normalized pedestal pressure (EPD) does not degrade at high density

• High asep likely due to challenging Timeasurement– Ti from CVI CER compromised by edge

effects near separatrix– Main ion Ti measurements becoming

available0.0 0.1 0.2 0.3 0.4 0.5 0.6

Separatrix Density (nsep/nGW)

αse

p/αcr

it

0.0

0.5

1.0

1.5

2.0

2.52MW5MW

13MWPinjscan

Attached Detached

Normalized Separatrix Pressure Gradient∇pe,sep + ∇pi,sep


0.0 0.1 0.2 0.3 0.4 0.5 0.6Separatrix Density (nsep/nGW)

λ ne,

SOL/λ

q,IT

PA

0.01.0

2.0

3.0

4.05.0

6.0

7.02MW5MW

13MWPinjscan

Attached Detached

0.0 0.1 0.2 0.3 0.4 0.5 0.6Separatrix Density (nsep/nGW)

λ Te,

SOL/λ

q,IT

PA

0.0

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1.0

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2MW5MW

13MWPinjscan

Attached Detached

SOL lq expands at high density and high power

lTelne

• lTe:– 𝜆S~

UV𝜆WI at high collisionality

– lTe increases for nsep ≥ 0.3 nGW

• lne:– SOL lne broadens twice that of lTe

during detachment– Divertor density width increases

consistent with midplane lne

– Deteached divertor density increases only modestly with power


Questions and implications of SOL MHD stability remain

• Separatrix MHD stability limit could potentially improve divertor performance– Increased SOL lq would reduce q||into divertor– Could reduce required nsep and/or nimp required for detachment– Would result in lower divertor density during detachment

• Will MHD stability improve divertor performance in DEMO?– Will nsep ≥ 0.5nGW be consistent with DEMO pedestal density?– Will enhanced MHD ballooning transport degrade pedestal?


Separatrix density is a key variable for divertor design

• Divertor conditions depend nonlinearly on upstream density

– 𝑻𝒅𝒊𝒗 ∝𝒒∥

⁄𝟏𝟎 𝟕

𝒏𝒔𝒆𝒑𝟐 𝑳∥⁄𝟒 𝟕


𝟏6𝒇𝒎𝒐𝒎 𝟐 , 𝒏𝒅𝒊𝒗 ∝𝒏𝒔𝒆𝒑𝟑 𝑳∥

⁄𝟔 𝟕

𝒒∥⁄𝟖 𝟕

𝟏6𝒇𝒎𝒐𝒎 𝟑


– A small change in separatrix density can make a big difference• Core operational scenarios specify (at best) pedestal top density

– What fraction of nped can we assume in divertor design?– Existing devices exhibit nsep/nped ~ 0.3 - 0.7 (Quite a range!)

• What do divertor designers need from core/pedestal physics?– Specification of core fueling, e.g. pellets for tritium fueling, beam fueling, etc.– A model of pedestal density transport; predictive capability for pedestal profile

from given core and edge source


• Closed divertor (upper) reduces recycling neutrals from outboard divertor reaching the midplane

• For similar divertor conditions pedestal responds to lower ionization source with lower density gradient

Pedestal density transport was examined in DIII-D through divertor geometry changes

MDSplus, shot = 166033, run = EFIT01, time = 2440.00MDSplus, shot = 166070, run = EFIT01, time = 3700.00

Tue Aug 15 09:56:26 2017

DIII-D Radial ion flux inferred from OSM modeling

A. Leonard IAEA 2016


Reduced pedestal fueling allows access to divertor detachment at fixed nped

Reduced fueling à lower ∇ne,ped à higher nsep/nped à detachmentHow much higher nsep/nped can we expect in future tokamaks with reduced edge fueling?

0.0

0.2

0.4

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1.0

0.0

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n e(10

20m−

3 )

(a)

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1.0

T e(ke

V)

(b)

0.90 0.95 1.00ψn

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P e(kP

a)

(c)

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n e(10

20m−

3 )

(d)

010

20

30

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5060

T e(eV

)

(e)

0.98 1.00 1.02 1.04ψn

0

20

40

60

80

100

J sat(A/cm

2 )

(f)

Upstream profiles Target (downstream) profiles

MDSplus, shot = 166033, run = EFIT01, time = 2440.00MDSplus, shot = 166070, run = EFIT01, time = 3700.00

Tue Aug 15 09:56:26 2017


Pedestal transport model development a critical need for divertor design

• US has initiated a coordinated effort to address this issue (following talk)– Experimental effort to measure and quantify pedestal transport– Theory effort to develop pedestal transport models

• Can a coordinated international effort be launched?• What are the biggest challenges?

– Diagnostics– Interpretive modeling of diagnostics– Model development


Allowed seeded SOL impurity density is also uncertain

• Seeded impurity density key parameter for divertor design – Heat dissipation ~ ∝ ⨍imp

• Core (pedestal) impurity limits set by a several issues– Fuel dilution– Maximum core radiation Psep>PLH

– Changes to current profile, NTMs• Ratio of nimp,sep/nimp,ped dependent on pedestal density profile

– Neoclassical pinch increases nimp,ped/nimp,sep in existing devices– A pedestal density transport model is needed to determine nimp,ped/nimp,sep

in future tokamaks


• Fuel dilution limits maximum tolerable impurity density

• Maximum impurity density for heat flux dissipation

– Psep≥ aPLH

– Required Psep dependent on core scenario (still uncertain)

• Core impurities may trigger NTMs due to modified current profile

Maximum core impurity level set by several limits

PLH = 4.9x104ne,20

0.72Bt0.8S0.94

Alcator C-mod

A. Loarte PoP 2011


Impurity density may be limited by core MHD stability, below that for Psep≥PLH

• NTMs arise in high bplasmas with higher Z impurity seeding

• Core plasma MHD stability at high bvery sensitive to current profileNTM

Onset

RadiatedPower


Neo-classical transport across pedestal in future tokamaks increase SOL impurity density limit

• Pedestal neoclassical pinch dependent on ratio of density to temperature gradient

• Shallower pedestal density gradient allows for higher nimp,SOL/nimp,ped

• The neoclassical effect for lower Z seeded impurities is smaller but still likely important

νD⎛

⎝⎜

⎞

⎠⎟neo

∝ Z d ln ni( ) dr −Hd ln Ti( ) dr( )0

5

10

n e [1019

m-3

]

10 5 0x [cm]

-10

1

v/D [c

m-1

]

2 3 4n sep [1019m-3]

10-2 1

102

f W

Pedestal Density

Pinch Velocity

W density ratio

ITER SimulationIp=15 MA, Bt= 5.3 T, Tped=4.5 keV

R. Dux, Nucl. Mater. Energy 2017


Pedestal Degradation

Sensitivity of X-point to cooling, neutral flux, etc. also a factor in divertor design

Pre D2 Early Late

WMHD (MJ) 0.62 0.59 0.52

pe,ped(kPa) 3.4 2.7 1.9

ne,ped(1020m-

3)6.9 9.6 11.4

Te,ped(eV) 330 190 120

Steady degradation in pe,ped with increasing D2 should be expected at these parameters

- Pedestal MHD stability is on ballooning branch- Will peeling limited pedestals also degrade with

detachment?

Standard H-mode in DIII-D


X-point along with divertor conditions to be correlated with pedestal profile evolution

m

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Te (eV)

Te (eV)

Te (eV)

Te (eV)

Te (eV)

2000 3000 4000 5000Time (msec)

0

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246

123

ne (1020m-3)

ne (1020m-3)

ne (1020m-3)

ne (1020m-3)

ne (1020m-3)

0246

01230123yn=0.988 (0.4 cm Rmid)

yn=0.996 (0.1cm Rmid)


Other core-edge issues are also important

• X-point sensitivity to cooling, neutral flux, etc.– Requirements for divertor detachment control– Not adequately studied in core scenario development

• Transients– What transients from core must divertor design handle?

• Shaping– Triangularity and Double-null are two features which can

significantly affect divertor design• Others?

core-pedestal constraints on divertor design

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