simulations of passively stable, fully detached regimes in ... · j. wiley. “on heat loading,...

37
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-PRES-??? M.V. Umansky 1 , B. LaBombard 2 , M.E. Rensink 1 , D. Brunner 2 , T. Golfinopoulos 2 , A.Q. Kuang 2 , T.D. Rognlien 1 , J.L. Terry 2 , M. Wigram 3 , D.G. Whyte 2 1 Lawrence, Livermore National Laboratory, Livermore, CA 94550, USA 2 MIT Plasma Science and Fusion Center, Cambridge, MA 02139, USA 3 York Plasma Institute, Dept. of Physics, Univ. of York, York, YO10 5DD, UK Presented at 2 nd IAEA Technical Meeting on Divertor Concepts,13-16 November 2017, Suzhou, China Simulations of Passively Stable, Fully Detached Regimes in Long-Legged Divertor Configurations

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Page 1: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

ThisworkwasperformedundertheauspicesoftheU.S.DepartmentofEnergybyLawrenceLivermoreNationalSecurity,LLC,LawrenceLivermoreNationalLaboratoryunderContractDE-AC52-07NA27344.

LLNL-PRES-???

M.V. Umansky1, B. LaBombard2, M.E. Rensink1,D. Brunner2, T. Golfinopoulos2, A.Q. Kuang2, T.D. Rognlien1, J.L. Terry2, M. Wigram3, D.G. Whyte2

1Lawrence, Livermore National Laboratory, Livermore, CA 94550, USA2MIT Plasma Science and Fusion Center, Cambridge, MA 02139, USA

3York Plasma Institute, Dept. of Physics, Univ. of York, York, YO10 5DD, UK

Presented at 2nd IAEA Technical Meeting on Divertor Concepts,13-16 November 2017, Suzhou, China

Simulations of Passively Stable, Fully Detached Regimes in

Long-Legged Divertor Configurations

Page 2: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Outline

• Motivation:– Tokamakdivertorchallengerequiresinnovativedivertors

• Recentlypublishedresults:– Stablefully-detachedregimefoundincomputationalstudyoflong-leggeddivertors

• Latest workresults:– Analysisofsensitivityofdetachedregimetomodelassumptionsgivesmore

confidenceinthesemodelingresults

• Summary&Conclusions:– Detachedregimefoundinsimulationsoflong-leggeddivertors looks promisingfor

high-powertokamaks

2

Page 3: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

3

Divertorheatexhaustisgoingtobeamajorchallengefornextgenerationoftokamaks

• SOLwidthlSOL small(~1mm)Þ divertorheatfluxlarge

• ForconstantlSOL animportantfigureofmeritisP/R

qdiv =P

2πRλSOL∝PR

200 MW/m

150 MW/m

100 MW/m

50 MW/m

Near-termfacilities

ITER

NHTX(PPPL)

FDF (GA)

CTF(PPPL)

ARIES-ST

Exhaust power [MW] Major radius [m]

Page 4: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

4

Divertorheatexhaustisgoingtobeamajorchallengefornextgenerationoftokamaks

• SOLwidthlSOL small(~1mm)Þ divertorheatfluxlarge

• ForconstantlSOL animportantfigureofmeritisP/R

• Moreover,therecentlyfoundscalinglSOL ~ 1/Ipindependentofmachinesize*isunfavorableforlargetokamaks€

qdiv =P

2πRλSOL∝PR

200 MW/m

150 MW/m

100 MW/m

50 MW/m

Near-termfacilities

ITER

NHTX(PPPL)

FDF (GA)

CTF(PPPL)

ARIES-ST

Exhaust power [MW] Major radius [m]

*T.Eich etal.,2013Nucl.Fusion53093031

• Fornextgenerationtokamaksinnovativedivertorsolutionsareneeded!

Page 5: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Innovativedivertors consideredbyseveralgroupsinrecentyears

X-pointtargetdivertor[4]

[1]H.Takase,J.Phys.Soc.Japan,70,609,2001.[3]M.Kotschenreuther etal.,2004IAEAFEC,paper IC/P6-43.[2]D.D.Ryutov.Phys.Plasmas,14,064502,2007.[4]B.LaBombardetal.,Nucl.Fusion55,053020,2015. 4

X-divertor Very similar to the cusp divertor: !

“This extra downstream X-point can be created with an extra pair of poloidal coils… Each divertor leg (inside and outside) needs such a pair of coils. …The distant main plasma is hardly affected because the line flaring happens only near the extra coils.” M. Kotschenreuther, P. M. Valanju, S. Mahajan, J. Wiley. “On heat loading, novel divertors, and fusion reactors.” Phys. Plas. 14, 072502 (2007)

Nucl. Fusion 55 (2015) 053020 B. LaBombard et al

0 50 100 1500

2

4

6

8

10

B [ T

]

LH ITERLH ACT1

LH ACT2

400 600

Maximum possiblePsol B/R from device

Psol B/R at L-Hpower threshold

*

LH

Original ITER QDT=10operation point*

MAST

NSTX-U

DIII-D

KSTAR

EAST

JT-60SA

JETAUG

C-Mod 5.4T

C-Mod 8T

ADX 6.5T

ADX 8T

TCV

SST-1

q// ~ Psol B/R [MW-T/m]

LH ARC

Figure 6. B and PSOLB/R for world tokamaks. (Arrows for EAST and KSTAR account for planned upgrades.) In order to simulate divertorconditions of a reactor, both B and PSOLB/R must be matched. A compact, high-field tokamak is the most cost-effective way to achievethis, as shown by Alcator C-Mod attaining parameters close to the range of ITER, ACT1 ACT2 and ARC. A similarly constructed ADX canpush to high PSOL values at small cost, because of its small size.

Figure 7. RF antennas can take advantage of the low-PMI,‘quiescent’ SOL that forms on the HFS in double-null plasmas andthe dominant power exhaust through the low-field side (LFS) SOL(represented by red arrows).

associated with the edge plasma pedestal [39]. As discussedby Hutchinson and Vlases [3], by matching B, n and q∥ ofa reactor it is also possible, at least in principle, to perform

an approximate ‘divertor similarity experiment’ in which fivekey scale parameters (Te, ν∗ = Ld/λei, #d/λ0, ρi/#d andβ, with Ld =divertor field line length, λei =electron–ioncollisional mean free path, #d =SOL thickness, λ0 =neutralmean free path, ρi =ion Larmor radius, β = 2µ0nT/B2) areidentical to those of a reactor. The poloidal flux expansionand divertor leg length could be adjusted to do this. Inany case, the overall message is clear: matching absolutereactor divertor parameters (B, q∥, ndiv, Te,div) is necessary tostudy reactor-relevant physics regimes. Based on the recentmulti-machine empirical scaling of parallel heat flux [14],the parallel heat flux scales as q∥ ∼ PSOLB/R. Thismeans that B, n and PSOLB/R in an ADX should be madesimilar to that in a reactor. From figure 6, it is clear thata compact, high-field tokamak is the natural choice for anADX—it is the way to perform meaningful tests of advanceddivertor prototypes without constructing a full-scale reactor;it removes the uncertainty and risk in trying to extrapolatedivertor performance from extremely complex and uncertaincomputational models, developed and tested in regimes thatare far from those expected in a reactor.

5. Motivation: low-PMI RF actuators; efficientcurrent drive, heating needed (milestone #4)

5.1. Challenges

It is recognized that RF current drive and heating technologiesmust evolve into primary actuators for fusion reactors,replacing the roles that neutral beams now play in most devices.As stated in a 2007 US DoE [12] report (addressing ‘gap G-7’on page 190): ‘The auxiliary systems typically used in currentexperiments, while extremely useful tools, are not generallysuitable for a reactor. RF schemes are the most likely systemsto be used and will require significant research to achieve thelevels of reliability and predictability that are required.’ ForICRF antennas and LHCD launchers, it means placing theseactuators close to the plasma, where the challenge of efficientpower coupling competes with minimizing PMI. For long pulse

7

divertor near the null point, !, will scale as !!!0"b /!0#2/3, whereas in a usual X-point divertor onewould have !!!0"b /!0#1/2.

According to Eq. "2#, the coils are situated at the dis-tance b$2a / "a−b# from the null point. In a reactor, the di-vertor coils should be placed outside the radiation shield, i.e.,they cannot be situated too close to the plasma. As a repre-sentative value of b, we take b=0.3a; then the coils will besituated at a distance !0.5a%2.5 m from the null point.This seems to be sufficiently far, given that the shield thick-ness is !1 m "e.g., Ref. 6#. The current per divertor coil,according to Eq. "3#, will be !0.45I, with the total current!0.9I. For nonradioactive experimental facilities, one can,of course, consider much more compact snowflake divertors,with a smaller ratio b /a.

A disadvantage of a snowflake configuration is its topo-logical instability: if the plasma "or divertor# current do notexactly satisfy Eq. "3#, the configuration becomes either anX-point configuration &Fig. 2"a#' if Id" Id0, or a double-X-point configuration &Fig. 2"b#' if Id# Id0. The position of thestrike point and the overall structure of the divertor plasmachange substantially for a small variation of a plasma currentif the initial current is exactly Id0.

We suggest making the configuration more robust byoperating at a divertor current somewhat higher than Eq. "3#.As we show below, in this case, minor variations of theplasma current and divertor current do not cause any sub-stantial changes of the configuration, and, at the same time, astrong flux expansion still occurs.

The opposite possibility, namely running the divertor atthe current that is somewhat smaller than optimum, also pro-vides the robustness to the configuration and significant fluxexpansion. However, as one can see from Fig. 2"b#, in thiscase the divertor region contacts the plasma core not in onepoint but rather along a line &CD, Fig. 2"b#'. Although thepossible effect of the line contact is at present not quite clear,we prefer to stay within a more customary geometry of Fig.2"a#. One obvious concern regarding the configuration ofFig. 2"b# is that the line contact may have an adverse effecton impurity penetration from divertor to the plasma core. Wewill call the configuration of Fig. 2"a# "with the divertor cur-rent somewhat higher than Id0# “snowflake-plus,” and theconfiguration of Fig. 2"b# “snowflake-minus.”

For a more detailed analysis of the magnetic field struc-ture in the divertor region, one can use a Taylor expansion ofthe magnetic field near the point x=z=0. Some ratherlengthy algebra leads to the following result for the normal-ized magnetic field &B̂= "ac /2I#B, the CGS system is used':

B̂x = 1 −Id

I

4ab

4b2 + d2 +z

a ⌊1 + 4Id

I

a2"4b2 − d2#"4b2 + d2#2 ⌋

+z2 − x2

a2 ⌊1 − 4Id

I

a2"4b2 − d2#"4b2 + d2#2 ⌋ , "4#

B̂z =x

a ⌊1 + 4Id

I

a2"4b2 − d2#"4b2 + d2#2 ⌋ +

2xz

a2 ⌊1 − 4Id

I

a2"4b2 − 3d2#"4b2 + d2#2 ⌋ . "5#

If conditions "2# and "3# hold, only quadratic terms survive,and we recover a configuration shown in the inset in Fig. 1.If, however, as we are now assuming, the divertor current issomewhat higher than Id0,

FIG. 1. A snowflake divertor. The separatrix near the null point forms acharacteristic hexagonal structure "an inset# reminiscent of a snowflake. Thedistances are measured in units of a "which is the distance between the nullpoint and the conductor imitating the plasma current#. The thick line repre-sents the separatrix; the thin lines outside and inside the separatrix representflux surfaces whose distance is 0.002a from the separatrix in the equatorialplane "i.e., 1 cm for the device with a=5 m#. At the scale of the figure, the1 cm of distance in the main SOL is too small to be resolved, whereas thedistance of the outer flux surface from the null point is approximately80 cm. In other words, the broadening of the scrape-off layer near the nullpoint is very large.

FIG. 2. The shape of the separatrix for the case in which the divertor currentis five percent higher "a# and five percent lower "b# than the current Id0, Eq."3#. We call the first of them “snowflake-plus” and the second “snowflake-minus.” Shown by the light line in "a# is the separatrix of a “standard”X-point divertor with the upper part of the separatrix not much differentfrom that of the snowflake-plus divertor with $=0.05. We compare thesetwo configurations in terms of the flux expansion properties in Fig. 4.

064502-2 D. D. Ryutov Phys. Plasmas 14, 064502 !2007"

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:128.15.195.22 On: Tue, 31 Dec 2013 22:59:19

Cuspdivertor[1]

Snowflakedivertor[2]

X-divertor[3]

5

Page 6: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Divertorparametersareconstrainedbyoveralltokamakdesign;butthereareafewdegreesoffreedomleftfordivertor

Lmax

Ld

λ

a

R Forgiventokamakdesignonecannotchange:• Exhaustpower• Majorradius• Minorradius• SOLwidth

But(withinsomelimits)onecanchange:• Divertorplatetilt/shaping• Divertorleglength• Divertorpoloidalfluxexpansion• Divertormagneticfieldtopology

6

Page 7: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

7

Increasing plasma-wetted area Aw geometrically is limited for given target major radius Rt

D.D.Ryutov etal.,Proc.2008FusionEnergyConf.,PaperIC/P4-8P.Valanju etal.,Phys.Plasmas16,056110,2009

q||γ

α

• For g<g0»1o - hot-spotformationduetosurfaceroughness

• Atminimumangleg=g0 Aw»2pRt [(lmid/g0) (Bp/Bt )mid ]• ForfurtherincreaseofAw largerRt needed*

Purelygeometricsolutionsforinnovativedivertorarelimited!

• Aw canbeincreasedbyplatetiltingandpoloidalfluxexpansion

• Foreithermethod,grazingangle g betweensurfaceandtotalBbecomessmall

Page 8: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Divertordetachment:plasmastaysawayfromplasma-facingcomponents,cushionedbyneutralgas

• Detacheddivertorwillberequired forreactor– reductionofheatfluxattarget– suppressionoferosion

• Challengeofdetachedoperation:– Needstable,controllablestate– Needlargeoperatingwindow– Needtomaintaingoodpedestal/core

8

Te fromdivertorThomson

A.McLeanetal.,APSDPP2015

Page 9: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Divertordetachment:plasmastaysawayfromplasma-facingcomponents,cushionedbyneutralgas

• Detacheddivertorwillberequired forreactor– reductionofheatfluxattarget– suppressionoferosion

• Challengeofdetachedoperation:– Needstable,controllablestate– Needlargeoperatingwindow– Needtomaintaingoodpedestal/core– FulldetachmentoftenleadstoMARFE

� radiationnearmainX-point� degradationofcoreconfinement

9

Te fromdivertorThomson

A.McLeanetal.,APSDPP2015

M.Fenstermacheretal.,reconstructedCIIIdatafromTVcamerasonDIII-D

Page 10: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

UEDGEisappliedtofourtokamakdivertorarrangementsbasedonsame(orsimilar)magneticconfigurations

10

• TokamakedgetransportcodeUEDGE[1]findsasteadystatesolutionofplasmafluidequationsinedgedomain

• UEDGEdomaincanincludeasecondaryX-point– importantformodelinginnovativedivertors

• UEDGEsetupusedhereisbasedondesignofADXtokamak[2]

[1]T.D.Rognlienetal.,J.Nucl.Mater.196–198,347(1992)[2]B.LaBombardetal.,Nucl.Fusion55,053020(2015)

• SVPD – StandardVerticalPlateDivertor• SXD – Super-XDivertor• XPTD– X-pointTargetDivertor• LVLD – LongVerticalLegDivertor

symmetry plane

SVPD

XPTD

SXD LVLD

symmetry plane

Z [m

]

R [m] R [m]

Z [m

]

1

3

2

4

Page 11: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

UEDGEmodelissettomatchprojectedADXdesign

11

• Modeledcasesbasedongeometry&parametersfromADXtokamakdesign[1]� MHDequilibrium� Powerintolowerhalf-domainP1/2� Densityatseparatrix~0.5e20m-3

� SOLprofileswidth

• UsingfullyrecyclingwallB.C.onallmaterialsurfaces

• UsingradiallygrowingdiffusioncoefficientDtomatchtheexpecteddensityprofilewidth~5mm

• Spatiallyconstantce,i issufficienttoachieve~3mmwidthofmid-planeTe,i

Mid-planeprofiles

[1]B.LaBombardetal.,Nucl.Fusion55,053020,2015.

1.0

0.5

0

NeTe

-4 -2 0 2 4 6 8 10 12R-Rsep [mm]

300

200

100

0

1020

[m-3

] [m

2 /s]

5.0

4.0

3.0

2.0

1.0

0

χe,i

D

[eV]

Page 12: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Results for XPTD, power P1/2 = 3.0 MW

12

Page 13: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Results for XPTD, power P1/2 = 1.6 MW

13

Page 14: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Results for XPTD, power P1/2 = 0.6 MW

14

Page 15: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Results for SXD, power P1/2 = 1.2 MW

15

Page 16: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Results for SXD, power P1/2 = 0.8 MW

16

Page 17: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Results for SXD, power P1/2 = 0.6 MW

17

Page 18: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Results for LVLD, power P1/2 = 1.2 MW

18

Page 19: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Results for LVLD, power P1/2 = 0.8 MW

19

Page 20: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Results for LVLD, power P1/2 = 0.6 MW

20

Page 21: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

VaryinginputpowerintoSOLshowshowtransitiontodetachmentdependsondivertorconfiguration

21

• Largeoperationalwindowwithdetacheddivertor(Tmax<5ev)foundforallthreelong-leggedconfigurations[1]

• Forstandarddivertor(SVPD),detachedplasmasolutionmayexistbutatratherlowinputpower

• Radiallyorverticallyextendedouterlegisgoodfordetachedoperation

• Longverticalleg(LVLD)achievesdetachmentataboutsamepowerasradiallyextendedleg(SXD)

• SecondaryX-pointinouterleg(XPTD)extendsdetachedoperationwindow

XPTD: plate 2 - top, plate 4 - bottom

P1/2 = power into the lower half-domain

Tmax onouterplate[s]vs.P1/2

[1]M.V.Umanskyetal.,Phys.Plasmas,24(5),2017.

Page 22: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Analysis needed to address important questions for these numerical solutions

• Whatisinterplayofmodelphysicstermsinthesedetachedregimes?

• Whatisgoingonwithplasma&neutraldensity,momentum,energyflux?

• Whatsetspositionofdetachmentfront?

• Whatarelimitsofpowerhandlingcapability?

• Howsensitiveisthisequilibriumtomodeldetails(impurity,neutrals)?

• Canthisregimebescaledtoreactorparameters?

22

Page 23: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Analysis of plasma & neutral density fluxes in divertor leg show stagnant poloidal flow picture

• Oneachsurfaceboundingthelegdomainionfluxismatchedbyopposingneutralflux

• Poloidalfluxesentering/leavingdomainaretinycomparedtoradialfluxes

• SOLflowisstagnant– why?

• Needtoanalyzeparallelmomentumbalance

Analyzingarepresentativecase:

Γ=180x1020 [1/s]

Γ=23x1020[1/s]

Γ=0.6x1020 [1/s]

Γ=6.5x1020 [1/s]

23SXD,P1/2=0.6MW

Page 24: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Plasma pressure conservation relation is helpful for understanding plasma parallel force balance

pei +miniui||uiθBp B

+ Rψ + Rη + Rin = const

pei +mini ui||

2 ≈ const

∂∂tmini ui||( )+∇• mini

!uiui|| −η!∇ui||( ) = −∇||pei −mininn Kcx ui|| −un||( )−mi Srui|| +mi Siun||

Integrationalongfieldlineleadsto“conservationlaw”

Radialtransport

Neutralforce

Plasmaviscosity

ReducedversionsimilartoBernoulliequation

Thermalpressure

Rampressure

Fin||

24

Page 25: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Parallel plasma pressure drop in the leg is mainly balanced by CX interaction with neutrals

Plasmapar.momentumbalancedby• Inradiatingzone:neutrals,viscosity,and

convection• Belowradiatingzone:neutrals

Analyzingarepresentativecase:• SXD,P1/2=0.6MW

B

A

Pres

sure

[Pa]

Poloidal index

P+ρv2

P...+Rin

...+Rη

...+Rψ

Target plate

A B

1.0e19

3.0e19

1.5e192.0e19

Ng [m-3]

20

5

1Te [eV]

Ni [m-3]1e19

1e203e19

3e20

1e1

1e71e51e3

Prad [W m-3]

25

Page 26: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Analysis of energy fluxes in divertor leg shows that most entering energy ends up on outer divertor wall

• About1/2ofpowerenteringouterleggoestoouterwallwithplasmaandneutralenergyflux

• Therestofpowerenteringouterleg islostwithimpurityandhydrogenradiation

Analyzingarepresentativecase:

qpol=187 kW

q⊥ei=54 kWq⊥bind=39 kW

qpol=3 kW

q⊥ei=10 kW

q⊥bind=5 kW

Radiation: C - 42 kW, H - 34 kW

26

Page 27: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Neutral particles confinement controls position of detachment front

Analyzingarepresentativecase:• SXD,P1/2=0.6MW Plasmarecyclingcoef:100%

Neutralalbedo:100%

1.0e19

3.0e19

1.5e192.0e19

Ng [m-3]

20

5

1Te [eV]

Ni [m-3]1e19

1e203e19

3e20

1e1

1e71e51e3

Prad [W m-3]

27

Page 28: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Neutral particles confinement controls position of detachment front

Plasmarecyclingcoef:100%

Neutralalbedo:99.5%

Analyzingarepresentativecase:• SXD,P1/2=0.6MW

Prad [W m-3]1e1

1e71e51e3

Ni [m-3]1e19

1e203e19

3e20

20

5

1Te [eV]

1.0e19

3.0e19

1.5e192.0e19

Ng [m-3]

28

Page 29: Simulations of Passively Stable, Fully Detached Regimes in ... · J. Wiley. “On heat loading, novel divertors, and fusion reactors.” As stated in a 2007 US DoE [Phys. Plas. 14,

Neutral particles confinement controls position of detachment front

Plasmarecyclingcoef:100%

Neutralalbedo:99.5%

Analyzingarepresentativecase:• SXD,P1/2=0.6MW

Prad [W m-3]1e1

1e71e51e3

Ni [m-3]1e19

1e203e19

3e20

20

5

1Te [eV]

1.0e19

3.0e19

1.5e192.0e19

Ng [m-3]• Similarresultsifreducing

plasmarecyclingcoefficient

• Neutralparticlesconfinementinthelegappearstocontroldetachmentfrontlocation

29

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Transportmodelvariation:changingspatialformsofc, Dinouterlegleadstosomequantitativedifference

30

Originaltransportmodel Newmodel:c=D=1.0inouterleg

Therearecertainquantitativechangesbutqualitativelythepictureisthesame

-4 -2 0 2 4 6 8 10 12R-Rsep [mm]

[m2 /

s]

5.0

4.0

3.0

2.0

1.0

0

χ⊥e,i

D⊥

• Original:spatiallydependentD(y)andc=0.25m2/sforwholeedgedomain

• New:uniformc=D=1.0inouterleg

New:inouterlegc=D=1.0

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ChangeofradialtransportandouterwallB.C.toconvectivemodelleavesoverallqualitativepicturethesame

31

• InsteadofdiffusiveradialtransportusingradialpinchadvectionforNi

• B.C.onouterwall:insteadofDirichlet(“D”)usingextrapolation(“X”)forNi,Te,i

• NewB.C.andtransportmodelmean“lessforcing”ofthesolution

• Butqualitativelytheresultsstillhold–fully-detachedstablesolutionsexist,withthresholdpowerandparameterssimilartodiffusivetransportcase

Radial profiles across leg

2

1

Ψpol [m]

Te [e

V]

Innerwall“D”

Outer wall “X” 1

2

Ψpol

Ψpol

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Increasingcarbonimpurityfractionfrom1%to2%leadstomodestincreaseofdetachmentpowerthreshold

32

1%carbonimpurity

ForLVLDandSXD,increasingcarbonimpurityfractionleadstosomeincreaseofdetachmentthresholdpower;notmucheffectonSVPD

2%carbonimpurity

Iffullyionized:

1%C=>Zeff=1.3

2%C=>Zeff=1.6

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WithNeimpurity,fullydetacheddivertorsolutionsarefoundtoo,similartothosewithCimpurity

P1/2=0.9MW,1%Neimpurity

• Using1%Ne(Zeff≤1.9)forSXDADXcase• Overallresultsaresimilarto1%Cimpuritycase• WithNe,radiationzoneextendsmorepoloidally• Te,i atX-pointislittleaffected,forrangeofP1/2

33

SXDADXcasew/1%Nevs.1%C

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Summaryandconclusions

34

• Several tightly baffled long-legged divertor configurations have been studied with UEDGE for parameters matching the design of ADX tokamak

• Stable steady state fully detached regime is found for long-legged divertors� Much higher power threshold to enter detachment than for standard divertor� Detachment front stays far away from the main X-point, no problem for core

• Key physics for this detached divertor regime combines strong convective plasma transport to outer wall, confinement of neutral gas in divertor volume, geometric effects including secondary X-point, and atomic radiation.

• With several essential model assumptions varied, the overall picture of stable fully-detached regime in tightly-baffled long-legged divertor still holds

• These simulations results suggest possibility of stable fully-detached operation for high-power tokamak

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Backups

35

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36

SOLradialdensitytransportisnon-diffusive,dominatedbyballistictransportofcoherentfilamentarystructures

1) M.V.Umansky,S.I.Krasheninnikov,B.LaBombardetal.,Phys.Plasmas,5(9):3373–3376,19982) B.LaBombard,M.V.Umanskyetal.,Nucl.Fusion,40(12):2041–2060,20003) S.I.Krasheninnikov,Phys.Lett.A283,368,2001

• Inlast20years,non-diffusivenatureofedgeplasmatransportwasestablished,startingfromseveralearlypapersfromC-Mod[1,2]

• Time-averageSOLtransportcanberepresentedbyradiallygrowingD(y)orradialoutwardpinch[2]

• Directlyconnectedtodynamicsoffilamentaryplasmastructures(blobs)intheedge[3]

• Overwhelmingevidencefrommanytokamaksandotherdevices,supportedbyvariousmodeling

FromTerryetal.,Phys.Plasmas10,1739(2003)

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37

Long-leggeddivertoriscurrentlypursuedforARCfusionreactordesign

1. B.N.Sorbom etal.,FusionEngineeringandDesign,100,378–405(2015)2. M.Wigram,B.LaBombard,M.V.Umanskyetal.,presentedatPET2017conference,submittedtoPPCF

• ARCexhaustpowerintoSOLisprojectedtobe~100MW[1]

• Inthefirstmodelingstudy[2],fullydetachedARCdivertorsolutionisfoundforexhaustpower88MW

• 0.5%Neimpurityused