Edge plasma modeling for divertor conﬁgurations with ... · LH ACT2 400 600 Maximum possible Psol...

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore Na?onal Security, LLC, Lawrence Livermore Na?onal Laboratory under Contract DE-‐AC52-‐07NA27344.

LLNL-‐PRES-‐643674

M.V. Umansky

Acknowledgments: M.E. Rensink, T.D. Rognlien D.D. Ryutov (LLNL) B. LaBombard, D. Brunner, J.L. Terry, D.G. Whyte (MIT)

Presented at BOUT++ Workshop, LLNL, Livermore, CA, Dec 16-18, 2015

Edge plasma modeling for divertor configurations with secondary x-points"

Outline

•  Divertor configurations with secondary X-points

•  Snowflake divertor experiments

•  X-Point target divertor

•  Topology and grids for edge domain with two x-points

•  UEDGE analysis of near-snowflake divertor configurations

•  UEDGE analysis of X-point target divertor configuration

•  Summary/Conclusions

2

Outline








3

4

Configurations with a secondary X-point in divertor considered by many groups in recent years; for example

[1] H. Takase, J. Phys. Soc. Japan, 70, 609, 2001. [3] M. Kotschenreuther et al., 2004 IAEA FEC, paper IC/P6-‐43. [2] D.D. Ryutov. Phys. Plasmas, 14, 064502, 2007. [4] B. LaBombard et al., Nucl. Fusion 55, 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

X-divertor [3]" X-point target divertor [4]"

Cusp divertor [1]" Snowflake divertor [2]"

SF+ SF-‐

Outline








5

Experiments on TCV tokamak indicate that enhanced transport zone may exist near the null-point

6

Large fracXon of power flows to secondary strike points •  when two X-‐points get closer •  more during ELM strike

Core

σ=D/a

X2

SOL

prim. SP1

(HFS)

sec. SP2 sec. SP3

prim. SP4

(LFS)

Primary

separatrix

Secondary

separatrix

Figure 1. Schematic of a ‘SF’ FRQÀJXUDWLRQ, indicatinJ the SULPDU\and VHFRQGDU\ x-points (X 1, X 2), the FRUUHVSRQGLQJ VHSDUDWULFHV, theVFUDSH�Rff OD\HU, the dimensionless 6)�SUR[LPLW\ SDUDPHWHUσ = D/a , and the labellinJ of the SPs.

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

σ

P SP3/P

SP1

Power redistribution

Lí mode (LP)ELM peak (IR)

Límode: 5% at σ = 0.4

Hímode: 40% at σ = 0.4

Figure 12. PSP3/P SP1, which is used as a measure for the powerredistribution, as a function of σ in both L-mode and at theELM-peak in H-mode. At a similar σ , the exhaust power reachesthe secondary SP far more efÀFLHQWOy during ELMs (high SOLpressure) than in L-mode (low SOL pressure).

~

~

Figures from Vijvers et al, NF 2014

σ -‐ distance between x-‐points

DIII-D: heat and particle fluxes shared among strike points in snowflake divertor (Soukhanovskii – FEC ’14)

Outline








8

X-point target divertor is similar to the super-X divertor,but with the second X-point in the plasma volume

XPTD: LaBombard et al. 2013 Bull. Am. Phys. Soc. 58 63, and Nucl. Fusion 55, 053020, 2015. SXD: P. Valanju et al., Phys. Plasmas 16, 056110 (2009)

•  Like Super-‐X, exploits 1/R geometric reducXon of divertor heat flux •  May produce stable ‘X-‐point MARFE’ in the divertor chamber •  Used as a part of the ADX tokamak concept

X-‐point X-‐point

9

X-point target divertor study is motivated by the ADX tokamak concept discussed at MIT PSFC

10

•  ADX = Advanced Divertor and RF tokamak eXperiment* •  Designed to address criXcal gaps on pathway to next-‐step devices •  Advanced divertors •  Advanced RF actuators •  Reactor-‐prototypical core plasma condiXons

*B. LaBombard et al., Nucl. Fusion 55, 053020, 2015.

Outline








11

Topological classification of configurations with secondary x-point in the divertor

12 Ryutov et al., PPCF 52 (2010) 105001

•  Derived from local expansion for inexact snowflake •  Applies to any configuraXon with secondary x-‐point •  θ = angle between X-‐point bisector and horizontal axis •  In addiXon to shown six cases, there are mirror reflecXons of cases b,c,d,e

Recent upgrades made in UEDGE include generalization of computational subdomains and mesh generation

13

SF-‐

x x

x

x

SF+

3 mesh regimes 0 < θ < 30o

30o < θ < 60o

60o < θ < 90o

Unique indexing rules for each regime completed

θ = angle between X-point bisector & horizontal axis

From the point of view of domain topology and grid connectivity there are two distinct SFM regimes

14

4

3 A1#2% A2#3% A3#4% A4#5% A5#6% A6#7% A8#9% A9#10% A10#11%

2 B1#2% B2#3% B3#4% B4#5% B5#6% B9#7% B8#9% B6#10% B10#11%

1 C1#2% C2#3% C3#4% C4#5% C5#6% C9#7% C8#9% C6#2% C10#11%

0 1& 2& 3& 4& 5& 6& 7 8 9& 10& 11& 12&

�1

�2

�3

�4

�5

�6

�7

�9

�8

�9�10

�11

A BC

ABC

AB C ABC

AB

C

A

B C

ABC

A

BC

A

B

C

�6�2

�7

�8�11

�10

�

�

�

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�

6B

7B

10C

11C

7C

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SFM2 – From core boundary down grad(ψ) can only get to SOL boundary

SFM1 – From core boundary there is a path down grad(ψ) to PF boundary

Interactive Grid Generator iGrid (under continuing development) has been used for constructing meshes

15

•  Variety of flux surface geometry is a challenge for tokamak edge grid generaXon

•  Human eye is sXll the best

tool for recognizing complex panerns

•  In iGrid the user guides the code by indicaXng with the mouse some needed reference points and direcXons

Orthogonal grids for SFM1 and SFM2 are generated for analytic “3-wire” geometry

16

SFM2 – From core boundary down grad(ψ) can only get to SOL boundary

SFM1 – From core boundary there is a path down grad(ψ) to PF boundary

Real tokamak geometry in near-snowflake configuration makes a challenge for grid numerics

17

Extremely fast convergence of flux surfaces Actual DIII-‐D geometry

Outline








18

UEDGE* (Unified EDGE code) solves a system of fluid equations in axisymmetric tokamak geometry

€

∂∂t(ni) + ∇ • (ni

u i) = −Sr + Si

niu⊥ = −D⊥i∇⊥ni

∂∂t(mniu||i) + ∇ • (mniu||i

u i −ηi∇u||i) = −∇||Pi + mnN niKcx (u||N − u||i) + mSru||N −mSiu||N

∂∂t(3/2neTe ) + ∇ • (5

2neTe u e + q e ) =

u e •∇(3/2neTe ) −Πe •∇ u e + Qe

∂∂t(3/2niTi) + ∇ • (5

2niTi u i + q i) =

u i •∇(3/2niTi) −Π i •∇ u i + Qi

q⊥ = −n χ⊥∇⊥T

∂∂t(nN ) + ∇ • (nN

u N ) = Sr − Si

nN u⊥N = −D⊥N∇⊥nN

∂∂t(mnN u||N ) + ∇ • (mnN u||N

u N −ηN∇u||N ) = −∇||PN −mnN niKcx (u||N − u||i) −mSru||N + mSiu||N

∇ • J(φ) = 0

J|| =en

0.51mνBx

B1n∂Pe

∂x− e∂φ

∂x+ 0.71∂Te

∂x+

, -

.

/ 0

Jr =σ⊥Er

φ =−Te

eln 2 π

J|| − enu||ienvte

+

, -

.

/ 0

3

4 5

6

7 8

plasma density"

ion || momentum"

electron thermal energy"

charge conservation"

ad-hoc radial transport"

neutral density"

sheath bound. cond."

neutral || momentum"

ion thermal energy"

*T. D. Rognlien et al., J. Nucl. Mater. 196–198, 347 (1992) 19

UEDGE SFM1 mesh for DIII-D shot 155479

X-‐point separaXon/ minor radius σ  = 0.1/0.5 = 0.2

50% greater mesh resolution used for simulations

VerXcal posiXon

(m)

Major radius (m)

SP1 SP2

SP3

SP4

2D UEDGE SF solutions for 2% carbon show strong variations across separatrices; radiation is well spread

ni Prad

Te Pp

Plate heat-fluxes are < 2 MW/m2; only radiative flux is visible in the middle between two strike points (2% carbon)

Distance across plate [m]

DIII-‐D 155479

SP1 SP2

SP3

SP4

UEDGE

Convective cell formation near null dubbed “the churning mode” may be responsible for heat redistribution*

A B

C D

*D.D. Ryutov et al., Physica Scripta 89, 8, 088002 (2014) ** M.V. Umansky and D.D. Ryutov, submined (2015)

g

T1 T2

x

y

6Z

Similar to thermal convecXon due to crossed gravity and temperature gradient

Driven by crossed magneXc curvature and grad(P) near null where poloidal beta is large Solving plasma fluid equaXons demonstrates formaXon of the churning mode**

Outline








24

Mesh constructed in UEDGE by combining two lower-‐half single-‐null domains (with scripts developed by M.E. Rensink) Use UEDGE fluid transport model •  Fluid neutrals (inerXal) •  Fixed fracXon impurity radiaXon •  No drips •  Four orthogonal target plates •  100% recycling on all walls Use geometry & parameters from LaBombard et al., NF 2015 •  MHD equilibrium provided by MIT •  Density at separatrix ~ 1e20 m-‐3

•  Power into lower-‐half domain 1-‐5 MW 1 4

2 3

ADX MESH #5

symmetry plane

0.4 0.6 0.8 1.0 "R (m)"

0"

0.5"

1.0"

Z (m

)"UEDGE is used to model both X-points in an XPTD for the lower half of up-down symmetric configuration

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A C-Mod like case with ADX parameters is used for comparison

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•  Two configuraXons – XPTD and SVPD •  Same underlying magneXc geometry, physics model, boundary condiXons, etc. •  In SVPD the legs cut short to roughly match C-‐Mod verXcal plate configuraXon

Standard Vertical Plate Divertor (SVPD)

X-Point Target Divertor (XPTD)

R [m]

Z [m]

R [m]

Radial transport parameters are set to match projected ADX upstream SOL characteristics

27

•  Using fully recycling wall B.C. on all material surfaces

•  Using radially growing diffusing coefficient to match the expected density profile width ~5 mm

•  SpaXally constant χe,i is sufficient to achieve ~3 mm width of mid-‐plane Te,I

•  Mid-‐plane profile projecXons are based on C-‐Mod data*

Mid-‐plane profiles

*LaBombard et al., Nucl. Fusion 55, 053020, 2015.

1.0e20

0.5e20

0

Ne [1/m3]

Nn [1/m3]

300

200

100

0

Te [eV]

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

D [m2/s]

5.0

4.0

3.0

2.0

1.0

0

! P1/2=3.000!MW! ! P1/2=2.058!MW! ! P1/2=2.052!MW! P1/2=1.420!MW!lg(Te![eV])! ! ! ! ! ! !

! !

!

!

!

! !lg(Ng![m:3])! ! ! ! ! ! !

! !

!

!

!

! !!

As the input power P1/2 is reduced, the divertor transitions to fully detached state

28

A B C D

XPTD, 1% C

As input power P1/2 is reduced, radiation front remains stable but shifts upstream

29

•  For higher input power the radiaXon front moves to larger R to increase the radiaXng volume*

•  P1/2 ≈ 2 MW onset of detachment

•  As P1/2 is reduced further either (i) the radiaXon front reaches the primary X-‐point, or (ii) no steady-‐state soluXons can be found => X-‐point MARFE

*Hutchinson, Nucl. Fusion 34 (1994) 1337

P1/2 = 1.8 MW P1/2 = 1.4 MW P1/2 = 1.0 MW Prad [MW/m3]

R [m] R [m] R [m]

Z [m

]

1% C0.0

2.5

5.0

7.5

10.0

Reducing input power P1/2 eventually leads to X-point MARFE

30

Reducing input power P1/2 eventually leads to X-point MARFE

31 •  QualitaXvely similar results also obtained with 1% Ne impurity

Outline








32

Summary, conclusions, plans

33

•  Capability to generate grids with a secondary X-‐point is developed

•  Capability to model configuraXons with a secondary X-‐point is developed in UEDGE

•  Near-‐SNF configuraXons in DIII-‐D have been analyzed with UEDGE;

points to strongly enhanced transport near the null (churning mode?)

•  X-‐point Target Divertor (XPTD) configuraXon is studied with UEDGE for parameters matching the design of ADX tokamak §  Steady state detachment found for XPTD, for a range of

parameters §  Easier to achieve detachment than for short leg divertor §  Detachment front stays far away from the main X-‐point §  Stable fully detached regimes for tokamak divertor?

Edge plasma modeling for divertor conﬁgurations with ... · LH ACT2 400 600 Maximum possible Psol...

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