Numerical Simulation of Profile Evolution

during SMBI at HL-2A with BOUT++

Z H Wang1,2, X Q Xu2, T Y Xia3, P W Xi4, L H Yao1

1Southwestern Institute of Physics, Chengdu, China

2Lawrence Livermore National Laboratory, Livermore, CA 94550, USA 3Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China

4School of Physics, Peking University, Beijing, China

Presented at

54th Annual Meeting of APS Division of Plasma Physics

Providence, Rhode Island, Oct 29-Nov 2, 2012

This work was performed under the auspices of Southwestern Institute of Physics, Chengdu, China and the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-PRES-598432.

Outline

• Motivation

• Physical Model

• Numerical Results

Transport During SMBI

SMBI at Low and High Plasmas

Comparisons Between SMBI and GP

Comparisons Between Simulation and Experiment

• Conclusions and Future Plans

2

SMBI Fuelling for Fusion

Laval

• SMBI (Supersonic molecular beam injection) is a simple and efficient fuelling source

by comparing with GP (gas puffing) and Pellet injection fueling methods.

– Results in a high density, directed particle source, with fuelling efficiencies often

in excess of 30%.

• SMBI is an useful tool for density control to

– maintain plasmas within stable operational boundaries

– actively manage deleterious ELMs

• SMBI is also an useful tool for:

– Confinement improvement, such as L-H transition

– Perturbative transport study, i.e., nonlocal transport

3

BOUT++ has been originally developed for modeling tokamak edge

turbulence* and is extending to include neutrals for 3Dplasma transport

BOUT++ is an unique code to simulate boundary

plasma turbulence in a complex geometry

− Proximity of open+closed flux surface

− Presence of X-point

BOUT++ is being to include neutrals for 3D plasma

transport in a new trans-neut module

− B2, SOLPS and UEDGE are 2D plasma transport

codes

− Added BOUT++ capabilities can handle the

localized 3D sources for neutrals, and late on for

impurities.

• X.Q. Xu and R.H. Cohen, Contrib. Plasma Phys. 38, 158 (1998), Xu, Umansky, Dudson & Snyder, CiCP, V. 4, 949-979 (2008);

• Dudson, Umansky, Xu et al., Comp. Phys. Comm. V.180 (2009) 1467; Xu, Dudson, Snyder et al., PRL 105, 175005 (2010).

4

Process of Molecule Reaction

5

2H 02HSupersonic Molecular Beam

SMB Molecules Atoms

Dissociation

Plasmas

eHHe 0

2 2

eH 22

Ionization

Charge Exchange(CX)

eHHe 20

HHHH 00

CXIdissVVV At Edge

plasma

Peter C. Stangeby The Plasma Boundary of Magnetic Fusion Devices, Institute of Physics publishing, 2000

Franck-Condon

scmeVTeVTVV eeethdissethI

3228

,, 1.031.0103ˆˆˆˆ

scmeVeVT

eVeVTV

i

iithCX /

)15(150

)15(5.1109.1107.1 3

3/13/1

3/13/1

88

,

Physical Model (1) - Plasmas

6

p

Ii

c

iiii SND=NV

t

N ˆˆˆˆˆˆ

ˆ2

||||

e

ie

i

ebinddissdissIeIe

c

eee

i

e TT

M

mWWWTTT

N=

t

T

ˆ

ˆˆ2ˆˆˆ3

2ˆ3

2ˆˆˆˆ3

2ˆˆˆ3

2

ˆ

ˆ2

||||||

aiICX

ii

ii

ii

ii

iVV

MN

PV

MN=VV

t

V||||

||

||||

0

||||||||

|| ˆˆˆˆˆˆ

ˆˆˆ

ˆˆ

1

3

4ˆˆˆ

ˆ

e

ie

i

eiIi

c

iiiii

i

iii TT

M

mTTVTT

N=TV

t

T

ˆ

ˆˆ2ˆˆˆˆ3

2ˆˆ3

2ˆˆˆ3

2ˆˆˆ

ˆ2

||||||||||||||

ethIaI VN ,ˆˆˆˆ

ithCXaCX VN ,ˆˆˆˆ

Ie

p

I NS ̂ˆˆ

CXi

p

CX NS ̂ˆˆ 00

25

||ˆ2.3ˆ

eieeie tTMM

00

25

||ˆ9.3ˆ

iiii tT

ethdissmdiss VN ,ˆˆˆˆ

Quasi-neutral ie NN ˆˆ

00,,

0

,||ˆˆ96.0ˆ

iiaiaiai tTN ithVLt ,00

Physical Model (2) - Atoms

diss

p

Ia

c

aaaa SSND=NV

t

N ˆ2ˆˆˆˆˆˆ

ˆ2

||||

a

a

dissai

a

CX

aa

a

aa

aa

aa

aV

N

SVV

MN

PV

MN=VV

t

V||||||

||

||||

0

||||||||

|| ˆˆ

ˆ2)ˆˆ(ˆ

ˆˆ

ˆˆˆ

ˆˆ

1

3

4ˆˆˆ

ˆ

a

CXai

c

a MTD ̂ˆˆˆ

Where, ethIe

a

I VN ,ˆˆˆˆ

ithCXi

a

CX VN ,ˆˆˆˆ

iaa TNP ˆˆˆ

7

dissediss NS ̂ˆˆ

ethdissmdiss VN ,ˆˆˆˆ

ia TT ˆˆ Due to ion CX, assumption:

Strong numerical instability

Flux limited conditions: min

,ˆˆˆ

aath

fl

a LVD

1

ˆ

1

ˆ

1ˆ

c

a

fl

a

e

aDD

D

Physical Model (3) - Molecules

dissmxmxm S=NV

t

N ˆˆˆˆ

ˆ

8

Local Const. Flux Boundary

xm0V̂

0ˆ

mN

][0258.0][300ˆ eVKTm

Flux limited thermal conductivities are also applied:

Constant room temperature

mm

mxxmxxm

xm

MN

P=VV

t

V

ˆˆ

ˆˆˆ

ˆ

ˆ

Where, mmm TNP ˆˆˆ dissediss NS ̂ˆˆ

1

||||

||ˆ

1

ˆ

1ˆ

j

fl

j

e

j

095,||ˆˆˆ LqV jth

fl

j iej ,

GP Model

0ˆxm0 V

Circular HL-2A Geometry w/ X point

9

mR

Z m[ ]

B

00 NNm

smVm /5000

Plasma Radial B.C.

;1.0 02

NNRi eVT

Rie 102

, SMBI

outside mid plane

iiesei MTTcV )(||

seeieeese cTNTq ||||||

seiiiiisi cTNTq ||||||

0|| iN

5.2i 7e

Parallel Sheath B.C.

319

0 /101 mN

1R

2R

0 2

0

ma 42.0mR 65.10

Private flux region B.C.

R1 and same as:

Sheath

12

2,0 21

;260ˆ

ˆ

1

R

iN

14000

ˆ

ˆ

1

,

R

ieT

smc

i

c

e /1ˆˆ 2

smDc

i /1 2

10

rad

mR

rad

mR mR

rad

mR

rad

2D Plasmas Profiles at Steady State Before SMBI

][ 0NNi ][eVTe

][eVTi]/[|| smV i

319

0 /101 mN

separatrix

separatrix

mR 03.2separatrix

separatrix

Neutrals Propagate First Inwards then Outwards due to Competition between Fueling Rate and Ionization/Dissociation Rate during SMBI Plotted at Outside Mid Plane

11

][mR][mR

][ 0NNa][ 0NNm

0.0 4.0 6.0 8.0 0.12.0 0.0 5.0 0.1 5.1 0.2

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms4.0mst 5.2

ms8.0ms2.1ms6.1][ 0NNa][ 0NNa

]/1[ sa

I ]/1[ sa

I

5.2

0.3

5.3

0.4

319

0 /101 mN

separatrix mR 03.2

separatrix mR 03.2

][mst

Ionization rate peeked inside separatrix Ionization rate peeked outside separatrix

Plasma Profiles Variation During Neutrals Inwards and Outwards Propagation Plotted at Outside Mid Plane

12

][mR ][mR ][mR

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms4.0mst 5.2

ms8.0ms2.1ms6.1

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms4.0mst 5.2

ms8.0ms2.1ms6.1

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms4.0mst 5.2

ms8.0ms2.1ms6.1

][ 0NN i ][eVTe ][eVTi319

0 /101 mN

separatrix mR 03.2

During SMBI, density increases while temperature decreases

separatrix

13

][rad ][rad ][rad

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms05.0mst 3.2

ms10.0ms15.0ms20.0

][ 0NN i ][eVTe][eVTi

Parallel Plasma Transports Due to Parallel Ion Velocity and Thermal Conductivities Plotted at R=2.04m

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms05.0mst 3.2

ms10.0ms15.0ms20.0

]/[|| smV i]/[ 2

0|| smNe ]/[ 2

0|| smNi

SMBI

319

0 /101 mN

SMBI creates poloidal locality

14

Poloidal Propagation of Plasma Density Ni During SMBI

0 10 20 30 4015 20 2510500.0 5.0 0.1 5.1 0.2

0 20 40 60 8030 40 6020100 5030 40 5020100

mst 35.2 mst 4.2

mst 45.2

mst 3.2

mst 5.2 mst 55.2

][mR ][mR ][mR

][mZ

][mZ

319

0 /101 mN ][ 0NNi ][ 0NNi ][ 0NNi

SMBI creates poloidal density blobs

15

2D Profiles of Plasmas and Neutrals Right after SMBI

rad

mR

rad

mR

rad

mR

rad

mR

rad

mR mR

rad

][eVTi][eVTe

]/[|| smV i

][ 0NNi

Nm[N0 ] Na[N0 ]

319

0 /101 mN

separatrix mR 03.2

separatrix mR 03.2

16

Plasmas Profiles Relaxing after SMBI to Reach Steady States Determined by Boundary Conditions Plotted about 10ms after SMBI

rad

mR

rad

mR mR

rad

][ 0NNi

mR

rad

319

0 /101 mN ][eVTe

][eVTi]/[|| smV i

Ni needs much more time to get steady state

separatrix mR 03.2

separatrix mR 03.2

After SMBI plasma density increases by about 100%

Neutrals Penetration Depths Influenced by Low and High Plasma Density and Temperature Profiles Plotted at Outside Mid Plane

17

][mR

][ 0NNa][ 0NNm

0.0 4.0 6.0 8.0 0.12.0 0.0 5.0 0.1 5.1 0.2

4.3

6.3

8.3

0.4

][mst

2.1

][mR

][mst

Low Ni Low Tei

keVTRie 1

1,

021

NNRi

Low Ni High Tei

High Ni Low Tei

keVTRie 1

1,

041

NNRi

4.3

6.3

8.3

0.4

4.3

6.3

8.3

0.4

][mst keVTRie 5

1,

021

NNRi

keVTRie 1

1,

021

NNRi

keVTRie 1

1,

041

NNRi

keVTRie 5

1,

021

NNRi

319

0 /101 mN

separatrix mR 03.2separatrix SMBI penetrates deeper in colder plasmas

Plasma Profiles Evolution during SMBI at Different Low and High Initial Plasma Density and Temperature Plotted at Outside Mid Plane

18 ][mR

][eVTe][ 0NN i

][mst

][mst

Low Ni Low Tei

Low Ni High Tei

High Ni Low Tei

4.3

6.3

8.3

0.4

4.3

6.3

8.3

0.4

200 40 8060 100 2000 400 800600 1000

200 40 8060 2000 400 800600

1000 2000 40003000 5000

1000

319

0 /101 mN

separatrix separatrix ][mR

5 10 2015

][mst

0

4.3

6.3

8.3

0.4

30 025

19

Neutrals Penetrate Deeper Using SMBI than GP

][mR][mR

][ 0NNa][ 0NNm

0.0 4.0 6.0 8.0 0.12.0 0.0 5.0 0.1 5.1 0.2

5.2

0.3

5.3

0.4

5.2

0.3

5.3

0.4

][mst

][mst SMBI SMBI

GP GP

edge localized

319

0 /101 mN

separatrix separatrix

Plasma Density Increases and Temperature Decreases More during SMBI than GP Plotted at Outside Mid Plane

20

][mR ][mR ][mR

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms05.0mst 3.2

ms10.0ms15.0ms20.0

][ 0NN i ][eVTe ][eVTi

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms05.0mst 3.2

ms10.0ms15.0ms20.0

ms05.0mst 3.2

ms10.0ms15.0ms20.0

SMBI

GP

319

0 /101 mN

separatrix mR 03.2

separatrix

SMBI provides more efficient fueling source

21

Total Injected Particles within 2ms SMBI in Simulation is about the Same Order as that in Experiment

319

0 /101 mNm smVm /5000

SMBI

ma 42.0

mstinjc 2

19

00

1008.2

injcinjcmmtotal tSNVN

208.22 mRwSinjc

0mT

0mN0mV

dwRmR 07.2

Yu DL et al NF 2012 52 082001

mw 16.0

Experiment Simulation

22

Line Averaged Plasmas Density and Temperatures Qualitatively Consist with Experiments

Yu DL et al NF 2012, 52 082001 Yao L H et al NF,2001, 41 817

][eVTe

][mst

cmR 195 cmZ 5.3

]1.0[ 0NNi

][mst

319

0 /101 mN

][mst0 10 15 205

0

2

46

][eVTi

][eVTe

][ 0NNi

400

500

600

400

500

600][eVTi

][eVTe

][ 0NNi

0 10 15 20502468

10

300

400

200

300

400

SMBI fueling efficiency ~ 30%

Simulation Simulation

Experiment Experiment

Conclusions and Future Plans • A eight-field physical model of fueling has been developed to study 3D

neutrals and plasmas transport and during SMBI (or GP);

• A new BOUT++ module trans_neut code has also been developed and the

simulations of SMBI in a real HL-2A geometry with X point has been done;

• In colder plasmas, the neutrals penetrate into the separatrix during SMBI

while neutrals are difficult to penetrate into the separatrix during GP;

• However, in hotter plasmas, neutral penetration depth decreases during SMBI

due to the increase of dissociation and ionization rates;

• Line averaged plasma density increases and temperatures decrease have been

observed during SMBI which are consistent with the experiments;

• Easily turn on the toroidal direction simulation in trans_neut code to study 3D

neutrals and plasmas transport;

• More Physics of SMBI fueling will be studied, such as fueling efficiency,

penetration depth, ELM mitigation etc.

23