X. Q. XuLawrence Livermore National Laboratory

Acknowledgement: P.W.Xi1,2, C. H. Ma1,2 , T.Y.Xia1,3, B.Gui1,3, G.Q.Li1,3, J. F. Ma1,4, A.Dimits1, I.Joseph1, M.V.Umansky1, S.S.Kim5, T.Rhee5, G.Y.Park5, H.Jhang5, P.H.Diamond6,7, B.Dudson8, P.B.Snyder9

1Lawrence Livermore National Laboratory, Livermore, California 94551, USA2School of Physics, Peking University, Beijing, China

3Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China4Institute for fusion studies, University of Texas, Austin, TX 78712, USA

5WCI Center for Fusion Theory, National Fusion Research Institute, Daejon, South Korea6CASS and Dept. of Physics, University of California, San Diego, La Jolla, CA, USA

7University of York, Heslington, York YO10 5DD, United Kingdom8General Atomics, San Diego, California 92186, USA

Presented atInstitute of Plasma Physics, CAS

November 27, 2013, Hefei, China

This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-PRES-645770

Overview of recent BOUT++ Simulation and validation results

Tokamak edge region encompasses boundary layer

between hot core plasma and material walls

Complex geometry

Rich physics (plasma, atomic, material)

Sets key engineering constraints for fusion reactor

Sets global energy confinement

Tokamakinterior

BOUT (BOUndary Turbulence) was originally developed at LLNL in late 1990s for modeling tokamak edge turbulence

BOUT++ is a successor to BOUT,

developed in collaboration with Univ. York*

2000 2005 2013

Original BOUT, tokamak applications on boundary turbulence and ELMs with encouraging results

BOUT-06: code refactoring using differential operator approach, high order FD, verification

BOUT++: OOP, 2D parallelization, applications to tokamak ELMs and linear plasmas

• X.Q. Xu and R.H. Cohen, Contrib. Plasma Phys. 38, 158 (1998)• Xu, Umansky, Dudson & Snyder, CiCP, V. 4, 949-979 (2008). • Umansky, Xu, Dudson, et al., , Comp. Phys. Comm. V. 180 , 887-903 (2008). • Dudson, Umansky, Xu et al., Comp. Phys. Comm. V.180 (2009) 1467.• Xu, Dudson, Snyder et al., PRL 105, 175005 (2010).

Gyro-fluid extension

RMPsNeutrals & impuritiesPreconditionerComputing on GPUs

B UT++Boundary Plasma Turbulence Code

BOUT and BOUT++ have been products of broad

international collaborations

Lodestar Research Corporation

Institute of plasma PhysicsChinese Academy of Sciences Southwestern

Institute of Physics

BOUT++ MAP

Principal Results

6

A suite of two-fluid models has been implemented in BOUT++ for

all ELM regimes and fluid turbulence

A suite of gyro-fluid models is under development for

pedestal turbulence and transport

Neutral models Fluid neutral models are developed for

• SMBI, GAS puffing, Recycling Coupled to EIRENE Monte Carlo code

to follow the neutral particles

A PIC module for impurity generation and transport

A framework for development of kinetic-fluid hybrid

A elm size dependence with density or collisionality for type-I ELMs mainly from edge bootstrap current and ion diamagnetic stabilization effects

7

BOUT++: A framework for nonlinear twofluid and gyrofluid simulationsELMs and turbulence

Different twofluid and gyrofluid models are developed under BOUT++ framework for ELM and turbulence simulations

Twofluid Gyrofluid Physics

3-field 1+0 Peeling-ballooning mode

4-field 2+0 + acoustic wave

5-field + Thermal transport no acoustic wave

6-fieldBraginskii equations

3+1Snyder+Hammett’s model

+ additional drift wave instabilities+ Thermal transport

A good agreement between BOUT++, ELITE and

GATO for both peeling and ballooning modes

• As edge current increases, the difference between BOUT++ and GATO/ELITE results becomes large

• This difference is due to the vacuum treatment

𝛾 /𝜔𝐴

n

cbm18_dens8

A

D For the real “vacuum” model, the effect of resistivity should be included

4-field model agrees well with 3-field

for both ideal and resistive ballooning modes

• ac value from eigenvalue solver agrees with BOUT simulation.• Non-ideal effects are consistent in both models

diamagnetic stabilization resistive mode with a <ac

increase n of maximum growth rate with decrease of a

The onset of ELMs is shifted to due to P-B turbulence,

which may explain those unknown questions observed in experiments

P. W. Xi, X.Q. Xu, P. H. Diamond, submitted to PRL, 2013

The occurrence of ELMs depends sensitively on the nonlinear dynamics of P-B turbulence;

The evolution of relative phase between P-B mode potential and the pressure perturbations is a key to ELMs

Phase coherence time determines the growing time of an instability by extraction of expansion free energy.

Nonlinear criterion sets the onset of ELMs

t

tPtn

n

n

,,ˆ,,ˆ

arg,,,

3/12'2

/10ln~

DVkc

cc

BOUT++ global GLF model agrees well

with gyrokinetic results • BOUT++ using Beer’s 3+1 model agrees well with gyrokinetic results. • Non-Fourier method for Landau damping shows good agreement with

Fourier method. Cyclone base case

Implemented in the BOUT++ Padé approximation for the

modified Bessel functions Landau damping Toroidal resonance Zonal flow closure in progress Nonlinear benchmark underway

Developing the GLF models to behave well at large perturbations for second-order-accurate closures

Conducting global nonlinear kinetic ITG/KBM simulations at pedestal and collisional drift ballooning mode across the separatrix in the SOL

SS Kim, et al.

Development of flux-driven edge simulation

Edge Transport Barrier formation with external sheared flow

T=0

T=100

T=200

Time

ExB shearing rate

normalized poloidal flux

SOL diffusion coefficient = 10-6

– Heat source inside the separatrix and sink outside the separatrix

– ETB is formed by the externally applied sheared flow, but sometimes triggered by turbulence driven flow when external flow is zero

normalized poloidal flux

Six-filed simulations show that Ion perturbation has a large initial crash

and electron perturbation only has turbulence spreading due to inward ExB convection

Te Ti

6-field module has the capability to simulate the heat flux in divertor geometry

14

Toro

idal

dire

ction

(m)

Toro

idal

dire

ction

(m)

Toro

idal

dire

ction

(m)

R (m) R (m) R (m)Inner target Outer target Outer mid-plane

Six-field (ϖ, ni, Ti, Te, A||, V||): based on Braginskii equations, the density, momentum and energy of ions and electrons are described in drift ordering [1,2].

[1]X. Q. Xu et al., Commun. Comput. Phys. 4, 949 (2008).[2]T. Y. Xia et al., Nucl. Fusion 53, 073009 (2013).

Left: electron temperature perturbation

Bottom: heat flux structures on toroidal direction.

Ne (10^19 m^-3)

1.0 3.0 5.0 7.0 9.0

1.91*10^-3 4.03*10^-2 1.59*10^-1 3.81*10^-1 0.72*

Collisionality at peak gradient radial position:

en boJ*

A set of equilibrium with different density profiles are generated

Pressure profile is fixed

S=10^8, SH =10^15, with ion diamagnetic effects and gyro-viscosity. As the ballooning term dominates the high n modes, the stabilization effects of the ion diamagnetic drifts become

less important when density is increased. The kink term dominates the low n modes. Therefore, as the density increases, the edge current decreases and

growth rate decreases. As the edge collisionality increases, the dominant P-B mode shifts to higher n and the width of the dispersion relation

increases. The relation between ELM size and collisionality has been shown to have the same trend as the scaling law.

As the edge density (collisionality) increases, the growth rate of the P-B mode increases for high n but decreases for low n (1<n<5)

SMBI particle fueling models has been implemented

Physical model – plasmas, atom, molecule

prec

pIi

ciii

i SSND=NVt

N ˆˆˆˆˆˆˆ

ˆ2

||||

e

ie

i

ebinddissdissIeIrecrece

ceee

i

e TT

M

mWWWTWTT

N=

t

T

ˆ

ˆˆ2ˆˆˆ3

2ˆ3

2ˆˆˆˆˆˆ3

2ˆˆˆ3

2ˆ

ˆ2

||||||

aiICX

ii

ii

ii

iii VV

MN

PV

MN=VV

t

V||||

||||||

0||||||||

|| ˆˆˆˆˆˆ

ˆˆˆ

ˆˆ1

3

4ˆˆˆ

ˆ

e

ie

i

eiIreci

ciiiii

i

iii TT

M

mTTVTT

N=TV

t

T

ˆ

ˆˆ2ˆˆˆˆˆ3

2ˆˆ3

2ˆˆˆ3

2ˆˆˆ

ˆ2

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

Quasi-neutral ie NN ˆˆ

dissprec

pIa

caa

ca

a SSSNDNDt

N ˆ2ˆˆˆˆˆˆˆ

ˆ2

||||||

dissmxmxm S=NVt

N ˆˆˆˆ

ˆ

xm0V̂

0ˆmN

mm

mxxmxxm

xm

MN

P=VV

t

Vˆˆ

ˆˆˆ

ˆ

ˆ

Local Const. Flux Boundary

mst 0ms0.1ms0.2

sim.

Simulation qualitatively consistent with Expts.

B

SMBI1ˆ 0.65

2ˆ 1.0

LCFS

0mV 0mN

Ongoing validation of MHD instability data from EAST

BOUT++ simulations show that the stripes from EAST visible camera match ELM filamentary structures

EAST#41019@3034msVisible camera shows bright

ELM structure$

BOUT++ simulation shows that the ELM stripe are filamentary

structures*

Z (m

)

2 2.25

0

-0.5

Major radius

R (m)

$Photo by J. H. Yang*Figure by W.H. Meyer

Pitch angle match! Mode number match!

T. Y. Xia, X.Q. Xu, Z. X. Liu, et al, TH/5-2Ra, 24th IEAE FEC, San Diego, CA, USA, 2012

Z.X.Liu, et al., POSTER SESSION I

Ongoing validation of MHD instability data from KSTARThe synthetic images from interpretive BOUT++ simulations show the similar patterns as ECEI

H Park, et al., APS DPP invited talk, Nov., 2013

M. Kim, et al., POSTER SESSION I

Principal Results

21

A suite of two-fluid models has been implemented in BOUT++ for

all ELM regimes and fluid turbulence

A suite of gyro-fluid models is under development for

pedestal turbulence and transport

Neutral models Fluid neutral models are developed for

• SMBI, GAS puffing, Recycling Coupled to EIRENE Monte Carlo code

to follow the neutral particles

A PIC module for impurity generation and transport

A framework for development of kinetic-fluid hybrid

A elm size dependence with density or collisionality for type-I ELMs mainly from edge bootstrap current and ion diamagnetic stabilization effects

BOUT++ background information & websites

22

The 2013 BOUT++ workshop website,

https://bout2013.llnl.gov

BOUT++ background information and continuing development on the following websites:https://bout.llnl.govhttp://www-users.york.ac.uk/~bd512//bouthttp://boutproject.github.io