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 extensionRMPsNeutrals & 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
ttPtn
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=NVtN ˆˆˆˆˆˆˆˆ
2||||
e
ie
i
ebinddissdissIeIrecrece
ceee
i
e TTMmWWWTWTT
N=
tT
ˆ
ˆˆ2ˆˆˆ32ˆ
32ˆˆˆˆˆˆ
32ˆˆ
ˆ32
ˆˆ
2||||||
aiICXii
iiii
iii VV
MN
PV
MN=VV
tV
||||||
||||0
|||||||||| ˆˆˆˆ
ˆˆ
ˆˆˆ
ˆˆ1
34ˆˆ
ˆ
ˆ
e
ie
i
eiIreci
ciiiii
iii
i TTMmTTVTT
N=TV
tT
ˆ
ˆˆ2ˆˆˆˆˆ32ˆˆ
32ˆˆ
ˆ32ˆˆ
ˆˆ
2||||||||||||||
Quasi-neutral ie NN ˆˆ
dissprec
pIa
caa
ca
a SSSNDNDtN ˆ2ˆˆˆˆˆˆˆˆ
2||||||
dissmxmxm S=NVtN ˆˆˆˆˆ
xm0V̂
0ˆmN
mm
mxxmxxm
xm
MNP=VV
tV
ˆˆˆˆˆ
ˆˆ
Local Const. Flux Boundary
mst 0ms0.1ms0.2sim.
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