High Performance Computing for Non-linear MHD Simulations for Fusion Plasmas - Shimpei Futatani (Universitat de Politècnica de Catalunya) - PRACE ...
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High Performance Computing for Non-linear MHD
Simulations for Fusion Plasmas
Shimpei Futatani
(Universitat de Politècnica de Catalunya)
Acknowledgements:
JOREK Team and Y. Suzuki (NIFS)
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S. Futatani, PRACEdays19, May 13-17, 2019
What makes stars shine?
“The starry night”, V. Willen van Gogh
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S. Futatani, PRACEdays19, May 13-17, 2019
What makes stars shine?
“The starry night”, V. Willen van Gogh
Can we use the energy of shining stars as an alternative
energy source?
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S. Futatani, PRACEdays19, May 13-17, 2019
What makes stars shine? – Nuclear fusion
Nuclear Fission
U235
Nuclear Fusion He
++
+
T
+
D n
E = Dmc2
[nasa.gouv]
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S. Futatani, PRACEdays19, May 13-17, 2019
Outline
Introduction
- Plasma / Fusion reactor / ITER Project
Physics background - Tokamak
- What is ELM?
- JOREK - Nonlinear MHD code
- www.jorek.eu
- The JOREK team and themes
- Numerical details and physics model
- Mechanism of pellet triggered ELM
- JOREK modelling of pellet triggered ELM
Physics background – Stellarator
- MIPS code
- MIPS simulation result
Conclusions and Perspectives
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S. Futatani, PRACEdays19, May 13-17, 2019
What is plasma?
For achivement the fusion à Plasma state is needed
- Plasma is the 4th state of matter, obtained at high temperature (>105 degrees)
- Plasma is an ionized gas which consists of ions and electrons.
[www.nasa.gov]
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S. Futatani, PRACEdays19, May 13-17, 2019
Galaxy fusion reactor in the universe
Key parameters for the fusion = high-temperature and high-density
è How can we confine the high-temperature plasma?
- In stars: plasma particles are confined mainly by gravity.
[www.setterfird.org] [wikipedia.org]
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S. Futatani, PRACEdays19, May 13-17, 2019
Fusion reactor on Earth
Key parameters for the fusion = high-temperature and high-density
è How can we confine the high-temperature plasma?
- On Earth: plasmas can be confined in Magnetic field lines
= Magnetic Confinement
• Charged particles spiral around
magnetic field lines.
• Toroidal (Donut shaped)
system avoids plasma hitting
the end of the container
è Tokamak
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S. Futatani, PRACEdays19, May 13-17, 2019
Fusion plasma reactors in the world
Tokamaks (not listed all here) in the world
JET (EU) and MAST (UK)
ASDEX Upgrade (Germany)
ITER
(international project)
JT60U (Japan)
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S. Futatani, PRACEdays19, May 13-17, 2019
What is ITER? [www.iter.org]
ITER is a major international collaboration in fusion energy research involving
China, the EU (plus Switzerland), India, Japan, the Russian Federation, South
Korea and the United States
[www.iter.org]
ITER
ITER site (January 2017)
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S. Futatani, PRACEdays19, May 13-17, 2019Overview of the ITER Tokamak Pit
Drone view of the tokamak pit and bioshield construction
[Figure from Pinches, ITER Organization]
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S. Futatani, PRACEdays19, May 13-17, 2019A big challenge for control of fusion plasma
Eruption of high temperature plasma
= solar flares (for sun)
= ELMs (for Magnetically confined plasma)
è Big challenge for the control of the plasma
Page 12
S. Futatani, PRACEdays19, May 13-17, 2019Edge Localized Modes (ELMs)
• Fusion plasma has a strong pressure gradient at the plasma boundary.
• Edge pressure gradient is limited by an MHD instability (ballooning mode)
• A crash of the edge profile occurs
• Release of hot plasmas onto a plasma facing components
• ELM removes up to 10% of the plasma energy in ~200 microseconds ELM
• Periodic and bursty behaviors
[Figure from Pitts, ITER Organization]
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S. Futatani, PRACEdays19, May 13-17, 2019Edge Localized Modes (ELMs)
• Fusion plasma has a strong pressure gradient at the plasma boundary.
• Edge pressure gradient is limited by an MHD instability (ballooning mode)
• A crash of the edge profile occurs
• Release of hot plasmas onto a plasma facing components
• ELM removes up to 10% of the plasma energy in ~200 microseconds ELM
• Periodic and bursty behaviors
Fast camera image of ELM (MAST) [A. Kirk et al.]
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S. Futatani, PRACEdays19, May 13-17, 2019Edge Localized Modes (ELMs)
[Linke 2007]
ELMs lead to a large erosion of and a limited lifetime of the plasma facing
components. èRequires physics understanding of ELMs and ELM control
• Techniques to control ELM:
• stabilisation by external magnetic perturbations
• triggered by pellet injection (pellet : deuterium solid ice cube)
• Etc…
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S. Futatani, PRACEdays19, May 13-17, 2019Demonstration of ELM pacing by pellets without fueling
Divertor [Baylor APS 2010]
- Pellets can control the ELM frequency
- Heat flux of the pellet triggered ELMs on the fusion reactor wall becomes small.
Theoretical and Numerical Modelling studies are needed.
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S. Futatani, PRACEdays19, May 13-17, 2019Non-linear MHD code JOREK
• JOREK has been developed with the specific aim to simulate ELMs, developed by Dr. G.
Huijsmans (CEA/Univ. Eindhoven).
• G.T.A. Huysmans, Plasma Phys. Control. Fusion 47, B165 (2005)
• G.T.A. Huysmans and O. Czarny, Nuclear Fusion 47, 659 (2007)
• O. Czarny and G. Huysmans, J. Comp. Phys. 16, 7423 (2008)
• See [https://www.jorek.eu/]
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S. Futatani, PRACEdays19, May 13-17, 2019Non-linear MHD code JOREK
• European Enabling Research Project (PI: M. Hoelzl)
• JOREK collaborations (>30 members, >10 international institutions):
• JOREK main development and application
• Involved institutes: CEA, IPP Garching, ITER, CCFE, Eindoven, UPC etc.
• Pellet triggering of ELMs / Shattered pellets for disruption
• S. Futatani , D. Hu etc.
• ELM mitigation/suppression by external fields
• F. Orain, M. Becoulet, K. Wittawat, M. Hoelzl, etc
• Full orbit particle tracer
• D. Van vugt, A. Dvornova, C. Somariva, etc.
• Disruptions (MGI, REs, etc)
• E. Nardon, C. Sommariva, V. Bandaru, M. Hoelzl, D. Meshcheriakov, F. Wieschollek, etc
• Simulation of ELMs
• G. Huijsmans, S. Pamela, M. Becoulet, F. Orain, M. Hoelzl, A. Cathey etc.
• Solvers (PaStiX, HIPS, Interface MURGE)
• P. Ramet, P. Henon, X. Lacoste, Univ. Bordeaux/INRIA
• Full MHD model/numerical methods
• B. N’Konga, G. Huijsmans, H. Guillard, S. Pamela
• Resistive Wall/Free boundary version (VDEs, RWMs, vertical kicks, ...)
• M. Hoelzl, J. Artola-Such, etc
• Numerical methods
• B. N’Konga, E. Sonnendruecker, H. Guillard, E. Franck etc
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S. Futatani, PRACEdays19, May 13-17, 2019Non-linear MHD code JOREK
• Numerical features:
• Discretisation: Xpoint geometry
• Cubic finite elements flux-aligned poloidal grid
• Fourier series in toroidal angle
• Time stepping:
• fully implicit Crank-Nicholson
• Solver sparse matrices (PastiX library)
• GMRES iterative solver with physical preconditioner
[Provided by
M. Hoelzl]
• Parallelisation using MPI/OPENMP
• ~30000 poloidal elements
• Typically 1880-3800 cores
• MareNostrum IV (BSC), Marconi-Fusion (CINECA),
CURIE (France), hydra (Germany), etc
Acknowledgement to PRACE project.
[Provided by
S. Pamela]
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S. Futatani, PRACEdays19, May 13-17, 2019Non-linear MHD code JOREK
• Reduced MHD model (JOREK also has the full MHD model).
• Braginskii parallel conductivity
• Spitzer resistivity
• Mach-1 boundary condition, free flow on divertor target
• Magnetic field and the velocity
• Mass density Coupled with the
pellet ablation model
• Poloidal momentum (vorticity)
• Parallel momentum
• Temperature
• Poloidal flux
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S. Futatani, PRACEdays19, May 13-17, 2019Pellet model and implementation in JOREK
• Realistic pellet ablation model (NGS model [Gal, NF(2008)]) is implemented
in JOREK :
• Pellet moves at fixed speed and direction
• Pellet is modelled as an adiabatic localized time-varying density source
rp: pellet radius [m]
ne: plasma electron density [m-3]
Sp: Density source Te: plasma electron temperature [eV]
JOREK solves a very complex, multi-physics which requires HPC
Interactions
Non-linear MHD physics Pellet ablation physics
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S. Futatani, PRACEdays19, May 13-17, 2019Mechanism of pellet triggered ELM
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S. Futatani, PRACEdays19, May 13-17, 2019Plasma dynamics after the pellet injection
1.1mm pellet 1.7mm pellet
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S. Futatani, PRACEdays19, May 13-17, 2019Heat flux on the divertor target
Heat flux profile on the divertor target ELM
[Wenninger et al. (2010)].
(a) spontaneous ELM (b) pellet triggered
ELM
Spontaneous ELM
Pellet density
Pellet triggered source creates
ELM (1.7mm) another
channel to the
divertor target.
è Distribution
of the heat flux
in a wide area.
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S. Futatani, PRACEdays19, May 13-17, 2019Simulations of stellarator plasma
• Stellarator is an alternative type of fusion reactor. It exploits
strangely-shaped magnets that is hard to build but potentially
easier to operate.
• The global MHD dynamics of the Large Helical Device (LHD)
in Japan has been analyzed with the MIPS-code.
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S. Futatani, PRACEdays19, May 13-17, 2019Fusion plasma reactors in the world
Stellarators (not listed all here) in the world
Wendelstein 7-X (Germany)
NCSX (US)
TJ-II (Spain)
LHD (Japan)
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S. Futatani, PRACEdays19, May 13-17, 2019MIPS code
• MIPS code solves the full MHD equations starting from the initial equilibrium.
[Y. Todo et al., PFR (2010), K. Ichiguchi et al., NF (2015)]
• Those equations are solved in the rectangular grids of the cylindrical coordinates
(R, f, Z).
• Any plasma geometry can be implemented by implementation of magnetic field.
• Good scaling of parallelization up to 4096 cpu cores.
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S. Futatani, PRACEdays19, May 13-17, 2019Pellet cloud profile
• Realistic pellet ablation model (NGS model [Gal, NF(2008)]) is implemented in MIPS.
• The pellet cloud profile shows the m/n=1/1 shape.
The density (pressure) source is
localized in the toroidal and the
poloidal direction
Pellet injection
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S. Futatani, PRACEdays19, May 13-17, 2019Pellet cloud profile
• Realistic pellet ablation model (NGS model
[Gal, NF(2008)]) is implemented in MIPS.
• The pellet cloud profile shows the m/n=1/1
shape.
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S. Futatani, PRACEdays19, May 13-17, 2019MHD excitation by pellet
• The three-dimensionally localized pressure perturbation excites the MHD modes.
• Magnetic energies evolve.
• m/n=2/1 (solid lines), m/n=2/2 (dashed lines), m/n=2/3 (dotted lines)
• The plasma is stable in the absence of the pellet.
• After the full pellet ablation, the energies suddenly go relax state (t=400-
500µs).
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S. Futatani, PRACEdays19, May 13-17, 2019Conclusions and perspectives
JOREK simulation
by G. Huijsmans
(CEA/ITER)
Conclusions
• JOREK has been performed to study the non-linear MHD physics.
• JOREK allows us to compute the ELM physics and calculate the heat flux onto the
plasma facing components.
• Qualitative agreements with the experiment results of JET are observed via
simulation.
• MIPS has been performed to study the pellet effect in stellarator plasma.
• The excitation of MHD modes caused by pellet injection is observed.
Future works
• JOREK pellet simulation will be performed including more physics effects to allow for
a more quantitative comparison.
• Improvement of physics model in MIPS will be carried out.
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S. Futatani, PRACEdays19, May 13-17, 2019You can also read
