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Fusion Energy Sciences Greenbook Presentation. prepared by: Carl Sovinec (U-WI), Alex Friedman (LLNL&LBNL), Stephane Ethier (PPPL), and Chuang Ren (UCLA). National Energy Research Scientific Computing Center User Group Meeting, June 25, 2004. OUTLINE. Fusion sciences overview

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fusion energy sciences greenbook presentation
Fusion Energy Sciences Greenbook Presentation

prepared by:

Carl Sovinec (U-WI), Alex Friedman (LLNL&LBNL),

Stephane Ethier (PPPL), and Chuang Ren (UCLA)

National Energy Research Scientific Computing Center User Group Meeting, June 25, 2004

  • Fusion sciences overview
    • Plasma properties and descriptions
    • Ranges of time- and space-scales
  • Large-scale computations in FES
    • Magnetic fusion energy (MFE)
    • Inertial fusion energy (IFE)
  • Input from FES NERSC users
fusion sciences overview
Fusion Sciences Overview
  • Fusion science is largely plasmascience.
    • Matter is in the plasma state at fusion conditions.
    • Collective plasma dynamics regulate confinement or focusing.
    • Heating and drive rely on interaction of electromagnetic waves with plasmas.
    • Macroscopic plasma dynamics impose stability limits.
    • Plasma-surface interaction (atomic physics) impacts feasibility.
  • With ITER being planned and NIF now operational, computation has a tremendous opportunity to contribute programmatically.

International Thermonuclear Experimental Reactor

National Ignition Facility

plasma properties and theoretical descriptions
Plasma Properties and Theoretical Descriptions
  • Particle-particle interactions are long-range but weak, so while classical statistics hold, plasmas are easily driven from local thermodynamic equilibrium.
  • Dominant interactions occur through collective motions and EM fields (E, B).
  • Kinetic theory provides an accurate and comprehensive plasma description:


Particle distribution evolution


Maxwell’s equations

  • fa(x,v,t) is the ensemble-averaged single-particle distribution function for each species (a=i,e).
  • This system is sometimes solved in primitive (6D+time) form, e.g. for the propagation of ion beams and lasers in plasmas. However, even with large-scale computation, various limits and physically motivated averages are usually applied to isolate different classes of behavior.
magnetic fusion energy scales and descriptions
Magnetic Fusion Energy Scales and Descriptions
  • Approximations used for MFE plasmas lead to tractable but limited theoretical descriptions that are suitable for different ranges of spatial scales and characteristic times.





scales for heavy ion beam physics

In driver














In chamber

Scales for Heavy Ion Beam Physics

Time scales:





electron drift


out of magnet













in magnet

log of timescale





in seconds






Length scales:

  • electron gyroradius in magnet ~10 mm
  • lD,beam ~ 1 mm
  • beam radius ~ cm
  • machine length ~ km\'s
large scale computation in mfe
Large-scale Computation in MFE
  • Existing computational efforts are addressing the following fundamental issues:
  • Nonlinear macroscopic plasma stability and the consequences of instability.
  • Cross-magnetic-field transport of plasma particles and energy from small-scale turbulence.
  • Heating / current drive / momentum input via RF waves.
  • Edge plasma dynamics and interactions with core plasma.
  • Atomic physics arising from plasma-surface interaction.
  • SCIDAC collaborations have helped extend the capabilities of the numerical models.
  • Integrated modeling will couple disparate descriptions to predict the nonlinear behavior of burning plasmas. (http://www.isofs.info/)
computations for macroscopic stability must address stiffness and anisotropy
Computations for macroscopic stability must address stiffness and anisotropy.
  • Nonlinear dynamics that change the topology of the confining magnetic field are modeled with single- and two-fluid systems of equations, augmented by kinetic closures and/or minority species in some simulations.
  • Anisotropy produces subtle balances of large forces, nearly singular behavior at rational surfaces, and vastly different parallel and perpendicular transport properties.
  • System stiffness reflects the large range of time-scales from Alfvén-wave propagation to slow nonlinear evolution (~transport scale).

This nonlinear simulation of a loss-of-confinement event in discharge #87009 of the GA DIII-D tokamak helped explain how internal MHD activity altered the heat deposition. (NIMROD data courtesy of Scott Kruger, Tech-X Corp.; SCIRUN graphics from Allen Sanderson, U. Utah)

SCIDAC Center for Extended MHD Modeling


performance of macroscopic computations is dominated by parallel linear algebra
Performance of macroscopic computations is dominated by parallel linear algebra.
  • Stiff PDE systems require implicit and/or semi-implicit methods that lead to ill-conditioned matrices.
  • The algebraic systems are solved at every time-step, and a complete nonlinear computation may require 104 or more time-steps.
  • SCIDAC collaborations (X. Li, SuperLU; TOPS-PETSc group) led to performance breakthroughs, but scaling to large #s of procs. remains challenging.

Fixed problem-size scaling with SuperLU (left) and NIMROD-native CG solver (right).

first principles computation of microturbulence leading to transport requires kinetic effects
First-principles computation of microturbulence leading to transport requires kinetic effects.
  • Ion gyro-orbits about magnetic field-lines are small with respect to the device size and parallel wavelengths but comparable to perpendicular wavelengths.
  • The gyrokinetic approximation removes fast dynamics.
  • Determining transport properties from correlations of fluctuations leads to disparate scales (stiffness) that must be resolved.
  • Both Eulerian (continuum) and Lagrangian (PIC) methods are used numerically.

The largest GTC run as of 5/03 required 1 billion particles and 125 million

grid points using 1024 processors on the IBM-SP at NERSC.

SCIDAC Plasma Micorturbulence Project


both particle and continuum codes scale well on present day machines
Both particle and continuum codes scale well on present-day machines.
  • Decomposition strategies (including MPI / loop parallelism) have been tuned.
  • Computation time with particle-based codes is presently dominated by scatter and gather operations.
  • As more electron and electromagnetic effects are added, electromagnetic “field-solves” (linear algebra) become an increasingly larger fraction of the CPU time.

Fixed problem-size scaling for the continuum GYRO code.

Increasing problem-size scaling for the PIC-based GTC code.

computations of wave plasma interactions investigate mode conversion and energy deposition
Computations of wave-plasma interactions investigate mode conversion and energy deposition.
  • The electromagnetic wave equation is solved in frequency-space with plasma current density being an integral operator on electric field.
  • Computations traditionally used spectral representations.
  • Recent developments include a plasma model valid for arbitrary gyroradius/wavelength scaling. (AORSA, E.F. Jaeger, ORNL)

AORSA computation results for a multiple-ion-species plasma in the Alcator C-Mod experiment at MIT showing mode conversion from the long-wavelength “fast-wave” to ion cyclotron waves.

SCIDAC Wave-Plasma Interactions Project


computational performance of rf plasma calculations is dominated by parallel linear algebra
Computational performance of RF-plasma calculations is dominated by parallel linear algebra.
  • In-core ScaLAPACK solves for the spectral representation achieved 1.6 Tflops on 1600 processors of Seaborg—67% efficiency!
  • Some computations are more effective with a configuration-space representation.
    • Current density computation can be trimmed from vacuum regions of 3D stellarator calculations.
    • In some cases, the matrix solve time is reduced by a factor of 100; computational efficiency decreases, however.

3D AORSA computation for the LHD stellarator.


While SCIDAC has already provided a boost to MFE computation, predicting plasma behavior in ITER will require continued hardware and algorithmic gains.

From the SCaLeS Report (www.pnl.gov/scales), Plasma Science Section by S. C. Jardin, PPPL.

prepared by alex friedman llnl lbnl heavy ion fusion virtual national laboratory

Large-scale Computation in IFE

HIF: Simulation of space-charge-dominated beams

Intense beams of heavy ions will drive targets for Inertial Fusion Energy & High Energy Density PhysicsThis beam science will benefit from the next NERSC computer - but the machine’s architecture will matter

Prepared by: Alex Friedman, LLNL & LBNL

Heavy Ion Fusion Virtual National Laboratory

NERSC Users Group, LBNL, JUne 25, 2004


Particle-in-cell simulation of injector based on merging 119 intense beamlets

Key question in Heavy Ion Fusion:How do intense ion beams behave as they are accelerated and compressed into a small volume in space and time?

  • Beams are non-neutral plasmas; long-range forces dominate
  • They are collisionless with “long memories” — must follow beam particle distribution from source to target
  • “Multiscale, multispecies, multiphysics” computing; ions encounter:
    • Good electrons: neutralization by plasma aids compression, focusing
    • Bad electrons: stray “electron cloud” and gas can afflict beam
  • PIC is main tool; new methods offer: resolution (AMR-PIC), dense plasmas (implicit, hybrid PIC+fluid), low noise (f), halo (Vlasov), short electron timescales (large-Dt advance), …








beam ions background ions electrons




  • Nonlinear-perturbative simulation of ion-electron two-stream instability reveals structure of eigenmode
  • 4D Vlasov testbed captures halo down to extremely low densities
  • Electromagnetic simulation of a single converging beam in target chamber
  • Simulation of diode using merged Adaptive Mesh Refinement & PIC
achieving hif goals requires many processor hours good machine architecture supportive center
Achieving HIF goals requires many processor-hours, good machine architecture, supportive center
  • Source-to-focus WARP PIC simulation of a beam in a full-scale HIF driver
    • On Seaborg: key kernels achieve 700-900 Mflop/s single-processor; aggregated parallel performance is ~100 Mflop/s per processor
    • Observe good scalability up to 256 proc’s on present-day problems; can assume further algorithmic improvements & larger problems
    • Next-step exp’t (minimal): 440 proc-hrs (128x128x4096, 16M part’s, 10k steps)
    • Full-scale system w/ electrons: 1.8 M proc-hrs (4x resolution, 4X longer beam, 4X longer path, two species, Dt halved, using new electron mover)
  • While performance on the SP is comparable to that of other large codes, the SP architecture is not ideal for this class of problem
    • A higher fraction of peak parallel speed was achieved on T3E than SP
    • WARP should adapt especially well to a vector/parallel machine
    • Hardware gather and scatter valuable; scatter-add even more so
    • Trends toward multi-physics complexity and implicitness imply that benefits would accrue from easy programmability, flexibility, good parallel performance
  • NERSC support has been excellent and is a key to successful supercomputing
fast ignition separating compression and heating

Compressed fuel


heating laser



Fast Ignition: Separating Compression and Heating
  • It is relative easy to compress fuel pellet to achieve core density >  range
    • Ignition needs a hot spot to start fusion
  • Near-perfect compression required to achieve hot spot in conventional ICF
  • FI: Using a 2nd laser to create hot spot (Tabak et al., 1994)
    • Heating window: 10 ps --> PW laser
    • Laser energy needs to be converted into energetic electrons or protons
  • FI relaxes compression requirement and increase energy gain.
key question in fi how much of ignition laser energy is coupled to target core
Key question in FI: how much of ignition laser energy is coupled to target core
  • Energetic particle production (PIC simulation)
    • Laser-underdense plasma interaction
      • Channeling
      • Laser stability, e.g. hose/filament
    • Laser-plasma interface & vicinity (n≤102 nc)
      • Hole-boring
      • Fast e- production
      • Fast e- transport: current filament/magnetic field generation
    • Laser-solid material interaction
      • Energetic proton production/focusing
      • Laser-gold cone interaction for coned target
  • Energetic particle transport/energy deposition in dense plasma (hybrid simulation)
    • Particle description for energetic components + fluid description for dense plasma (n~102-104 nc)
    • Need to incorporate proper model for resistivity/collisionality
fi simulations requires tremendous computational resources
FI simulations requires tremendous computational resources.
  • For explicit PIC 3D simulations,
    • Total memory scales as L3n3/2
    • Total particle-step scales as L3Tn2
  • To simulate a (50m)3 plasma with n=100nc for 10ps requires ~6102 TB memory (1013 particles) and 109 processor-hour (on Seaborg)
  • State-of-art large PIC runs at Livermore used 7.2109 particles
  • Analyzing 109-particle data requires running in parallel and interactively data processing software such as IDL.
fes nersc user input
FES NERSC User Input
  • NERSC services and support are excellent.
  • The latency of Seaborg’s inter-node connection is too high and bandwidth is too low—data access relative to CPU speed should be considered carefully in the next purchase.
  • Scheduling policies are too selective in the type of scientific computations that are supported.
  • Those who have been able to take advantage of the large-job reimbursement program like it.
  • Diagnosing large PIC simulations will require support for large parallel interactive sessions.
  • At least 4 different (and different types of) fusion codes have demonstrated improved performance on the Cray X1

Assessment from CRS: as different types of FES computations expand their physical models and employ more sophisticated algorithms, communication will become a greater burden.