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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
- 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 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

- 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

- Approximations used for MFE plasmas lead to tractable but limited theoretical descriptions that are suitable for different ranges of spatial scales and characteristic times.

RF

Transport

Gyro-kinetics

MHD

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

In chamber

Scales for Heavy Ion Beam PhysicsTime scales:

depressed

betatron

betatron

t

electron drift

pb

out of magnet

»

transit

lattice

thru

electron

period

fringe

beam

cyclotron

pulse

fields

residence

in magnet

log of timescale

pulse

beam

t

pe

in seconds

residence

t

pi

t

pb

Length scales:

- electron gyroradius in magnet ~10 mm
- lD,beam ~ 1 mm
- beam radius ~ cm
- machine length ~ km\'s

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.

- 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

w3.pppl.gov/CEMM

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.

- 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

fusion.gat.com/theory/pmp/

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.

- 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

www.ornl.gov/sci/fed/scidacrf

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.

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), …

10-5

10-4

10-3

10-2

10-1

1

beam ions background ions electrons

x

target

df

- 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

- 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

e-

heating laser

overdense

plasma

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

- 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.

- For explicit PIC 3D simulations,
- Total memory scales as L3n3/2
- Total particle-step scales as L3Tn2
- To simulate a (50m)3 plasma with n=100nc for 10ps requires ~6102 TB memory (1013 particles) and 109 processor-hour (on Seaborg)
- State-of-art large PIC runs at Livermore used 7.2109 particles
- Analyzing 109-particle data requires running in parallel and interactively data processing software such as IDL.

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.

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