Parallel coupling: problems arising in the context of magnetic fusion

John R. CaryProfessor, University of Colorado

CEO, Tech-X Corporation

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The nuclear fusion produces energy: D + T (He4 + 3.53 MeV) + (n + 14.06 MeV)

Neutron energy (14 MeV) collected at

walls

Courtesy of Don Batchelor, ORNL

Alpha energy (3.5 MeV) deposited in

plasma

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Heat (to overcome repulsion) and hold particles in magnetic traps

• Heat the particles so that the average energy is ~ 100,000,000F (plasma)

• Contain plasma for many reactions to happen

• Not overheat, which can lead to instability or confinement reduction

+ +

-

-B

Figures from Don Batchelor

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MHD codes compute growth of harmful structures

• Particles move rapidly along field lines

• Topology change means hot particle near inside can reach outside

• Temperature flattens over width of island

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ICRF fast waves and mode converted ion Bernstein and ion cyclotron waves in Alcator C-Mod and ASDEX Upgrade.

RF codes used to predict deposition of wave energy and momentum

http://psfcwww2.psfc.mit.edu/rf2005/

TORIC:•Solves both the ICRF and LHRF wave equation •Uses a mixed finite element - spectral basis representation. •Solves block tri-diagonal with Scalapack.

•Scalable solver allows millimeter resolution

Full-wave LHRF field solutions at millimeter wavelengths over the entire tokamak cross-section.

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Coupling RF and MHD can eliminate the harmful

structures• Localized momentum

deposition differential on the particles

• Currents can be induced– Local: counteract current

spike near island– Global: counteract island

drive (′, q)• Not much current required

(IRF/Iplasma ~ 3%)

Center island current out of

plane

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Prediction of process requires coupling of very different parallel codes

• TORIC: RF code computing– Toroidally fourier– Poloidally fourier– Finite element in minor radius– 1D decomposition

• NIMROD: MHD evolution– Toroidally fourier– Finite elements radially and poloidally– 2D decomposition

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Spatial Domain TransformationsAll needed transformations are linear, and can be

implemented as matrix-vector multiplication

vgB(t) = FBCBvB(t)

vgA(t) = GTABvg

B(t)

vA(t) = CA(MA)-1FAvgA(t)

Code B representation

Transformation to cylindrical coordinate system

Possible Fourier synthesis

MxN coupler

Evaluation at Gauss quadrature points

Possible Fourier analysis

Mass matrix inversion to find representation for code B

Transformation from cylindrical coordinate system

Code A representation

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Questions• Should we be generic?

– Is the performance hit of being generic excessive?

– Should we do a particular problem first?– How will we overlap communication and

computation?• How do we get there?

– Is retrofitting old codes the way to go– Do we need a new framework for component

management?