Parallel coupling: problems arising in the context of magnetic fusion John R. Cary Professor, University of Colorado CEO, Tech-X Corporation

2 The nuclear fusion produces energy: D + T  (He MeV) + (n MeV) Neutron energy (14 MeV) collected at walls Courtesy of Don Batchelor, ORNL Alpha energy (3.5 MeV) deposited in plasma

3 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

4 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

5 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 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.

6 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 (I RF /I plasma ~ 3%) Center island current out of plane

7 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

8 Spatial Domain Transformations All needed transformations are linear, and can be implemented as matrix-vector multiplication v g B (t) = F B C B v B (t) v g A (t) = GT AB v g B (t) v A (t) = C A (M A ) -1 F A v g A (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

9 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?