Modeling of RF Wave Propagation in Plasmas Sci

Modeling of RF Wave Propagation in Plasmas Sci. DAC PI Meeting Charleston, SC March 23, 2004 Lee A. Berry for the RF Sci. DAC team Support from OFES and OASCR is gratefully acknowledged.

Numerical Computation of Wave-Plasma Interactions in Multi-Dimensional Systems D. B. Batchelor, L. A. Berry, M. D. Carter, E. F. Jaeger, E. D’Azevedo C. K. Phillips, R. Dumont (now CEA), H. Okuda D. N. Smithe R. W. Harvey P. T. Bonoli J. C. Wright Lodestar Research Corporation D. A. D’Ippolito, J. Myra Visit our web site at http: //www. ornl. gov/fed/scidacrf

THE MAGNETIC FIELDS IN A TOROIDAL FUSION SYSTEM CONFINE PLASMA ON FIELD LINES THAT DEFINE FLUX SURFACES DIII-D Tokamak (GA, San Diego) Magnetic flux surfaces, “r” = constant Toroidal angle f Magnetic axis Poloidal angle q

RADIO-FREQUENCY WAVES ARE USED TO HEAT AND DRIVE CURRENTS • Absorption physics is dominated by wave-particle interactions: • Currents may be driven when the wave absorption is not symmetric in the parallel wave number. Power is used to heat to fusion temperatures (~10 ke. V): current provides steady-state and controls profiles. Forces (and resulting plasma flows) may be driven by wave momentum absorption and transport. Flows can help reduce turbulent plasma transport. • •

PHYSICS APPROXIMATIONS HAVE LIMITED OUR UNDERSTANDING OF PLASMA-WAVE INTERACTIONS • Limited dimensionality— 1 -D for high resolution instead of the required 2 -D or 3 -D. • Geometric optics (ray tracing) instead of full Maxwell’s equations. • Interactions limited to low-harmonics of the ion cyclotron frequency. • Plasma conductivity restricted to Maxwellian particle distribution functions. • Lack of self consistency between waves and distribution functions. The goal of the Sci. DAC project was to remove these restrictions through use of improved algorithms and utilization of computing capability at NERSC and Oak Ridge

WE NEED TO SOLVE F = MA AND MAXWELL’S EQUATIONS analytic for Fourier basis for E iterate analytic for Maxwellian f 0 We have made a pass through the loop, and expect to begin iterating in the next few months.

RESULTING MATRICES ARE DENSE, AND REQUIRE ~TERABYTES OF STORAGE AND TENS OF TERAFLOP-HOURS TO FACTOR

PLASMA RESONANCES COUPLE SHORT AND LONG WAVELENGTH MODES: HENCE “MODE CONVERSION” 3. 00 E+03 incident fast wave mode converted IBW 2. 00 E+03 Re(Ex) 1. 00 E+03 0. 00 E+00 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 -1. 00 E+03 -2. 00 E+03 two-ion hybrid resonance -3. 00 E+03 Normalized Major Radius 0. 7 0. 8 0. 9 1

Mode conversion flow drive has been simulated in 2 -D for a He 3 -H-D plasma in the Alcator C-Mod tokamak He 3 Doppler broadened ion cyclotron resonance (H) H Antenna Ion Cyclotron Wave (ICW) Z (m) R (m)

MODERATE RESOLUTION NOW POSSIBLE IN 3 -D

FFTs TO XYZ-SPACE REMOVES ZEROES => HIGHER RESOLUTION ELECTRON HEATING ON PROPOSED QUASI-POLOIDAL STELLARATOR 64 x 64 GRID ON 2048 PROCESSORS =0 = /2 2 = 3 = 3 /2 Antenna Wave electric field 4 3 2 1 3 2 P(e) = 91% P(H) = 9% 2 2 2 1 3 (Fred Jaeger)

LIMITATIONS IN COMPUTATIONAL TOOLS HAVE LIMITED OUR UNDERSTANDING OF LOWER HYBRID PHYSICS • Lower hybrid waves are in the few-GHz range and have ~mm wavelengths: – can be absorbed by electrons, distort the distribution function, and drive current; – important for steady state and plasma control; – have been effective experimentally. • The “how” of LH is not clearly understood: – the “spectral gap”; i. e. , what is the dynamic path from Maxwellian to final state—too few electrons in initial state to provide effective source for driving current. • Full-wave calculations have not been possible: geometric optics (ray tracing) has been the only available method. • Resolved full wave calculations are now possible.

RESOLVED LH CALCULATIONS NOW POSSIBLE WITH THE TORIC FINITE-LARMOR RADIUS FULL WAVE MODEL E+ Electric Field Component • Problem leads to system with 480 Nr x [6 x 1023 Nm blocks] system. • A Thomas-algorithm was implemented. • Blocks are inverted with Sca. LAPACK and stored to disk. • Waves are confined to the outside of the torus.

FULL WAVE ANALYSIS SHOWS STRONGER ABSORPTION (BETTER CURRENT DRIVE) THAN DOES RAY-TRACING ray-tracing ACCOME full wave (TORIC) [ John Wright, Paul Bonoli (MIT)]

ALPHA PARTICLE ABSORPTION IN ITER Analytic slowing down for alphas e Numerical slowing down e T alpha However—we don’t have non-linear evolution! P(alpha) = 2% P(alpha) = 5. 4%

SUMMARY • 2 -D is important for mode conversion—new plasma control possibilities. • 3 -D RF modeling is now possible and providing guidance to experimental design. • The LH spectral gap is (at least partially) filled by diffraction. • Wave modeling with non-Mawellian components is helping experimental understanding and guiding future design. • Self consistent modeling of waves and distribution function is now underway The keys to this progress has been teaming of solution experts and physicists and the availability of teraflop computers.

THE FUTURE—TODAY’S PROPOSAL • Contributions to program run time by linear algebra is now small=> – data redistribution (N to N problem) dominant; – interpolation/optimized quadrature needed. • Multiphysics will begin to dominate: – coupling of rf to distribution function evolution; – coupling of rf to other physics modules. • Better basis functions needed: – oblate spherical harmonics? (George Fann).