A self-consistent description of plasma heating in the ion cyclotron range of frequencies (ICRF) requires simulation of two different aspects of the wave-plasma interaction: (1) wave propagation and absorption in the plasma, and (2) the quasilinear response of the plasma distribution function to the wave heating. This is a nonlinear problem in which the energetic ions generated by the waves can significantly alter the wave propagation and absorption in the plasma. The energetic ions can also absorb power at high harmonics of the ion cyclotron frequency where finite Larmor radius expansions are not valid. Thus, an electromagnetic field solver is required that is valid to all orders in the ion Larmor radius as well as for arbitrary non-Maxwellian distribution functions. In this work, the all-orders global-wave solver AORSA [1] is combined with the CQL3D bounce-averaged Fokker-Planck code [2] to simulate the quasilinear evolution of non-thermal ion distributions in ICRF heating. The time required for evaluation of the non-Maxwellian ion conductivity operator has been significantly reduced through collaboration with the applied mathematics community, and a novel re-formulation of the quasilinear operator has enabled calculation of the velocity space diffusion coefficients directly from the global wave fields. Self-consistency between the wave fields and resonant ion distribution function is achieved by iterating between the global wave and Fokker-Planck solutions. These calculations would not be possible without the massively parallel architectures required for the global-wave solver. The combined self-consistent model has been applied to a variety of wave-plasma interactions including high harmonic interactions with fast neutral beam particles in NSTX and DIII-D, as well as second harmonic interactions with tritium ions in ITER. Calculations of minority ion heating in Alcator C-Mod show the formation of an 80 keV ion tail near the resonance layer in approximate agreement with measurements from charge exchange neutral particle analyzers [3]. Recently, the AORSA global-wave solver has been ported to the new Cray XT-3 (Jaguar) at ORNL where it demonstrates excellent scaling with the number of processors. Preliminary calculations using 4096 processors have allowed the first simulations of mode conversion in ITER. Mode conversion from the fast wave to the ion cyclotron wave (ICW) has been identified in ITER using mixtures of deuterium, tritium and helium3 at 53 MHz.
Bounce-averaged velocity distribution function for ions heated by ion cyclotron resonance heating in a tokamak plasma. Contours in perpendicular and parallel velocity are shown along the minor radius of the tokamak with the plasma center at the lower right and the plasma edge at the upper left.
[1] E. F. Jaeger, L. A. Berry, J. R. Myra, et al., Phys. Rev. Lett. 90, 195001-1 (2003).
[2] R. W. Harvey and M. G. McCoy, Proceedings of the IAEA Technical Committee Meeting on Simulation and Modeling of Thermonuclear Plasmas, Montreal, Canada, 1992 (USDOC NTIS Document No. DE93002962).
[3] V. Tang, R. Parker, P. Bonoli et al., Bulletin of the American Physical Society 50, 195 (2005).