The object of this review is to summarize the achievements of research on the Alcator C-Mod tokamak [Hutchinson et al., Phys. Plasmas 1, 1511 (1994) and Marmar, Fusion Sci. Technol. 51, 261 (2007)] and to place that research in the context of the quest for practical fusion energy. C-Mod is a compact, high-field tokamak, whose unique design and operating parameters have produced a wealth of new and important results since it began operation in 1993, contributing data that extends tests of critical physical models into new parameter ranges and into new regimes. Using only high-power radio frequency (RF) waves for heating and current drive with innovative launching structures, C-Mod operates routinely at reactor level power densities and achieves plasma pressures higher than any other toroidal confinement device. C-Mod spearheaded the development of the vertical-target divertor and has always operated with high-Z metal plasma facing components—approaches subsequently adopted for ITER. C-Mod has made ground-breaking discoveries in divertor physics and plasma-material interactions at reactor-like power and particle fluxes and elucidated the critical role of cross-field transport in divertor operation, edge flows and the tokamak density limit. C-Mod developed the I-mode and the Enhanced Dα H-mode regimes, which have high performance without large edge localized modes and with pedestal transport self-regulated by short-wavelength electromagnetic waves. C-Mod has carried out pioneering studies of intrinsic rotation and demonstrated that self-generated flow shear can be strong enough in some cases to significantly modify transport. C-Mod made the first quantitative link between the pedestal temperature and the H-mode's performance, showing that the observed self-similar temperature profiles were consistent with critical-gradient-length theories and followed up with quantitative tests of nonlinear gyrokinetic models. RF research highlights include direct experimental observation of ion cyclotron range of frequency (ICRF) mode-conversion, ICRF flow drive, demonstration of lower-hybrid current drive at ITER-like densities and fields and, using a set of novel diagnostics, extensive validation of advanced RF codes. Disruption studies on C-Mod provided the first observation of non-axisymmetric halo currents and non-axisymmetric radiation in mitigated disruptions. A summary of important achievements and discoveries are included.

/pdf/20-years-of-research-on-the-alcator-c-mod-tokamak-15fba2d02u.pdf

20 years of research on the Alcator C-Mod tokamak

Nonlinear interactions of ion cyclotron range of frequency (ICRF) waves with fusion plasmas are reviewed. Although the linear theory of ICRF waves, including fast waves (FWs), high-harmonic fast waves and ion Bernstein waves (IBWs), is widely applicable, nonlinear effects can still be important, especially in the edge plasma or for novel core applications. Here the topics of flow drive, ponderomotive forces, radiofrequency (rf) sheaths, parametric decay and related interactions with the edge plasma are considered. Primary emphasis is placed on the basic underlying physics and tokamak applications. For FW antennas, the parallel electric field near launching structures is known to drive rf sheaths which can give rise to convective cells, interaction with plasma 'blobs', impurity production and edge power dissipation. In addition to sheaths, IBW waves in the edge plasma are subject to strong ponderomotive effects and parametric decay. In the core plasma, slow waves can sometimes induce nonlinear effects. Mechanisms by which these waves can influence the radial electric field and its shear are summarized and related to the general (reactive-ponderomotive and dissipative) force on a plasma from rf waves. Standard ICRF codes have begun to incorporate the nonlinear topics described here. Further progress in integrated simulation should allow new predictive modelling capabilities.

/pdf/nonlinear-icrf-plasma-interactions-4mjjju6omh.pdf

Nonlinear ICRF-plasma interactions

Simulation of dense plasmas in the radiofrequency range are typically performed in the frequency domain, i.e., by solving Laplace-transformed Maxwell’s equations. This technique is well-suited for the study of linear heating and quasilinear evolution, but does not generalize well to the study of nonlinear phenomena. Conversely, time-domain simulation in this range is difficult because the time scale is long compared to the electron plasma wave period, and in addition, the various cutoff and resonance behaviors within the plasma insure that any explicit finite-difference scheme would be numerically unstable. To resolve this dilemma, explicit finite-difference Maxwell terms are maintained, but a carefully time-centered locally implicit method is introduced to treat the plasma current, such that all linear plasma dispersion behavior is faithfully reproduced at the available temporal and spatial resolution, despite the fact that the simulation time step may exceed the electron gyro and electron plasma time sc...

Finite-difference time-domain simulation of fusion plasmas at radiofrequency time scales

Gaussian elimination is a canonical linear algebra procedure for solving linear systems of equations. In the last few years, the algorithm has received a lot of attention in an attempt to improve its parallel performance. This article surveys recent developments in parallel implementations of Gaussian elimination for shared memory architecture. Five different flavors are investigated. Three of them are based on different strategies for pivoting: partial pivoting, incremental pivoting, and tournament pivoting. The fourth one replaces pivoting with the Partial Random Butterfly Transformation, and finally, an implementation without pivoting is used as a performance baseline. The technique of iterative refinement is applied to recover numerical accuracy when necessary. All parallel implementations are produced using dynamic, superscalar, runtime scheduling and tile matrix layout. Results on two multisocket multicore systems are presented. Performance and numerical accuracy is analyzed. Copyright © 2014 John Wiley & Sons, Ltd.

/pdf/a-survey-of-recent-developments-in-parallel-implementations-1xmagu3dud.pdf

A survey of recent developments in parallel implementations of Gaussian elimination

A simple method intended to quickly assess the net acceleration of particle populations due to wave heating is proposed. It adopts the philosophy proposed by Stix (1975 Nucl. Fusion 15 737; 1992 Waves in Plasmas (New York: AIP) pp 510–3) to compute the 1D distribution function of ion cyclotron resonance frequency heated species, but extends it on various fronts to allow describing tail formation of both minority and majority populations at any cyclotron harmonic. All plasma constituents are evolved by solving a set of coupled Fokker–Planck equations iteratively. As electrons easily reach high velocities, the relativistic collision operator for electron self-collisions has been implemented. Including a constant finite energy confinement time allows us to incorporate local losses qualitatively.

/pdf/simple-1d-fokker-planck-modelling-of-ion-cyclotron-resonance-2g712xtt4b.pdf

Simple 1D Fokker–Planck modelling of ion cyclotron resonance frequency heating at arbitrary cyclotron harmonics accounting for Coulomb relaxation on non-Maxwellian populations

The AORSA global-wave solver is combined with the CQL3D bounce-averaged Fokker-Planck code to simulate the quasilinear evolution of non-thermal distributions in ion cyclotron resonance heating of tokamak plasmas. A novel re-formulation of the quasilinear operator enables calculation of the velocity space diffusion coefficients directly from the global wave fields. To obtain self-consistency between the wave fields and particle distribution function, AORSA and CQL3D have been iteratively coupled using Python. The combined selfconsistent model is applied to minority ion heating in the Alcator C-Mod tokamak. Results show the formation of a 70 keV ion tail near the minority ion cyclotron resonance layer in approximate agreement with measurements from charge exchange neutral particle analyzers.

Quasilinear evolution of non-thermal distributions in ion cyclotron resonance heating of tokamak plasmas

Global wave solutions with self-consistent velocity distributions are calculated for ion cyclotron heating in non-Maxwellian plasmas. The all-orders spectral algorithm (AORSA) global wave solver is generalized to treat non-thermal velocity distributions arising from fusion reactions, neutral beam injection and wave driven diffusion in velocity space. Quasi-linear diffusion coefficients are derived directly from the wave electric field and used to calculate ion velocity distribution functions with the CQL3D Fokker–Planck code. Alternatively, the quasi-linear coefficients can be calculated numerically by integrating the Lorentz force equations along particle orbits. Self-consistency between the wave electric field and resonant ion distribution function is achieved by iterating between the global-wave and Fokker–Planck solutions.

Global-wave solutions with self-consistent velocity distributions in ion cyclotron heated plasmas

Magnetically confined plasmas can contain significant concentrations of nonthermal plasma particles arising from fusion reactions, neutral beam injection, and wave-driven diffusion in velocity space. Initial studies in one-dimensional and experimental results show that nonthermal energetic ions can significantly affect wave propagation and heating in the ion cyclotron range of frequencies. In addition, these ions can absorb power at high harmonics of the cyclotron frequency where conventional two-dimensional global-wave models are not valid. In this work, the all-orders global-wave solver AORSA [E. F. Jaeger et al., Phys. Rev. Lett. 90, 195001 (2003)] is generalized to treat non-Maxwellian velocity distributions. Quasilinear diffusion coefficients are derived directly from the wave fields and used to calculate energetic ion velocity distributions with the CQL3D Fokker-Planck code [R. W. Harvey and M. G. McCoy, Proceedings of the IAEA Technical Committee Meeting on Simulation and Modeling of Thermonuclear ...

Self-consistent full-wave and Fokker-Planck calculations for ion cyclotron heating in non-Maxwellian plasmasa)

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Quasilinear evolution of non-thermal distributions in ion cyclotron resonance heating of tokamak plasmas

Global-wave solutions with self-consistent velocity distributions in ion cyclotron heated plasmas

Self-consistent full-wave and Fokker-Planck calculations for ion cyclotron heating in non-Maxwellian plasmasa)