Rapid Fourier space solution of linear partial differential equations in toroidal magnetic confinement geometries

Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson's equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al., (2007) [5]), with a regular (non-field-aligned) mesh. (C) 2009 Published by Elsevier B.V

ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry

This paper presents the current state of the global gyrokinetic code ORB5 as an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177 409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of equations using a PIC scheme and also includes collisions and strong flows. The code assumes multiple gyrokinetic ion species at all wavelengths for the polarization density and drift-kinetic electrons. Variants of the physical model can be selected for electrons such as assuming an adiabatic response or a ``hybrid'' model in which passing electrons are assumed adiabatic and trapped electrons are drift-kinetic. A Fourier filter as well as various control variates and noise reduction techniques enable simulations with good signal-to-noise ratios at a limited numerical cost. They are completed with different momentum and zonal flow-conserving heat sources allowing for temperature-gradient and flux-driven simulations. The code, which runs on both CPUs and GPUs, is well benchmarked against other similar codes and analytical predictions, and shows good scalability up to thousands of nodes

Kinetic ballooning mode studies and the treatment of electromagnetic microinstabilities and turbulence in complex geometry

Magnetically confined thermonuclear fusion is promising as a future power source. However, the viability of fusion power plants is strongly influenced by how well the thermal energy can be confined in the plasma fuel. Often, the dominant process governing confinement is microinstability-driven plasma turbulence. This thesis studies microinstabilities and turbulence using gyrokinetic simulations, which may ultimately inform fusion reactor design and operation. The effect of plasma triangularity on stability in spherical tokamaks (STs) is examined using linear simulations of hypothetical ST equilibria. It is found that the kinetic ballooning mode (KBM), an electromagnetic pressure-driven microinstability, likely prohibits negative triangularity in ST power plants, since negative triangularity closes the "second stability window" for n = infinity ideal magnetohydrodynamic (MHD) ballooning modes. ST equilibria with positive triangularity can access the second stability window, although remain weakly unstable to KBMs. Secondly, microinstabilities are studied for the optimised stellarator Wendelstein 7-X (W7-X). Electrostatic "stability valley" results are reproduced using stella: a gyrokinetic code which offers flexibility in time-marching schemes by using operator splitting. stella is extended to include A_parallel and B_parallel fluctuations linearly using both implicit and explicit schemes. Benchmarking against the code GS2 shows good agreement for electromagnetic tokamak simulations. Using this implementation, the W7-X stability valley at finite beta (=plasma pressure/magnetic pressure) is preliminarily explored. The electromagnetic instabilities observed may be relevant to future W7-X experiments. Finally, a non-interpolating semi-Lagrangian scheme, aiming to efficiently simulate electromagnetic turbulence by eliminating the Courant-Freidrichs-Lewy timestep constraint in nonlinear gyrokinetics, is implemented in stella. A new operator splitting scheme is developed and used to mix single and multi-step numerical methods. Unfortunately, nonlinear tests show low accuracy and currently unexplained numerical instability. Elucidating the reasons for this would be an interesting area of future research

Full-wave modeling of lower hybrid waves on Alcator C-Mod

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 225-237).This thesis focuses on several aspects of the Lower Hybrid (LH) wave physics, the common theme being the development of full-wave simulation codes based on Finite Element Methods (FEM) used in support of experiments carried out on the Alcator C-Mod tokamak. In particular, two non-linear problems have been adressed: high power antenna-plasma coupling and current drive (CD). In both cases, direct solution of the wave equation allowed testing the validity of approximations which were historically done and consider full-wave effects and realistic geometries. The first code, named POND, takes into account the interaction of high power LH waves and the plasma edge based on the non-linear ponderomotive force theory. Simulations found the effect of ponderomotive forces to be compatible with the density depletion which is measured in front of the antenna in presence of high power LH waves. The second code, named LHEAF, solves the problem of LH wave propagation in a hot non- Maxwellian plasma. The electron Landau damping (ELD) effect was expressed as a convolution integral along the magnetic field lines and the resultant integro-differential Helmholtz equation was solved iteratively. A 3D Fokker-Planck code and a synthetic Hard X-Ray (HXR) diagnostic modules are used to calculate the self-consistent electron distribution function and evaluate the resulting CD and bremsstrahlung radiation. LHEAF has been used to investigate the anomalous degradation of LHCD efficiency at high density. Results show that while a small fraction of the launched power can be absorbed in the SOL by collisions, it is a strong upshift in the nii spectrum that makes the overall LHCD efficiency low by allowing the waves to Landau damp near the edge. Wavelet analysis of the full-wave fields identified spectral broadening to occur after the waves reflect and propagate in the SOL. This work explains why on Alcator C-Mod the eikonal approximation is valid only in the low to moderate density regime, and why parasitic phenomena introduced in previous work can reproduce phenomenologically well the experimental results.by Orso Meneghini.Ph.D

Establishment of an Institute for Fusion Studies. Technical progress report, November 1, 1994--October 31, 1995

The Institute for Fusion Studies is a national center for theoretical fusion plasma physics research. Its purposes are to (1) conduct research on theoretical questions concerning the achievement of controlled fusion energy by means of magnetic confinement--including both fundamental problems of long-range significance, as well as shorter-term issues; (2) serve as a national and international center for information exchange by hosting exchange visits, conferences, and workshops; and (3) train students and postdoctoral research personnel for the fusion energy program and plasma physics research areas. During FY 1995, a number of significant scientific advances were achieved at the IFS, both in long-range fundamental problems as well as in near-term strategic issues, consistent with the Institute`s mandate. Examples of these achievements include, for example, tokamak edge physics, analytical and computational studies of ion-temperature-gradient-driven turbulent transport, alpha-particle-excited toroidal Alfven eigenmode nonlinear behavior, sophisticated simulations for the Numerical Tokamak Project, and a variety of non-tokamak and non-fusion basic plasma physics applications. Many of these projects were done in collaboration with scientists from other institutions. Research discoveries are briefly described in this report