Gyrokinetic simulations of fusion plasmas using a spectral velocity space representation
arXiv:1603.04727
Abstract
Magnetic confinement fusion reactors suffer severely from heat and particle losses through turbulent transport, which has inspired the construction of ever larger and more expensive reactors. Numerical simulations are vital to their design and operation, but particle collisions are too infrequent for fluid descriptions to be valid. Instead, strongly magnetised fusion plasmas are described by the gyrokinetic equations, a nonlinear integro-differential system for evolving the particle distribution functions in a five-dimensional position and velocity space, and the consequent electromagnetic field. Due to the high dimensionality, simulations of small reactor sections require hundreds of thousands of CPU hours on High Performance Computing platforms. We develop a Hankel-Hermite spectral representation for velocity space that exploits structural features of the gyrokinetic system. The representation exactly conserves discrete free energy in the absence of explicit dissipation, while our Hermite hypercollision operator captures Landau damping with few variables. Calculation of the electromagnetic fields becomes purely local, eliminating inter-processor communication in, and vastly accelerating, searches for linear instabilities. We implement these ideas in SpectroGK, an efficient parallel code. Turbulent fusion plasmas may dissipate free energy through linear phase mixing to fine scales in velocity space, as in Landau damping, or through a nonlinear cascade to fine scales in physical space, as in hydrodynamic turbulence. Using SpectroGK to study saturated electrostatic drift-kinetic turbulence, we find that the nonlinear cascade suppresses linear phase mixing at energetically-dominant scales, so the turbulence is fluid-like. We use this observation to derive Fourier-Hermite spectra for the electrostatic potential and distribution function, and confirm these spectra with simulations.
arXiv commentDoctoral Thesis, University of Oxford, 189 pages, 41 figures
References in corpus (20)
- MHD Turbulence Revisited
- A Model of Turbulence in Magnetized Plasmas: Implications for the Dissipation Range in the Solar Wind
- Kinetic Simulations of Magnetized Turbulence in Astrophysical Plasmas
- Computing Nearly Singular Solutions Using Pseudo-Spectral Methods
- The Anisotropy of Electron MHD Turbulence
- Current Sheets and Collisionless Damping in Kinetic Plasma Turbulence
- Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence
- Critical balance in magnetohydrodynamic, rotating and stratified turbulence: towards a universal scaling conjecture
- Critically balanced ion temperature gradient turbulence in fusion plasmas
- Direct multiscale coupling of a transport code to gyrokinetic turbulence codes
- AstroGK: Astrophysical Gyrokinetics Code
- Fast collisionless reconnection and electron heating in strongly magnetized plasmas
- A Kinetic Alfven wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU
- Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems
- Zero-Turbulence Manifold in a Toroidal Plasma
- Energy transfer and dual cascade in kinetic magnetized plasma turbulence
- Gyrokinetic simulation of entropy cascade in two-dimensional electrostatic turbulence
- The Zero Turbulence Manifold in Fusion Plasmas
- Irreversible energy flow in forced Vlasov dynamics
- On the velocity space discretization for the Vlasov-Poisson system: comparison between Hermite spectral and Particle-in-Cell methods. Part 2: fully-implicit scheme