Implementation of 2D Domain Decomposition in the UCAN Gyrokinetic Particle-in-Cell Code and Resulting Performance of UCAN2

The massively parallel, nonlinear, three-dimensional (3D), toroidal, electrostatic, gyrokinetic, particle-in-cell (PIC), Cartesian geometry UCAN code, with particle ions and adiabatic electrons, has been successfully exercised to identify non-diffusive transport characteristics in present day tokamak discharges. The limitation in applying UCAN to larger scale discharges is the 1D domain decomposition in the toroidal (or z-) direction for massively parallel implementation using MPI which has restricted the calculations to a few hundred ion Larmor radii or gyroradii per plasma minor radius. To exceed these sizes, we have implemented 2D domain decomposition in UCAN with the addition of the y-direction to the processor mix. This has been facilitated by use of relevant components in the P2LIB library of field and particle management routines developed for UCLA's UPIC Framework of conventional PIC codes. The gyro-averaging specific to gyrokinetic codes is simplified by the use of replicated arrays for efficient charge accumulation and force deposition. The 2D domain-decomposed UCAN2 code reproduces the original 1D domain nonlinear results within round-off. Benchmarks of UCAN2 on the Cray XC30 Edison at NERSC demonstrate ideal scaling when problem size is increased along with processor number up to the largest power of 2 available, namely 131,072 processors. These particle weak scaling benchmarks also indicate that the 1 nanosecond per particle per time step and 1 TFlops barriers are easily broken by UCAN2 with 1 billion particles or more and 2000 or more processors.This work was supported in part in the USA by Grant No. DE-FG02-04ER54741 to the University of Alaska, Fairbanks, AK, from the Office of Fusion Energy Sciences, Office of Science, United States Department of Energy. It was also supported in part at Universidad Carlos III, Madrid, Spain, by Spanish National Project No. ENE2009-12213-C03-03. This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. It also took advantage of resources at the Barcelona Supercomputing Center (BSC), Centro Nacional de Supercomputación, Barcelona, Spain. One of us (Leboeuf) would particularly like to thank David Vicente from BSC and Zhengji Zhao from NERSC for their help in the porting, debugging, and optimization of UCAN2 on the mainframes at their respective centers

Electron-scale reduced fluid models with gyroviscous effects

Reduced fluid models for collisionless plasmas including electron inertia and finite Larmor radius corrections are derived for scales ranging from the ion to the electron gyroradii. Based either on pressure balance or on the incompressibility of the electron fluid, they respectively capture kinetic Alfv\'en waves (KAWs) or whistler waves (WWs), and can provide suitable tools for reconnection and turbulence studies. Both isothermal regimes and Landau fluid closures permitting anisotropic pressure fluctuations are considered. For small values of the electron beta parameter $\beta_e$, a perturbative computation of the gyroviscous force valid at scales comparable to the electron inertial length is performed at order $O(\beta_e)$, which requires second-order contributions in a scale expansion. Comparisons with kinetic theory are performed in the linear regime. The spectrum of transverse magnetic fluctuations for strong and weak turbulence energy cascades is also phenomenologically predicted for both types of waves. In the case of moderate ion to electron temperature ratio, a new regime of KAW turbulence at scales smaller than the electron inertial length is obtained, where the magnetic energy spectrum decays like $k_\perp^{-13/3}$, thus faster than the $k_\perp^{-11/3}$ spectrum of WW turbulence.Comment: 29 pages, 4 figure

Microturbulent transport of non-Maxwellian alpha particles

A burning Deuterium-Tritium plasma is one which depends upon fusion-produced alpha particles for self-heating. Whether a plasma can reach a burning state requires knowledge of the transport of alpha particles, and turbulence is one such source of transport. The alpha particle distribution in collisional equilibrium forms a non-Maxwellian tail which spans orders of magnitude in energy, and it is this tail that is responsible for heating the plasma. Newly-born high-energy alpha particles are not expected to respond to turbulence as strongly as alpha particles that have slowed down to the bulk plasma temperature. This dissertation presents a low-collisionality derivation of gyrokinetics relevant for alpha particles and describes the upgrades made to the GS2 flux-tube code to handle general non-Maxwellian energy distributions. With the ability to run self-consistent simulations with a population of alpha particles, we can examine certain assumptions commonly made about alpha particles in the context of microturbulence. It is found that microturbulence can compete with collisional slowing-down, altering the distribution further. One assumption that holds well in electrostatic turbulence is the trace approximation, which is built upon to develop a model for efficiently calculating the coupled radial-energy turbulent transport of a non-Maxwellian species. A new code was written for this purpose and corrections to the global alpha particle heating profile due to microturbulence in an ITER-like scenario are presented along with sensitivity studies

Saturation Physics of Threshold Heat-Flux Reduction

The saturation physics of ion-temperature-gradient-driven turbulence is examined in relation to the temperature-gradient variation of the heat flux, which can exhibit an upshift of the critical gradient for significant flux relative to the linear instability threshold. Gyrokinetic measurements of saturation properties and spectral energy transfer, which will be defined in Sec. II, are presented, indicating that the physics of saturation is fundamentally unchanged on either side of the upshifted gradient. To analyze heat transport below and above the upshifted critical gradient, a fluid model for toroidal ion-temperature-gradient turbulence is modified to include the kinetic instability threshold. The model and the heat flux are rendered in the eigenmode decomposition to track the dominant mode-coupling channel of zonal-flow-catalyzed transfer to a conjugate stable mode. Given linear and nonlinear symmetries, the stable mode level and the cross-correlation of the unstable and stable mode amplitudes are related to the unstable mode level via linear physics. The heat flux can then be written in terms of the unstable-mode level, which through a nonlinear balance depends on the eigenmode-dependent coupling coefficients and the triplet correlation time of the dominant coupled modes. Resonance in these quantities leads to suppressed heat flux above the linear threshold, with a nonlinear upshift of the critical gradient set by the resonance broadening of a finite perpendicular wavenumber and collisionality.</p

Turbulent and neoclassical transport in tokamak plasmas

One of the greatest challenges of thermonuclear fusion is to understand, predict and to some extent control particle and energy transport in fusion plasmas. In the present thesis we consider theoretical and experimental aspects of collisional and turbulent transport in tokamak plasmas.First the collisionality dependence of quasilinear particle flux due to ion temperature gradient (ITG) and trapped electron modes is investigated. A semi-analytical gyrokinetic model of electrostatic microinstabilities is developed and used to study various parametric dependences of ITG stability thresholds and quasilinear particle and energy fluxes, focusing on the effect of collisions.Then corrections to the neoclassical plateau regime transport in transport barriers are calculated. It is found that the ion temperature gradient drive of the bootstrap current can be enhanced significantly, and the ion heat diffusivity and the poloidal flow of trace impurities are also modified in the presence of strong radial electric fields.Furthermore, we investigate the characteristics of microinstabilities in electron cyclotron heated and ohmic discharges in the T10 tokamak using linear gyrokinetic simulations, aiming to find insights into the effect of auxiliary heating on the transport, with special emphasis on impurity peaking.The effect of primary ion species of differing charge and mass on instabilities and transport is studied through linear and nonlinear gyrokinetic simulations. We perform transport analysis of three balanced neutral beam injection discharges from the DIII-D tokamak which have different main ion species (deuterium, hydrogen and helium).Finally the magnitude and characteristics of the error in alkali beam emission spectroscopy density profile measurements due to finite beam width are analyzed and a deconvolution based correction algorithm is introduced

Turbulent and neoclassical transport in tokamak plasmas

One of the greatest challenges of thermonuclear fusion is to understand, predict and to some extent control particle and energy transport in fusion plasmas. In the present thesis we consider theoretical and experimental aspects of collisional and turbulent transport in tokamak plasmas.First the collisionality dependence of quasilinear particle flux due to ion temperature gradient (ITG) and trapped electron modes is investigated. A semi-analytical gyrokinetic model of electrostatic microinstabilities is developed and used to study various parametric dependences of ITG stability thresholds and quasilinear particle and energy fluxes, focusing on the effect of collisions.Then corrections to the neoclassical plateau regime transport in transport barriers are calculated. It is found that the ion temperature gradient drive of the bootstrap current can be enhanced significantly, and the ion heat diffusivity and the poloidal flow of trace impurities are also modified in the presence of strong radial electric fields.Furthermore, we investigate the characteristics of microinstabilities in electron cyclotron heated and ohmic discharges in the T10 tokamak using linear gyrokinetic simulations, aiming to find insights into the effect of auxiliary heating on the transport, with special emphasis on impurity peaking.The effect of primary ion species of differing charge and mass on instabilities and transport is studied through linear and nonlinear gyrokinetic simulations. We perform transport analysis of three balanced neutral beam injection discharges from the DIII-D tokamak which have different main ion species (deuterium, hydrogen and helium).Finally the magnitude and characteristics of the error in alkali beam emission spectroscopy density profile measurements due to finite beam width are analyzed and a deconvolution based correction algorithm is introduced

Gyrokinetic simulation of multimode plasma turbulence

Durch Mikroturbulenz verursachter Wärme- und Teilchentransport in magnetisch eingeschlossenen Hochtemperaturplasmen ist eines der drängendsten Probleme der Fusionsforschung.In dieser Arbeit werden die gyrokinetischen Gleichungen, die magnetisierte Plasmen bei fusionsrelevanten Parametern beschreiben, für allgemeine magnetische Geometrien unter Berücksichtigung von Stößen präsentiert, weiterhin werden Aspekte der numerischen Implementierung in den massiv parallelen Plasmaturbulenz-Code GENE diskutiert. Nichthermitescher Entartungen in lineare Modenübergängen werden mit Hilfe eines Eigenwertlösers untersucht. Statistische Untersuchungen der ExB-Nichtlinearität im Fall reiner Trapped Electron Mode (TEM) Turbulenz zeigen, dass diese durch einen Diffusionsterm approximiert werden kann, was ein schon bekanntes quasilineares Transportmodell stützt. Es werden Übergänge zwischen TEM- und Ion Temperature Gradient (ITG) Turbulenz untersucht, eine Koexistenz führt zu interessanten Effekten beim Teilchentransport. Abschließend werden verschiedene Aspekte der ITG-Turbulenz im Stellarator W7-X mit adiabatischen und kinetischen Elektronen diskutiert