Trinity: A Unified Treatment of Turbulence, Transport, and Heating in Magnetized Plasmas

To faithfully simulate ITER and other modern fusion devices, one must resolve electron and ion fluctuation scales in a five-dimensional phase space and time. Simultaneously, one must account for the interaction of this turbulence with the slow evolution of the large-scale plasma profiles. Because of the enormous range of scales involved and the high dimensionality of the problem, resolved first-principles global simulations are very challenging using conventional (brute force) techniques. In this thesis, the problem of resolving turbulence is addressed by developing velocity space resolution diagnostics and an adaptive collisionality that allow for the confident simulation of velocity space dynamics using the approximate minimal necessary dissipation. With regard to the wide range of scales, a new approach has been developed in which turbulence calculations from multiple gyrokinetic flux tube simulations are coupled together using transport equations to obtain self-consistent, steady-state background profiles and corresponding turbulent fluxes and heating. This approach is embodied in a new code, Trinity, which is capable of evolving equilibrium profiles for multiple species, including electromagnetic effects and realistic magnetic geometry, at a fraction of the cost of conventional global simulations. Furthermore, an advanced model physical collision operator for gyrokinetics has been derived and implemented, allowing for the study of collisional turbulent heating, which has not been extensively studied. To demonstrate the utility of the coupled flux tube approach, preliminary results from Trinity simulations of the core of an ITER plasma are presented.Comment: 187 pages, 53 figures, Ph.D. thesis in physics at University of Maryland, single-space versio

Recent development of fully kinetic particle-in-cell method and its application to fusion plasma instability study

This paper reviews the recent advancements of the algorithm and application to fusion plasma instability study of the fully kinetic Particle-in-Cell (PIC) method. The strengths and limitations of both explicit and implicit PIC methods are described and compared. Additionally, the semi-implicit PIC method and the code ECsim used in our research are introduced. Furthermore, the application of PIC methods in fusion plasma instabilities is delved into. A detailed account of the recent progress achieved in the realm of tokamak plasma simulation through fully kinetic PIC simulations is also provided. Finally the prospective future development and application of PIC methods are discussed as well

Gyrokinetic particle simulation for thermonuclear plasma turbulence studies in magnetic confinement

Thermal transport in a magnetised plasma is believed to be substantially enhanced due to turbulence. The ELMFIRE code has been developed for tokamak plasma turbulence studies in high temperature magnetized plasmas. ELMFIRE calculates the evolution of the Boltzmann equation in a magnetized plasma, including long scale interactions between particles calculated through field equations. In this work we concentrate on benchmarking the ELMFIRE against published results from other turbulence codes, for instabilities (linear benchmarking) and turbulent heat flux (non-linear benchmarking). We investigate the effects of spatial and velocity-space resolution in the benchmarking cases.Lämmön kuljetus magneettisesti koossapidetyssä plasmassa havaittiin odotettua suuremmaksi turbulenssin vuoksi. Simulointimalli nimeltä ELMFIRE on kehitetty Aalto Yliopiston ja VTT:n yhteistyössä tokamakissa havaittavan tehostuneen lämmön kuljetuksen tutkimiseen. ELMFIREssa käytetty malli perustuu kaasujen kineettiseen teoriaan, jota hyödyntäen voidaan simuloida fuusioreaktorissa tapahtuvia ilmiöitä ilman, että joudutaan olettamaan termodynaaminen tasapainotila (jota ei tokamakissa saavuteta). Tutkimme tässä työssä ELMFIREn tuloksia kansainvälisessä kirjallisuudessa julkaistuihin tuloksiin, niin epävakaisuuksien kuin niistä syntyvän turbulenssin osalta

Gyrokinetic particle-in-cell global simulations of ion-temperature-gradient and collisionless-trapped-electron-mode turbulence in tokamaks

The goal of thermonuclear fusion research is to provide power plants, that will be able to produce one gigawatt of electricity. Among the different ways to achieve fusion, the tokamak, based on magnetic confinement, is the most promising one. A gas is heated up to hundreds of millions of degrees and becomes a plasma, which is maintained – or confined – in a toroidal vessel by helical magnetic field lines. Then, deuterium and tritium are injected and fuse to create an α particle and an energetic neutron. In order to have a favorable power balance, the power produced by fusion reactions must exceed the power needed to heat the plasma and the power losses. This can be cast in a very simple expression which stipulates that the product of the density, the temperature and the energy confinement time must exceed some given value. Unfortunately, present-days tokamaks are not able to reach this condition, mostly due to plasma turbulence. The latter phenomenon enhances the heat losses and degrades the energy confinement time, which cannot be predicted by analytical theories such as the so-called neoclassical theory in which the heat losses are caused by Coulomb collisions. Therefore, numerical simulations are being developed to model plasma turbulence, mainly caused by the Ion and Electron Temperature-Gradient and the Trapped-Electron-Mode instabilities. The plasma is described by a distribution function which evolves according to the Vlasov equation. The electromagnetic fields created by the particles are self-consistently obtained through Maxwell's equations. The resulting Vlasov-Maxwell system is greatly simplified by using the gyrokinetic theory, which consists, through an appropriate ordering, of eliminating the fast gyromotion (compared to the typical frequency of instabilities). Nevertheless, it is still extremely difficult to solve this system numerically due to the large range of time and spatial scales to be resolved. In this thesis, the Vlasov-Maxwell system is solved in the electrostatic and collisionless limit with the Particle-In-Cell (PIC) ORB5 code in global tokamak geometry. This Monte-Carlo approach suffers from statistical noise which unavoidably degrades the quality of the simulation. Consequently, the first part of this work has been devoted to the optimization of the code with a view to reduce the numerical noise. The code has been rewritten in a new coordinate system which takes advantage of the anisotropy of turbulence, which is mostly aligned with the magnetic field lines. The overall result of the optimization is that for a given accuracy, the CPU time has been decreased by a factor two thousand, the total memory has been decreased by a factor ten and the numerical noise has been reduced by a factor two hundred. In addition, the scaling of the code with respect to plasma size is presently optimal, suggesting that ORB5 could compute heat transport for future fusion devices such as ITER. The second part of this thesis presents the validation of the code with numerical convergence tests, linear (including dispersion relations) and nonlinear benchmarks. Furthermore, the code has been applied to important issues in gyrokinetic theory. It is shown for the first time that a 5D global delta-f PIC code can achieve a thermodynamic steady state on the condition that some dissipation is present. This is a fundamental result as the main criticism against delta-f PIC codes is their inability to deal with long time simulations. Next, the role of the parallel nonlinearity is studied and it is demonstrated in this work that this term has no real influence on turbulence, provided the numerical noise is sufficiently low. This result should put an end to the controversy that recently occurred, in which gyrokinetic simulations using different numerical approaches yielded contradictory results. Finally, thanks to the optimization of the code, the gyrokinetic model has been extended to include the kinetic response of trapped-electrons, in place to the usual adiabatic (Boltzmann) approximation. For the first time, global TEM nonlinear simulations are presented, and the role of the zonal flow on heat transport is analyzed. This study will help in acquiring some knowledge on the less-known TEM turbulence (as compared to ITG). In conclusion, this thesis is one of the main steps of the development of ORB5, which is now a state-of-the-art gyrokinetic code for collisionless ITG and TEM turbulence, and has brought several contributions to the understanding of these phenomena