Basic Investigation of Turbulent Structures and Blobs of Relevance for Magnetic Fusion Plasmas

Similarly to neutral fluids, plasmas often exhibit turbulent behavior. Turbulence in plasmas is usually more complex than in neutral fluids due to long range interactions via electric and magnetic fields, and kinetic effects. It gives rise to many interesting phenomena such as self-generated magnetic fields (dynamos), zonal-flows, transport barriers, or particle pinches. Plasma turbulence plays a crucial role for the success of nuclear fusion as a potentially clean, safe, and long-term source for electric power production. Turbulent processes in the edge and scrape-off layer (SOL) of magnetic fusion plasmas determine, to a large extent, the overall confinement properties. They also influence the life time of plasma facing components, impurity production and influx, main chamber recycling, tritium retention, and helium ash removal. Edge turbulence is often dominated by blobs or filaments, magnetic-field-aligned plasma structures observed in the edge of virtually all magnetized plasmas. This thesis investigates basic aspects of edge turbulence and blobs in simple magnetized toroidal TORPEX plasmas. TORPEX includes important ingredients of SOL physics, such as pressure gradients, "∇B" and curvature of the magnetic field, together with open field lines. A relatively simple magnetic geometry, full diagnostics access and the possibility of controlled parameter scans allow isolating and studying instabilities and turbulence effects that occur in more complicated forms in fusion and astrophysical plasmas. Using a number of optimized probe diagnostic methods, the mechanisms for the generation of blobs from ideal interchange waves and for their subsequent propagation are elucidated. A blob velocity scaling law is introduced that takes into account several damping effects of blob cross-field velocity. This scaling law is in good agreement both with blob simulations and experiments on TORPEX. Studies on blob parallel dynamics shed light on blob induced parallel currents and the transport of parallel momentum. Based on this understanding of blob motion, several tools to influence blobs and turbulence as a whole are developed. A methodology for plasma turbulence code validation is established. Using a large set of observables, the agreement between experiments and both 2D and global 3D two-fluid simulations is quantified.

Turbulent regimes in the tokamak scrape-off layer

Annamaria Mosetto

The tokamak scrape-off layer (SOL) is the plasma region characterized by open field lines that start and end on the vessel walls. The plasma dynamics in the SOL plays a crucial role in determining the overall performance of a tokamak, since it controls the plasma-wall interactions, being responsible of exhausting the tokamak power, it regulates the overall plasma confinement, and it governs the plasma refueling and the removal of fusion ashes. Scrape-off layer physics is intrinsically non-linear and characterized by phenomena that occur on a wide range of spatio-temporal scales. Free energy sources drive a number of unstable modes that develop into turbulence and lead to transport of particles and heat across the magnetic field lines. Depending on the driving instability, different SOL turbulent regimes can be identified. As the SOL turbulent regimes determine the plasma confinement properties and the SOL width (and, consequently, the power flux on the vessel wall, for example), it is of crucial importance to understand which turbulent regimes are active in the SOL, under which conditions they develop, and which are the main properties of the associated turbulent transport. In the present thesis we define the SOL turbulent regimes, and we provide a framework to identify them, given the operational SOL parameters. Our study is based on the drift-reduced Braginskii equations and it is focused on a limited tokamak SOL configuration. We first describe the main SOL linear instabilities, such as the inertial and resistive branches of the drift waves, the resistive, inertial and ideal branches of the ballooning modes, and the ion temperature gradient mode. Then, we find the SOL turbulent regimes depending on the instability driving turbulent transport, assuming that turbulence saturates when the radial gradient associated to the pressure fluctuations is comparable to the equilibrium one. Our methodology for the turbulent regime identification is supported by the analysis of non-linear turbulence simulations performed with the GBS code, a flux-driven, 3D code that solves the drift-reduced Braginskii equations without separation between background and fluctuations. We find that drift waves drive transport at low resistivity and negative magnetic shear, while ballooning modes dominate at high resistivity and positive magnetic shear. The ion temperature gradient instability plays a negligible role in the SOL dynamics, since the ion temperature gradient is generally below the threshold necessary for the development of this instability

EPFL2014

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

Sébastien Jolliet

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.

EPFL2009

The role of the sheath in magnetized plasma turbulence and flows

Joaquim Loizu Cisquella

Controlled nuclear fusion could provide our society with a clean, safe, and virtually inexhaustible source of electric power production. The tokamak has proven to be capable of producing large amounts of fusion reactions by confining magnetically the fusion fuel at sufficiently high density and temperature, thus in the plasma state. Because of turbulence, however, high temperature plasma reaches the outermost region of the tokamak, the Scrape-Off Layer (SOL), which features open magnetic field lines that channel particles and heat into a dedicated region of the vacuum vessel. The plasma dynamics in the SOL is crucial in determining the performance of tokamak devices, and constitutes one of the greatest uncertainties in the success of the fusion program. In the last few years, the development of numerical codes based on reduced fluid models has provided a tool to study turbulence in open field line configurations. In particular, the GBS (Global Braginskii Solver) code has been developed at CRPP and is used to perform global, three-dimensional, full-n, flux-driven simulations of plasma turbulence in open field lines. Reaching predictive capabilities is an outstanding challenge that involves a proper treatment of the plasma-wall interactions at the end of the field lines, to well describe the particle and energy losses. This involves the study of plasma sheaths, namely the layers forming at the interface between plasmas and solid surfaces, where the drift and quasineutrality approximations break down. This is an investigation of general interest, as sheaths are present in all laboratory plasmas. This thesis presents progress in the understanding of plasma sheaths and their coupling with the turbulence in the main plasma. A kinetic code is developed to study the magnetized plasma-wall transition region and derive a complete set of analytical boundary conditions that supply the sheath physics to fluid codes. These boundary conditions are implemented in the GBS code and simulations of SOL turbulence are carried out to investigate the importance of the sheath in determining the equilibrium electric fields, intrinsic toroidal rotation, and SOL width, in different limited configurations. For each study carried out in this thesis, simple analytical models are developed to interpret the simulation results and reveal the fundamental mechanisms underlying the system dynamics. The electrostatic potential appears to be determined by a combined effect of sheath physics and electron adiabaticity. Intrinsic flows are driven by the sheath, while turbulence provides the mechanism for radial momentum transport. The position of the limiter can modify the turbulence properties in the SOL, thus playing an important role in setting the SOL width.

EPFL2013