Evidence of Critical Balance in Kinetic Alfven Wave Turbulence Simulations

A numerical simulation of kinetic plasma turbulence is performed to assess the applicability of critical balance to kinetic, dissipation scale turbulence. The analysis is performed in the frequency domain to obviate complications inherent in performing a local analysis of turbulence. A theoretical model of dissipation scale critical balance is constructed and compared to simulation results, and excellent agreement is found. This result constitutes the first evidence of critical balance in a kinetic turbulence simulation and provides evidence of an anisotropic turbulence cascade extending into the dissipation range. We also perform an Eulerian frequency analysis of the simulation data and compare it to the results of a previous study of magnetohydrodynamic turbulence simulations.Comment: 10 pages, 9 figures, accepted for publication in Physics of Plasma

Chaotic motion of charged particles in toroidal magnetic configurations

We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron gyration using Hamiltonian formalism. We take advantage of a symplectic integrator allowing us to make long-time simulations. First considering an idealized magnetic configuration, we add a non generic perturbation corresponding to a magnetic ripple, breaking one of the invariant of the motion. Chaotic motion is then observed and opens questions about the link between chaos of magnetic field lines and chaos of particle trajectories. Second, we return to a axi-symmetric configuration and tune the safety factor (magnetic configuration) in order to recover chaotic motion. In this last setting with two constants of the motion, the presence of chaos implies that no third global constant exists, we highlight this fact by looking at variations of the first order of the magnetic moment in this chaotic setting. We are facing a mixed phase space with both regular and chaotic regions and point out the difficulties in performing a global reduction such as gyrokinetics

Full particle orbit effects in regular and stochastic magnetic fields

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic. The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the $q$-profile implies the existence of magnetic ITBs which correspond to shearless flux surfaces located in the vicinity of the $q$-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depends in a non-trivial way on the energy and pitch angle of the particles.Comment: 25 pages, accepted for publication in Phys. Plasma

Implementation of Guiding Center Rotation Drifts in Simulations of Tokamak Plasmas with Large Flows

Tokamak magnetic confinement experiments are the most researched prospect for controlled thermonuclear fusion energy production. The quasi-toroidal geometry along with the large, twisting toroidal magnetic field pose great engineering and physics challenges. Plasma physicists use large-scale simulations of Tokamak plasmas in order to further understand their physics and inform experimental design to strive towards the goal of reliable fusion energy [20]. One type of simulation uses a gyrokinetic formulation to study plasmas in strong magnetic fields. A fundamental concept in gyrokinetic plasma physics is that of the guiding center drifts, which influence the motion of the guiding center of a gyrating charged particle in electric and magnetic fields. Previously, the significant toroidal and poloidal equilibrium flows of a tokamak plasma were not fully included in simulation models. Experiments have suggested that these flows have noticeable effects on tokamak physics [5][17]. In this thesis, we discuss the formulation of a gyrokinetic model that includes these flows by shifting velocity space to the frame moving with the plasma flow [18]. Many of the previous calculations can be used with relatively small modifications of the standard lab frame model. However, in this new frame, the centrifugal and Coriolis forces, which are well established physics concepts in rotating reference frames, manifest themselves as new drift terms in the drift gyrokinetic equation [2]. In this thesis, we will step through the calculation of these terms in cylindrical coordinates starting with the Sugama-Horton model for drift velocity [18] to obtain the established result from the literature. We will also use the guiding center Hamiltonian formulation [15] in a tokamak plasma by explaining the previous work on this topic from a few references in detail to obtain an equivalent result [17][9]. The original work of this thesis is the implementation of the new drift terms in the simulation\u27s magnetic field-following coordinate system in a usable way for the purposes of large-scale tokamak simulations. We will examine the effect of the equilibrium flow by visualizing results for the simple test case of a linear eigenmode in a tokamak. We find that the fundamental structure of the mode is unchanged, but the ExB drift connected to the flow results in a tilt of the poloidal mode structure in accordance with our expectations. Finally, future work using the gyrokinetic model that includes large equilibrium flows is discussed

Visualization and analysis tools for assisting in evaluating fusion simulations

poste

Gaussian Process Regression models for the properties of micro-tearing modes in spherical tokamak

Spherical tokamaks (STs) have many desirable features that make them an attractive choice for a future fusion power plant. Power plant viability is intrinsically related to plasma heat and particle confinement and this is often determined by the level of micro-instability driven turbulence. Accurate calculation of the properties of turbulent micro-instabilities is therefore critical for tokamak design, however, the evaluation of these properties is computationally expensive. The considerable number of geometric and thermodynamic parameters and the high resolutions required to accurately resolve these instabilities makes repeated use of direct numerical simulations in integrated modelling workflows extremely computationally challenging and creates the need for fast, accurate, reduced-order models. This paper outlines the development of a data-driven reduced-order model, often termed a {\it surrogate model} for the properties of micro-tearing modes (MTMs) across a spherical tokamak reactor-relevant parameter space utilising Gaussian Process Regression (GPR) and classification; techniques from machine learning. These two components are used in an active learning loop to maximise the efficiency of data acquisition thus minimising computational cost. The high-fidelity gyrokinetic code GS2 is used to calculate the linear properties of the MTMs: the mode growth rate, frequency and normalised electron heat flux; core components of a quasi-linear transport model. Five-fold cross-validation and direct validation on unseen data is used to ascertain the performance of the resulting surrogate models

Highly Parallel Geometric Characterization and Visualization of Volumetric Data Sets

Volumetric 3D data sets are being generated in many different application areas. Some examples are CAT scans and MRI data, 3D models of protein molecules represented by implicit surfaces, multi-dimensional numeric simulations of plasma turbulence, and stacks of confocal microscopy images of cells. The size of these data sets has been increasing, requiring the speed of analysis and visualization techniques to also increase to keep up. Recent advances in processor technology have stopped increasing clock speed and instead begun increasing parallelism, resulting in multi-core CPUS and many-core GPUs. To take advantage of these new parallel architectures, algorithms must be explicitly written to exploit parallelism. In this thesis we describe several algorithms and techniques for volumetric data set analysis and visualization that are amenable to these modern parallel architectures. We first discuss modeling volumetric data with Gaussian Radial Basis Functions (RBFs). RBF representation of a data set has several advantages, including lossy compression, analytic differentiability, and analytic application of Gaussian blur. We also describe a parallel volume rendering algorithm that can create images of the data directly from the RBF representation. Next we discuss a parallel, stochastic algorithm for measuring the surface area of volumetric representations of molecules. The algorithm is suitable for implementation on a GPU and is also progressive, allowing it to return a rough answer almost immediately and refine the answer over time to the desired level of accuracy. After this we discuss the concept of Confluent Visualization, which allows the visualization of the interaction between a pair of volumetric data sets. The interaction is visualized through volume rendering, which is well suited to implementation on parallel architectures. Finally we discuss a parallel, stochastic algorithm for classifying stem cells as having been grown on a surface that induces differentiation or on a surface that does not induce differentiation. The algorithm takes as input 3D volumetric models of the cells generated from confocal microscopy. This algorithm builds on our algorithm for surface area measurement and, like that algorithm, this algorithm is also suitable for implementation on a GPU and is progressive