53 research outputs found

    ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry

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    This paper presents the current state of the global gyrokinetic code ORB5 as an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177 409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of equations using a PIC scheme and also includes collisions and strong flows. The code assumes multiple gyrokinetic ion species at all wavelengths for the polarization density and drift-kinetic electrons. Variants of the physical model can be selected for electrons such as assuming an adiabatic response or a ``hybrid'' model in which passing electrons are assumed adiabatic and trapped electrons are drift-kinetic. A Fourier filter as well as various control variates and noise reduction techniques enable simulations with good signal-to-noise ratios at a limited numerical cost. They are completed with different momentum and zonal flow-conserving heat sources allowing for temperature-gradient and flux-driven simulations. The code, which runs on both CPUs and GPUs, is well benchmarked against other similar codes and analytical predictions, and shows good scalability up to thousands of nodes

    Turbulence-driven ion beams in space plasmas

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    The description of the local turbulent energy transfer and the high-resolution ion distributions measured by the Magnetospheric Multiscale mission together provide a formidable tool to explore the cross-scale connection between the fluid-scale energy cascade and plasma processes at subion scales. When the small-scale energy transfer is dominated by Alfv´enic, correlated velocity, and magnetic field fluctuations, beams of accelerated particles are more likely observed. Both space observations and numerical simulations suggest the nonlinear wave-particle interaction as one possible mechanism for the energy dissipation in space plasmas

    The Berk-Breizman Model as a Paradigm for Energetic Particle-driven Alfven Eigenmodes

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    The achievement of sustained nuclear fusion in magnetically confined plasma relies on efficient confinement of high-energy ions produced by the fusion reaction. Such particles can excite Alfven Eigenmodes (AEs), which significantly degrade their confinement and threatens the vacuum vessel of future reactors. To develop diagnostics and control schemes, a better understanding of linear and nonlinear features of resonant interactions between plasma waves and high-energy particles, is required. In the case of an isolated single resonance, the problem is homothetic to the so-called Berk-Breizman (BB) problem, which is an extension of the classic bump-on-tail electrostatic problem, including external damping to a thermal plasma, and collisions. A semi-Lagrangian simulation code, COBBLES, is developed to solve the initial-value BB problem. The nonlinear behavior of instabilities in experimentally-relevant conditions is categorized into steady-state, periodic, chaotic, and frequency-sweeping (chirping) regimes. The chaotic regime is shown to extend into a linearly stable region, and a mechanism for such subcritical instabilities is proposed. Analytic and semi-empirical laws for nonlinear chirping characteristics, such as sweeping-rate, lifetime, and asymmetry, are developed and validated. Long-time simulations demonstrate the existence of a quasi-periodic chirping regime. Collisional drag and diffusion are shown to be essential to reproduce the alternation between major chirping events and quiescent phases, which is observed in experiments. Based on these findings, a fitting procedure between COBBLES simulations and chirping AE experiments is developped. This procedure, which yields local linear drive and external damping rate, is applied to Toroidicity-induced AEs (TAEs) on JT-60U and MAST tokamaks. This suggests the existence of TAEs relatively far from marginal stability

    Resolving velocity space dynamics in continuum gyrokinetics

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    Many plasmas of interest to the astrophysical and fusion communities are weakly collisional. In such plasmas, small scales can develop in the distribution of particle velocities, potentially affecting observable quantities such as turbulent fluxes. Consequently, it is necessary to monitor velocity space resolution in gyrokinetic simulations. In this paper, we present a set of computationally efficient diagnostics for measuring velocity space resolution in gyrokinetic simulations and apply them to a range of plasma physics phenomena using the continuum gyrokinetic code GS2. For the cases considered here, it is found that the use of a collisionality at or below experimental values allows for the resolution of plasma dynamics with relatively few velocity space grid points. Additionally, we describe implementation of an adaptive collision frequency which can be used to improve velocity space resolution in the collisionless regime, where results are expected to be independent of collision frequency.Comment: 20 pages, 11 figures, submitted to Phys. Plasma

    Limitations of stationary Vlasov-Poisson solvers in probe theory

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    Physical and numerical limitations of stationary Vlasov-Poisson solvers based on backward Liouville methods are investigated with five solvers that combine different meshes, numerical integrators, and electric field interpolation schemes. Since some of the limitations arise when moving from an integrable to a non-integrable configuration, an elliptical Langmuir probe immersed in a Maxwellian plasma was considered and the eccentricity (ep) of its cross-section used as integrability-breaking parameter. In the cylindrical case, ep=0, the energy and angular momentum are both conserved. The trajectories of the charged particles are regular and the boundaries that separate trapped from non-trapped particles in phase space are smooth curves. However, their computation has to be done carefully because, albeit small, the intrinsic numerical errors of some solvers break these conservation laws. It is shown that an optimum exists for the number of loops around the probe that the solvers need to classify a particle trajectory as trapped. For ep≠0, the angular momentum is not conserved and particle dynamics in phase space is a mix of regular and chaotic orbits. The distribution function is filamented and the boundaries that separate trapped from non-trapped particles in phase space have a fractal geometry. The results were used to make a list of recommendations for the practical implementation of stationary Vlasov-Poisson solvers in a wide range of physical scenarios.This work was supported by the European Union's Horizon 2020 Research and Innovation Programme under grant agreement No 828902 (E.T.PACK project). GSA work is supported by the Ministerio de Ciencia, Innovación of Spain under the Grant RYC-2014-15357. The authors thank the Reviewers for their valuable comments and suggestions about the use of energy-conserving numerical integrators

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

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    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

    Collisions in Global Gyrokinetic Simulations of Tokamak Plasmas using the Delta-f Particle-In-Cell Approach:Neoclassical Physics and Turbulent Transport

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    The present work takes place within the general context of research related to the development of nuclear fusion energy. More specifically, this thesis is mainly a numerical and physical contribution to the understanding of turbulence and associated transport phenomena occuring in tokamak plasmas, the most advanced and promising form of magnetically confined plasmas. The complexity of tokamak plasma phenomena and related physical models, either fluid or kinetic, requires the development of numerical codes to perform simulations of the plasma behaviour under given conditions defined by the magnetic geometry as well as density and temperature profiles. The studies presented in this work are based on electrostatic kinetic simulations, taking advantage of a reduced kinetic model (the gyrokinetic model) which is particularly suitable for studying turbulent transport in magnetically confined plasmas, in effect solving an approximate form of the Vlasov equation for the distribution function of each species (electrons, ions) along with a reduced form of the Poisson equation providing the self-consistent electric fields. The main tool of this work, the gyrokinetic ORB5 code making use of numerical particles according to the Particle-In-Cell (PIC) method, has been upgraded during this thesis with different linearized collision operators related to both ions and electrons. The BIRDIE code, enabling to study collisional effects on the evolution of Langmuir waves in an unmagnetized plasma, has been written in order to serve as a test-bed for the collision operators ultimately implemented in ORB5. Some essential algorithms related to collisional simulations have been jointly implemented, such as the two-weight scheme which is extensively described in this work. The collision operators in ORB5 have been further carefully tested through neoclassical simu- lations and benchmarked against other codes, providing reliable levels of collisional transport. Together with different procedures controlling the numerical noise, the collision operators have then been applied to the study of collisional turbulent transport in two different regimes, the Ion-Temperature-Gradient (ITG) regime and the Trapped-Electron-Mode (TEM) regime re- quiring a trapped electron kinetic response. Although not dominant in core tokamak plasmas, collisional effects nevertheless lead to interesting modifications in the turbulence behaviour which are not captured by the often considered collisionless gyrokinetic models. The so-called coarse-graining procedure, a noise-control algorithm which is suitable for collisional gyrokinetic simulations with particles, is shown to enable carrying out relevant simulations over many col- lision times. Consequently, reliable conclusions regarding turbulent transport in the presence of collisions could be drawn in this thesis. Namely, the turbulent transport in the ITG regime is found to be enhanced by ion collisions through interactions with so-called zonal flows as- sociated to axisymmetric modes, while it is reduced by electron collisions in the TEM regime through electron detrapping processes. The zonal flow dynamics in collisionless and collisional ITG turbulence simulations is studied, emphasizing the limitation of the zonal flow level due to Kelvin-Helmoltz-type instabilities. Additionally, some purely collisionless issues related to tokamak physics are discussed, such as the finite plasma size effects in TEM-dominated regime which are found to be important in non-linear simulations but unimportant in linear simu- lations. The role of zonal flows in temperature-gradient-driven TEM turbulence saturation is confirmed to be weak, in agreement with previous studies. Finally, a realistic global gy- rokinetic simulation, accounting for a proper TCV tokamak magnetic equilibrium and related experimental profiles, has been successfully carried out thus demonstrating the relevance of the ORB5 code for predictions related to physics of real tokamaks. A good agreement with GAM experimental measurements is indeed obtained

    ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation

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    Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli (1993) generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.Comment: Code and illustration movies available at: http://www.vlasix.org/index.php?n=Main.ColDICE - Article submitted to Journal of Computational Physic
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