Collisional transport of trace impurity ions and the role of the radial electric field in spherical tokamak plasmas

The mitigation and control of impurities, or non-fuel ions, in tokamak plasmas is vital for reducing energy losses and an understanding of impurity transport is required in order to predict the performance of present and future tokamak devices. The development and application of a full orbit, test particle code to the study of the collisional transport of test impurity ions in spherical tokamak plasmas is presented. This code is tested against the standard analytic description of collisional transport in magnetised plasmas and is demonstrated to be particularly suited to the study of the tight aspect ratio of the spherical tokamak design. The principle results of the present work concern the investigation of the role of the radial electric field, a feature of high performance tokamak plasmas, on collisional ion transport. It is found that a static radial electric field leads to a significant reduction in the radial transport of test impurity ions. This effect may be explained in terms of a novel radial drift of the test ions arising due to the introduction of collisional Langevin terms to the full orbit, test particle equations of motion. This has significant implications for the confinement of impurity ions in high performance, steady state tokamak discharges. A scaling of this modification with impurity particle mass and charge numbers is derived analytically and verified numerically and a scaling with electric field parameters is derived numerically. A time dependent radial electric field, which models a number of transient events in tokamak plasmas such as the low- to high-mode transition and edge localised modes, is also investigated and attempts at a preliminary comparison between experimental and numerical observations of impurity transport in spherical tokamak devices is presented

A gyrokinetic model for the plasma periphery of tokamak devices

A gyrokinetic model is presented that can properly describe strong flows, large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and large deviations from thermal equilibrium. The formulation of the gyrokinetic model is based on a second order description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts, assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behavior of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function and includes a non-linear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a velocity-space Hermite-Laguerre polynomial basis and the gyrokinetic equation is projected onto the same basis, obtaining the spatial and temporal evolution of the Hermite-Laguerre expansion coefficients. The Hermite-Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell's equations derived from a variational principle, with the velocity integrals of the gyroaveraged distribution function explicitly evaluated

Drift reduced Landau fluid model for magnetized plasma turbulence simulations in BOUT++ framework

Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture n=0 axisymmetric mode evolution in realistic tokamak configurations. These improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transient (e.g., ELM, disruption) and transport time-scale simulations.Comment: 26 pages, 14 figure

Exploring the mechanisms behind nondiffusive transport in a simple turbulence model

Thesis (Ph.D.) University of Alaska Fairbanks, 2017Elements for nondiffusive transport have been identified in a plasma turbulence model based on the slab drift-wave model. Motivated by the self-organized criticality paradigm, a standard set of drift-wave equations in doubly-periodic spatial domain has been elevated to include a flux-driven background profile with critical gradients. The profile is maintained by the turbulence induced flux from the source to the sink. Tracers that follow the Lagrangian trajectories are the primary transport characterization technique. The competition between down-gradient relaxations and self-generated flows highlights the dual reactions to local steepening of profile gradients, which leads to different transport regimes. An additional external sheared flow further inhibits down-gradient transfer and acts as another critical threshold condition that can lead to flow-driven instabilities. Superdiffusive transport is observed primarily when radial relaxation events dominate while subdiffusive character become more prominent with self-generated and external poloidal flows. Diffusive transport exists when the superdiffusive and subdiffusive components are in balance. The interplay between turbulent relaxation and self-generated sheared poloidal flows, that form the basis for the transport explored in this model, is absent unless a flux-driven setup is used. Most of the rich dynamics were not present when running the simplified model without an equation for background profile evolution. Nondiffusive transport characteristics can also be recovered from a passive scalar field that is advected by the turbulent flow with an inherent diffusivity. The spread of a highly localized cloud of tracers and a passive scalar field reasserts the equivalence between the Lagrangian and quasi-Lagrangian frames. The coincidence between the passive scalar field with the tracers provide a regime of validity where existing experimental technique can be used to characterize transport from two-dimensional experimental data. The results from this work highlight the key features of flux-driven turbulent transport leading to nondiffusive transport. Specifcally, the dual reactions to the local steepening of profile gradients exposes the multiscale feature of turbulent transport that becomes more apparent under a flux-driven profile. The quantification of nondiffusive transport characteristics from the evolution of a passive scalar can have important implication towards the fundamental understanding of fluid turbulence and turbulent transport

Non-equilibrium quasi-stationary states in a magnetized plasma

International audienceNon-equilibrium quasi-stationary states resulting from curvature driven interchange instabilities and drift-wave instabilities in a low beta, weakly ionized, magnetized plasma are investigated in the context of laboratory experiments in a toroidal configuration. Analytic modelling, numerical simulations and experimental results are discussed with emphasis on identifying the unstable modes and understanding the physics of anomalous particle and energy fluxes and their linkage to self-organized pressure profiles

Dispersion of ion gyrocenters in models of anisotropic plasma turbulence

Turbulent dispersion of ion gyrocenters in a magnetized plasma is studied in the context of a stochastic Hamiltonian transport model and nonlinear, self-consistent gyrokinetic simulations. The Hamiltonian model consists of a superposition of drift waves derived from the linearized Hasegawa-Mima equation and a zonal shear flow perpendicular to the density gradient. Finite Larmor radius (FLR) effects are included. Because there is no particle transport in the direction of the density gradient, the focus is on transport parallel to the shear flow. The prescribed flow produces strongly asymmetric non-Gaussian probability distribution functions (PDFs) of particle displacements, as was previously known. For kρ=0, where k is the characteristic wavelength of the flow and ρ is the thermal Larmor radius, a transition is observed in the scaling of the second moment of particle displacements. The transition separates nearly ballistic superdiffusive dispersion from weaker superdiffusion at later times. FLR effects eliminate this transition. Important features of the PDFs of displacements are reproduced accurately with a fractional diffusion model. The gyroaveraged ExB drift dispersion of a sample of tracer ions is also examined in a two-dimensional, nonlinear, self-consistent gyrokinetic particle-in-cell (PIC) simulation. Turbulence in the simulation is driven by a density gradient and magnetic curvature, resulting in the unstable ρ scale kinetic entropy mode. The dependence of dispersion in both the axial and radial directions is characterized by displacement and velocity increment distributions. The strength of the density gradient is varied, using the local approximation, in three separate trials. A filtering procedure is used to separate trajectories according to whether they were caught in an eddy during a set observation time. Axial displacements are compared to results from the Hasegawa-Mima model. Superdiffusion and ballistic transport are found, depending on filtering and strength of the gradient. The radial dispersion of particles, as measured by the variance of tracer displacements, is diffusive. The dependence of the running diffusion coefficient on ρ for each value of the density gradient is considered

Turbulence-driven ion beams in space plasmas

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