arXiv subjects

E. L. Shi

Publications and source records attributed to E. L. Shi.

6 recordsLinked to original sources

arXiv2017

Gyrokinetic Continuum Simulation of Turbulence in Open-Field-Line Plasmas

The properties of the boundary plasma in a tokamak are now recognized to play a key role in determining the achievable fusion power and the lifetimes of plasma-facing components. Accurate quantitative modeling and improved qualitative understanding of the boundary plasma ultimately require five-dimensional gyrokinetic turbulence simulations, which have been successful in predicting turbulence and transport in the core. The additional challenges of boundary-plasma simulation necessitate the development of new gyrokinetic codes or major modifications to existing core gyrokinetic codes. In this thesis, we develop the first gyrokinetic continuum code capable of simulating plasma turbulence on open magnetic field lines, which is a key feature of a tokamak scrape-off layer. In contrast to prior attempts at this problem, we use an energy-conserving discontinuous Galerkin discretization in space. To model the interaction between the plasma and the wall, we design conducting-sheath boundary conditions that permit local currents into and out of the wall. We start by designing spatially one-dimensional kinetic models of parallel SOL dynamics and solve these systems using novel continuum algorithms. By generalizing these algorithms to higher dimensions and adding a model for collisions, we present results from the first gyrokinetic continuum simulations of turbulence on two types of open-field-line systems. The first simulation features uniform and straight field lines, such as found in some linear plasma devices. The second simulation is of a hypothetical model we developed of the NSTX scrape-off layer featuring helical field lines. These developments comprise a major step towards a gyrokinetic continuum code for quantitative predictions of turbulence and transport in the boundary plasma of magnetic fusion devices.

physics.plasm-ph↗

arXiv2017

Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma

3D2V continuum gyrokinetic simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using the full-$f$ discontinuous-Galerkin code Gkeyll. These simulations include the basic elements of a fusion-device scrape-off layer: localized sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath model boundary conditions. The set of sheath boundary conditions used in the model allows currents to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device (LAPD), a linear device featuring straight magnetic field lines, are presented.

physics.plasm-ph↗

arXiv2016

Zonal-flow dynamics from a phase-space perspective

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. We derive a modified theory that takes both of these effects into account, while still treating DW quanta ("driftons") as particles in phase space. The drifton dynamics is described by an equation of the Wigner-Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. Numerical simulations are presented to illustrate the importance of these additional terms. The proposed formulation can be considered as a phase-space representation of the second-order cumulant expansion, or CE2.

physics.plasm-ph↗

arXiv2016

Scrape-Off Layer Turbulence in Tokamaks Simulated with a Continuum Gyrokinetic Code

We are developing a new continuum gyrokinetic code, Gkeyll, for use in edge plasma simulations, and here present initial simulations of turbulence on open field lines with model sheath boundary conditions. The code implements an energy conserving discontinuous Galerkin scheme, applicable to a general class of Hamiltonian equations. Several applications to test problems have been done, including a calculation of the parallel heat-flux on divertor plates resulting from an ELM crash in JET, for a 1x/1v SOL scenario explored previously, where the ELM is modeled as a time-dependent intense upstream source. Here we present initial simulations of turbulence on open field lines in the LAPD linear plasma device. We have also done simulations in a helical open-field-line geometry. While various simplifications have been made at present, this still includes some of the key physics of SOL turbulence, such as bad-curvature drive for instabilities and rapid parallel losses with sheath boundary conditions. This is useful for demonstrating the overall feasibility of this approach and for initial physics studies of SOL turbulence. We developed a novel version of DG that uses Maxwellian-weighted basis functions while still preserving exact particle and energy conservation. The Maxwellian-weighted DG method achieves the same error with 4 times less computational cost in 1v, or 16 times lower cost in the 2 velocity dimensions of gyrokinetics (assuming memory bandwidth is the limiting factor).

physics.plasm-ph↗

arXiv2015

A Gyrokinetic 1D Scrape-Off Layer Model of an ELM Heat Pulse

An electrostatic gyrokinetic-based model is applied to simulate parallel plasma transport in the scrape-off layer to a divertor plate. The authors focus on a test problem that has been studied previously, using parameters chosen to model a heat pulse driven by an edge-localized mode (ELM) in JET. Previous work has used direct particle-in-cell equations with full dynamics, or Vlasov or fluid equations with only parallel dynamics. With the use of the gyrokinetic quasineutrality equation and logical sheath boundary conditions, spatial and temporal resolution requirements are no longer set by the electron Debye length and plasma frequency, respectively. This test problem also helps illustrate some of the physics contained in the Hamiltonian form of the gyrokinetic equations and some of the numerical challenges in developing an edge gyrokinetic code.

physics.plasm-ph↗

arXiv2014

On discontinuous Galerkin discretizations of second-order derivatives

Some properties of a Local discontinuous Galerkin (LDG) algorithm are demonstrated for the problem of evaluting a second derivative $g = f_{xx}$ for a given $f$. (This is a somewhat unusual problem, but it is useful for understanding the initial transient response of an algorithm for diffusion equations.) LDG uses an auxiliary variable to break this up into two first order equations and then applies techniques by analogy to DG algorithms for advection algorithms. This introduces an asymmetry into the solution that depends on the choice of upwind directions for these two first order equations. When using piecewise linear basis functions, this LDG solution $g_h$ is shown not to converge in an $L_2$ norm because the slopes in each cell diverge. However, when LDG is used in a time-dependent diffusion problem, this error in the second derivative term is transient and rapidly decays away, so that the overall error is bounded. I.e., the LDG approximation $f_h(x,t)$ for a diffusion equation $\partial f / \partial t = f_{xx}$ converges to the proper solution (as has been shown before), even though the initial rate of change $\partial f_h / \partial t$ does not converge. We also show results from the Recovery discontinuous Galerkin (RDG) approach, which gives symmetric solutions that can have higher rates of convergence for a stencil that couples the same number of cells.

physics.comp-ph↗