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Colella, P.

Publications and source records attributed to Colella, P..

Conservative fourth-order finite-volume Vlasov–Poisson solver for axisymmetric plasmas in cylindrical (r,v r ,v θ ) phase space coordinates

In this paper, a fourth-order finite-volume Vlasov–Poisson algorithm is developed for simulating axisymmetric plasma configurations in ( r , v r , v θ ) phase space coordinates. The Vlasov equation for cylindrical phase space coordinates is cast into conservation-law form and is discretized on a structured grid. The conservative finite-volume discretization is based on fifth-order upwind reconstructions of the distribution function and a fourth-order quadrature rule that accounts for transverse variations of fluxes along control volume surfaces. High-order specular reflection boundary conditions enable high-fidelity treatment of plasma distribution functions at the axis and at wall boundaries. The numerical method is applied to simulate a confined uniform neutral gas to assess convergence properties for an equilibrium system in which effects of finite-temperature and acceleration due to centrifugal and Coriolis forces are present. The discretization is also applied to a Z-pinch configuration to study electrostatic ion confinement and the dynamics of the associated breathing mode. Simulations show that the ion distribution function exhibits non-Maxwellian features and that a temperature anisotropy develops and is sustained. Finally, the finite-volume implementation is demonstrated to converge at fourth-order for both applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A 4 th -Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov–Poisson Equation

Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new particle-in- cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. H. Miller, and P. Colella, SIAM J. Sci. Comput. , 33 (2011), pp. 3509-3537]. It treats all of the stages of the standard PIC update|charge deposition, force interpolation, the field solve, and the particle push|with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. Here, we demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2 nd -order method. As expected, the 4 th -order method can achieve accuracy comparable to that of the 2nd-order method and with considerably fewer resolution elements.

97 MATHEMATICS AND COMPUTING↗

High-order continuum kinetic method for modeling plasma dynamics in phase space

Continuum methods offer a high-fidelity means of simulating plasma kinetics. While computationally intensive, these methods are advantageous because they can be cast in conservation-law form, are not susceptible to noise, and can be implemented using high-order numerical methods. Advances in continuum method capabilities for modeling kinetic phenomena in plasmas require the development of validation tools in higher dimensional phase space and an ability to handle non-cartesian geometries. To that end, a new benchmark for validating Vlasov-Poisson simulations in 3D (x,v x ,v y ) is presented. The benchmark is based on the Dory-Guest-Harris instability and is successfully used to validate a continuum finite volume algorithm. To address challenges associated with non-cartesian geometries, unique features of cylindrical phase space coordinates are described. Preliminary results of continuum kinetic simulations in 4D (r,z,v r ,v z ) phase space are presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical modelling of geodesic acoustic mode relaxation in a tokamak edge

Here, the edge of a tokamak in a high confinement (H mode) regime is characterized by steep density gradients and a large radial electric field. Recent analytical studies demonstrated that the presence of a strong radial electric field consistent with a subsonic pedestal equilibrium modifies the conventional results of the neoclassical formalism developed for the core region. In the present work we make use of the recently developed gyrokinetic code COGENT to numerically investigate neoclassical transport in a tokamak edge including the effects of a strong radial electric field. The results of numerical simulations are found to be in good qualitative agreement with the theoretical predictions and the quantitative discrepancy is discussed. In addition, the present work investigates the effects of a strong radial electric field on the relaxation of geodesic acoustic modes (GAMs) in a tokamak edge. Numerical simulations demonstrate that the presence of a strong radial electric field characteristic of a tokamak pedestal can enhance the GAM decay rate, and heuristic arguments elucidating this finding are provided.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simulation of neoclassical transport with the continuum gyrokinetic code COGENT

The development of the continuum gyrokinetic code COGENT for edge plasma simulations is reported. The present version of the code models a nonlinear axisymmetric 4D (R, v∥, μ) gyrokinetic equation coupled to the long-wavelength limit of the gyro-Poisson equation. Here, R is the particle gyrocenter coordinate in the poloidal plane, and v∥ and μ are the guiding center velocity parallel to the magnetic field and the magnetic moment, respectively. The COGENT code utilizes a fourth-order finite-volume (conservative) discretization combined with arbitrary mapped multiblock grid technology (nearly field-aligned on blocks) to handle the complexity of tokamak divertor geometry with high accuracy. Furthermore, topics presented are the implementation of increasingly detailed model collision operators, and the results of neoclassical transport simulations including the effects of a strong radial electric field characteristic of a tokamak pedestal under H-mode conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Progress with the COGENT Edge Kinetic Code: Collision operator options

In this study, COGENT is a continuum gyrokinetic code for edge plasmas being developed by the Edge Simulation Laboratory collaboration. The code is distinguished by application of the fourth order conservative discretization, and mapped multiblock grid technology to handle the geometric complexity of the tokamak edge. It is written in v∥-μ (parallel velocity – magnetic moment) velocity coordinates, and making use of the gyrokinetic Poisson equation for the calculation of a self-consistent electric potential. In the present manuscript we report on the implementation and initial testing of a succession of increasingly detailed collision operator options, including a simple drag-diffusion operator in the parallel velocity space, Lorentz collisions, and a linearized model Fokker-Planck collision operator conserving momentum and energy (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fusion Simulation Program Execution Plan

The overall science goal of the FSP is to develop predictive simulation capability for magnetically confined fusion plasmas at an unprecedented level of integration and fidelity. This will directly support and enable effective U.S. participation in research related to the International Thermonuclear Experimental Reactor (ITER) and the overall mission of delivering practical fusion energy. The FSP will address a rich set of scientific issues together with experimental programs, producing validated integrated physics results. This is very well aligned with the mission of the ITER Organization to coordinate with its members the integrated modeling and control of fusion plasmas, including benchmarking and validation activities. Initial FSP research will focus on two critical areas: 1) the plasma edge and 2) whole device modeling including disruption avoidance. The first of these problems involves the narrow plasma boundary layer and its complex interactions with the plasma core and the surrounding material wall. The second requires development of a computationally tractable, but comprehensive model that describes all equilibrium and dynamic processes at a sufficient level of detail to provide useful prediction of the temporal evolution of fusion plasma experiments. The initial driver for the whole device model (WDM) will be prediction and avoidance of discharge-terminating disruptions, especially at high performance, which are a critical impediment to successful operation of machines like ITER. If disruptions prove unable to be avoided, their associated dynamics and effects will be addressed in the next phase of the FSP. The FSP plan targets the needed modeling capabilities by developing Integrated Science Applications (ISAs) specific to their needs. The Pedestal-Boundary model will include boundary magnetic topology, cross-field transport of multi-species plasmas, parallel plasma transport, neutral transport, atomic physics and interactions with the plasma wall. It will address the origins and structure of the plasma electric field, rotation, the L-H transition, and the wide variety of pedestal relaxation mechanisms. The Whole Device Model will predict the entire discharge evolution given external actuators (i.e., magnets, power supplies, heating, current drive and fueling systems) and control strategies. Based on components operating over a range of physics fidelity, the WDM will model the plasma equilibrium, plasma sources, profile evolution, linear stability and nonlinear evolution toward a disruption (but not the full disruption dynamics). The plan assumes that, as the FSP matures and demonstrates success, the program will evolve and grow, enabling additional science problems to be addressed. The next set of integration opportunities could include: 1) Simulation of disruption dynamics and their effects; 2) Prediction of core profile including 3D effects, mesoscale dynamics and integration with the edge plasma; 3) Computation of non-thermal particle distributions, self-consistent with fusion, radio frequency (RF) and neutral beam injection (NBI) sources, magnetohydrodynamics (MHD) and short-wavelength turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗