110 research outputs found
Trinity: A Unified Treatment of Turbulence, Transport, and Heating in Magnetized Plasmas
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
Viriato: a Fourier-Hermite spectral code for strongly magnetised fluid-kinetic plasma dynamics
We report on the algorithms and numerical methods used in Viriato, a novel
fluid-kinetic code that solves two distinct sets of equations: (i) the Kinetic
Reduced Electron Heating Model (KREHM) equations [Zocco & Schekochihin, Phys.
Plasmas 18, 102309 (2011)] (which reduce to the standard Reduced-MHD equations
in the appropriate limit) and (ii) the kinetic reduced MHD (KRMHD) equations
[Schekochihin et al., Astrophys. J. Suppl. 182:310 (2009)]. Two main
applications of these equations are magnetised (Alfvenic) plasma turbulence and
magnetic reconnection. Viriato uses operator splitting (Strang or Godunov) to
separate the dynamics parallel and perpendicular to the ambient magnetic field
(assumed strong). Along the magnetic field, Viriato allows for either a
second-order accurate MacCormack method or, for higher accuracy, a
spectral-like scheme composed of the combination of a total variation
diminishing (TVD) third order Runge-Kutta method for the time derivative with a
7th order upwind scheme for the fluxes. Perpendicular to the field Viriato is
pseudo-spectral, and the time integration is performed by means of an iterative
predictor-corrector scheme. In addition, a distinctive feature of Viriato is
its spectral representation of the parallel velocity-space dependence, achieved
by means of a Hermite representation of the perturbed distribution function. A
series of linear and nonlinear benchmarks and tests are presented, including a
detailed analysis of 2D and 3D Orszag-Tang-type decaying turbulence, both in
fluid and kinetic regimes.Comment: 42 pages, 15 figures, submitted to J. Comp. Phy
High-order Discretization of a Gyrokinetic Vlasov Model in Edge Plasma Geometry
We present a high-order spatial discretization of a continuum gyrokinetic
Vlasov model in axisymmetric tokamak edge plasma geometries. Such models
describe the phase space advection of plasma species distribution functions in
the absence of collisions. The gyrokinetic model is posed in a four-dimensional
phase space, upon which a grid is imposed when discretized. To mitigate the
computational cost associated with high-dimensional grids, we employ a
high-order discretization to reduce the grid size needed to achieve a given
level of accuracy relative to lower-order methods. Strong anisotropy induced by
the magnetic field motivates the use of mapped coordinate grids aligned with
magnetic flux surfaces. The natural partitioning of the edge geometry by the
separatrix between the closed and open field line regions leads to the
consideration of multiple mapped blocks, in what is known as a mapped
multiblock (MMB) approach. We describe the specialization of a more general
formalism that we have developed for the construction of high-order,
finite-volume discretizations on MMB grids, yielding the accurate evaluation of
the gyrokinetic Vlasov operator, the metric factors resulting from the MMB
coordinate mappings, and the interaction of blocks at adjacent boundaries. Our
conservative formulation of the gyrokinetic Vlasov model incorporates the fact
that the phase space velocity has zero divergence, which must be preserved
discretely to avoid truncation error accumulation. We describe an approach for
the discrete evaluation of the gyrokinetic phase space velocity that preserves
the divergence-free property to machine precision
A Hybrid Gyrokinetic Ion and Isothermal Electron Fluid Code for Astrophysical Plasma
This paper describes a new code for simulating astrophysical plasmas that
solves a hybrid model composed of gyrokinetic ions (GKI) and an isothermal
electron fluid (ITEF) [A. Schekochihin et al., Astrophys. J. Suppl.
\textbf{182}, 310 (2009)]. This model captures ion kinetic effects that are
important near the ion gyro-radius scale while electron kinetic effects are
ordered out by an electron-ion mass ratio expansion. The code is developed by
incorporating the ITEF approximation into {\tt AstroGK}, an Eulerian
gyrokinetics code specialized to a slab geometry [R. Numata et al., J. Compute.
Pays. \textbf{229}, 9347 (2010)]. The new code treats the linear terms in the
ITEF equations implicitly while the nonlinear terms are treated explicitly. We
show linear and nonlinear benchmark tests to prove the validity and
applicability of the simulation code. Since the fast electron timescale is
eliminated by the mass ratio expansion, the Courant--Friedrichs--Lewy condition
is much less restrictive than in full gyrokinetic codes; the present hybrid
code runs times faster than
{\tt AstroGK}\ with a single ion species and kinetic electrons where
is the ion-electron mass ratio. The improvement of
the computational time makes it feasible to execute ion scale gyrokinetic
simulations with a high velocity space resolution and to run multiple
simulations to determine the dependence of turbulent dynamics on parameters
such as electron--ion temperature ratio and plasma beta
Mini-Workshop: Innovative Trends in the Numerical Analysis and Simulation of Kinetic Equations
In multiscale modeling hierarchy, kinetic theory plays a vital role in connecting microscopic Newtonian mechanics and macroscopic continuum mechanics. As computing power grows, numerical simulation of kinetic equations has become possible and undergone rapid development over the past decade. Yet the unique challenges arising in these equations, such as highdimensionality, multiple scales, random inputs, positivity, entropy dissipation, etc., call for new advances of numerical methods. This mini-workshop brought together both senior and junior researchers working on various fastpaced growing numerical aspects of kinetic equations. The topics include, but were not limited to, uncertainty quantification, structure-preserving methods, phase transitions, asymptotic-preserving schemes, and fast methods for kinetic equations
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