26,402 research outputs found
The Complete Flux Scheme : error analysis and application to plasma simulation
The Complete Flux scheme (CFS) (J.H.M. ten Thije Boonkkamp et al., J. Sci. Comput. 46 (2011) 47–70) is an extension of the widely used exponential di¿erence scheme for advection-di¿usion-reaction equations. In the present paper we provide a rigorous proof that the convergence order of this scheme is 2 for all grid Péclet numbers, whereas that of the exponential scheme reduces to 1 for high grid Péclet numbers in the presence of source terms. The performance of both schemes is compared in two case studies: a model system and a real-world model of a parallel-plate glow discharge. The results indicate that the usage of CFS allows a considerable reduction of the number of grid points that is required to obtain the same accuracy. The MATLAB/Octave source code that has been used in these studies has been made available
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
A Discontinuous Galerkin Method for Ideal Two-Fluid Plasma Equations
A discontinuous Galerkin method for the ideal 5 moment two-fluid plasma
system is presented. The method uses a second or third order discontinuous
Galerkin spatial discretization and a third order TVD Runge-Kutta time stepping
scheme. The method is benchmarked against an analytic solution of a dispersive
electron acoustic square pulse as well as the two-fluid electromagnetic shock
and existing numerical solutions to the GEM challenge magnetic reconnection
problem. The algorithm can be generalized to arbitrary geometries and three
dimensions. An approach to maintaining small gauge errors based on error
propagation is suggested.Comment: 40 pages, 18 figures
Thermal Diagnostics with the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory: A Validated Method for Differential Emission Measure Inversions
We present a new method for performing differential emission measure (DEM)
inversions on narrow-band EUV images from the Atmospheric Imaging Assembly
(AIA) onboard the Solar Dynamics Observatory (SDO). The method yields positive
definite DEM solutions by solving a linear program. This method has been
validated against a diverse set of thermal models of varying complexity and
realism. These include (1) idealized gaussian DEM distributions, (2) 3D models
of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a
non-linear force-free field, and (3) thermodynamic models from a
fully-compressible, 3D MHD simulation of AR corona formation following magnetic
flux emergence. We then present results from the application of the method to
AIA observations of Active Region 11158, comparing the region's thermal
structure on two successive solar rotations. Additionally, we show how the DEM
inversion method can be adapted to simultaneously invert AIA and XRT data, and
how supplementing AIA data with the latter improves the inversion result. The
speed of the method allows for routine production of DEM maps, thus
facilitating science studies that require tracking of the thermal structure of
the solar corona in time and space.Comment: 21 pages, 18 figures, accepted for publication in Ap
Generalized, energy-conserving numerical simulations of particles in general relativity. II. Test particles in electromagnetic fields and GRMHD
Direct observations of compact objects, in the form of radiation spectra,
gravitational waves from VIRGO/LIGO, and forthcoming direct imaging, are
currently one of the primary source of information on the physics of plasmas in
extreme astrophysical environments. The modeling of such physical phenomena
requires numerical methods that allow for the simulation of microscopic plasma
dynamics in presence of both strong gravity and electromagnetic fields. In
Bacchini et al. (2018) we presented a detailed study on numerical techniques
for the integration of free geodesic motion. Here we extend the study by
introducing electromagnetic forces in the simulation of charged particles in
curved spacetimes. We extend the Hamiltonian energy-conserving method presented
in Bacchini et al. (2018) to include the Lorentz force and we test its
performance compared to that of standard explicit Runge-Kutta and implicit
midpoint rule schemes against analytic solutions. Then, we show the application
of the numerical schemes to the integration of test particle trajectories in
general relativistic magnetohydrodynamic (GRMHD) simulations, by modifying the
algorithms to handle grid-based electromagnetic fields. We test this approach
by simulating ensembles of charged particles in a static GRMHD configuration
obtained with the Black Hole Accretion Code (BHAC)
- …