Master's Thesis-Defense by Steffen Filtenborg-Simonsen – Niels Bohr Institute - University of Copenhagen

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Master's Thesis-Defense by Steffen Filtenborg-Simonsen

Coupling Plasma Approximation towards a Computational Multi-physics Plasma Model

The effects of weight functions and operator order in a Particle in-Cell model

Abstract:

Matter exists in four different states, of which the plasma state is the most common one in the universe. The plasma state consists of ionised atoms and free electrons, or a mixture of this with neutral atoms and molecules. This results in electric currents and magnetic fields being generated and evolved. Applications that require modeling and understanding plasma evolution are many, including for example Solar flares, Coronal Mass Ejections (CMEs) and the associated space weather, magnetospheric physics, and star and planet formation processes.

In order to understand plasma evolution one can use different approaches, either studying the large scale evolution using a macroscopic evolution model such as the Magneto-Hydro-Dynamic (MHD) approximation, or using a description of the particle evolution on a microscopic scale by adopting the Particle-In-Cell (PIC) approximation. These methods handle the evolution using different physics, characteristic lengths and time scales, with modeling costs that can differ with many orders of magnitude. As a result, sometimes neither of the models can give a full description of a given problem -- the MHD model may not be comprehensive enough and the PIC model may be too expensive -- and it would therefore be advantageous to be able to combine them into a more advanced hybrid method, where different regions of a simulation may be evolved with the appropriate plasma model.

A problem with this approach is due to the major differences in the approximations used. The PIC model, which is of a statistical nature, unavoidably introduces statistical noise   into the simulation, as a result of using a limited number of particles to represent the plasma. The overall effects of this statistical noise will be described, and possible methods that may be used to reduce the amount of noise will be discussed.

The effects are tested using simple numerical experiments with a magnetic flux tube. Different particle smoothing methods are used to minimize the statistical noise, along with different orders of differential and interpolation operators, both inside the PIC model and across the interfaces between the two types of models. Critical parameters for getting consistent simultaneous evolution of the two domains are identified; these are related to the different characteristic time and length scales of the models. These need to be chosen carefully to make meaningful hybrid MHD/PIC simulations.

Supervisors: Klaus Galsgaard, Åke Nordlund