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A 2D Finite Elembent/1D Fourier Solution To The Fokker-Planck Equation

Plasma, the fourth state of matter, is a gas in which a significant portion of the atoms are ionized. It is estimated that more than 99% of the material in the visible universe is in the plasma state. The process that stars, including our sun, combine atomic nuclei and produce large amounts of energy is called thermonuclear fusion. It is anticipated future energy demands will be met by large terrestrial devices harnessing the energy of nuclear fusion. A gas hot enough to produce the number of atomic collisions needed for fusion is necessarily in the plasma state. Therefore, plasmas are of great interest to researchers studying nuclear fusion. Stars are massive enough that the gravitational attraction heats and confines the plasma. Gravitational confinement cannot be used to confine fusion plasmas on Earth. Material containers cause cooling, which prevent a plasma from maintaining the high temperature needed for fusion. Fortunately plasmas have electrical properties, which allow them to be controlled by strong magnetic fields.
Although serious research into controlled thermonuclear fusion began over 60 years ago, only a couple of man-made devices are even close to obtaining more energy from fusion than is put into them. One difficulty lies in understanding the physics of particle collisions. A relative few particle collisions result in the fusion of atomic nuclei, while the vast majority of collisions are understood in terms of the electrostatic force between particles. My work has been to create an a computer code, which can be executed in parallel on supercomputers, to quickly and accurately calculate the evolution of a plasma due to particle collisions. This work explains the physics and mathematics underlying our code, as well as several tests which demonstrate the code is working as expected.

Identiferoai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-2247
Date01 May 2012
CreatorsSpencer, Joseph Andrew
PublisherDigitalCommons@USU
Source SetsUtah State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceAll Graduate Theses and Dissertations
RightsCopyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact Andrew Wesolek (andrew.wesolek@usu.edu).

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