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Type: | Thesis |

Title: | On the motion of an electron in spatially dependent electromagnetostatic fields |

Author: | Headland, M. |

Issue Date: | 1975 |

School/Discipline: | Mawson Institute for Antarctic Research |

Abstract: | This thesis is concerned with finding exact drift velocity expressions and trajectories for the notion of an electron in spatially dependent magnetic and electromagnetic field configurations. Electron notion in static magnetic fields will be analysed first. The fields will be dependent on x and pointing in the Z direction. Exact drift velocities will be obtained for electron motion in an exponentially varying magnetic field. Such a field is monotonically increasing with x and pointing in the positive Z direction. Drift expressions will also be found for a magnetic field with a power law dependence, which is slightly more complicated than the first case. For x greater than zero the magnetic field nay be either monotonically increasing or decreasing. This is governed by the power law dependence, o, being greater or less than zero. The drift velocity expressions obtained are compared with the Alfven drift velocity results in the limit of an adiabatically affected magnetic field. The exact drift expressions simplify to the perturbation results of Alfven. The trajectories for the motion of an electron in the above mentioned magnetostatic fields will also be found, both for bound and unbound orbits. The notion of an electron in a sinusoidal magnetic field varying with x will be analysed and it will be shown that the exact drift results degenerate to the Alfven drift velocity when the field is adiabatically affected. Trajectories for both bound and unbound orbits will again be considered. All the drift velocity results obtained are in terns of well known functions of mathenatical physics. The integral expressions obtained for the trajectories are found to be incomplete forms of the integrals obtained in the drift velocity expressions. In dealing with electromagnetic phenomena spatially dependent electromagnetic fields will be considered. It will be shown that if the electric scalar potential and the magnetic vector potentials have the same functional dependence, then for bound orbits the electron moves with a generalized electric drift velocity combined with an exact magnetic drift expression. Similar trajectory results exist for unbound orbits. Tractable results. will be shown to exist for field configurations in which the electric scalar potential varies as the square of the magnetic vector potential. Solutions to the electron motion will be shown to vary greatly with a parameter Q which is dependent on the constant ô relating the scalar and vector potentials. It will then be shown how the integrals change when the speed of the electron approaches the speed of light. To illustrate these three results a magnetic field with a simple exponential dependence on x together with the corresponding electric fields will be used. Further generalizations of the work by piecewise smoothing techniques will be indicated. It will also be shown how this work nay be used in upper atmospheric physics, especially in the realm of electron notion in the magnetic tail of the earth. The applicability of the work to problems in laboratory physics will also be discussed, and it will be shown that for special cases the above results nay be used to describe electron motion in the meridian plane of an axially symmetric field. |

Advisor: | Seymour, P. W. |

Dissertation Note: | Thesis (MSc) -- University of Adelaide, Mawson Institute for Antarctic Research, 1976 |

Provenance: | This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals |

Appears in Collections: | Research Theses |

Files in This Item:

File | Description | Size | Format | |
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Headland1975_MSc.pdf | 5.6 MB | Adobe PDF | View/Open |

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