DSpace Collection:
https://dspace.lboro.ac.uk/2134/6623
2017-04-29T01:31:51ZPath integral calculation of the Wigner function
https://dspace.lboro.ac.uk/2134/24509
Title: Path integral calculation of the Wigner function
Authors: Lindsey, Neil
Abstract: Elementary Wigner function calculations of the infinite square well and Schroedinger cat
states are presented as an introduction to the quasi-probability function. An entangled
cat state is calculated and the Wigner function of the state is found. Properties
of the entanglement of the state and the nature of its entanglement are found to be
distinguishable by this distribution.
This work is mostly concerned with obtaining the Wigner function via a path integral
method, following a previously published technique. The method approximates the
ground state Wigner function by finding the classical path associated with each point
in phase space, assuming the P-function of the Hamiltonian of the system is able to
be found. The imaginary part of action determines the phase of the path integral
and depends on the geometry of the path; specifically the area which it encloses. An
investigation into two systems, the Morse potential and the double well potential, was
performed to try and find classical paths enclosing area and thus recreating the negative
features of the exact Wigner function. The minimisation of the action found the classical
path for each phase space point. This was performed numerically using tools created in
Excel and Mathematica. In general, it was discovered that the classical paths did not
enclose any area and therefore the Wigner function approximations were everywhere
positive. The majority of those paths which were found to enclose some area produce a
phase which is not large enough to change the sign of the path integral.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2008-01-01T00:00:00ZSecondary electron yield measurements of anti-multipacting surfaces for accelerators
https://dspace.lboro.ac.uk/2134/23255
Title: Secondary electron yield measurements of anti-multipacting surfaces for accelerators
Authors: Wang, Sihui
Abstract: Electron cloud is an unwanted effect limiting the performance of particle accelerators with positively charged particle beams of high-intensity and short bunch spacing. However, electron cloud caused by beam induced multipacting can be sufficiently suppressed if the secondary electron yield (SEY) of accelerator chamber surface is lower than unity. Usually, the SEY is reduced by two ways: modification of surface chemistry and engineering the surface roughness. The objective of this PhD project is a systematic study of SEY as a function of various surface related parameters such as surface chemistry and surface morphology, as well as an effect of such common treatments for particle accelerators as beam pipe bakeout and surface conditioning with a beam, ultimately aiming to engineer the surfaces with low SEY for the electron cloud mitigation. In this work, transition metals and their coatings and laser treated surface were studied as a function of annealing treatment and electron bombardment. The transition metal thin films have been prepared by DC magnetron sputtering for further test.
In the first two Chapter of this thesis, the literature review on electron emission effect is introduced, which includes the process of the electron emission, the influence factor and examples of low SEY materials. In the third Chapter, the experimental methods for SEY measurements and surface investigation used in this work are described. In Chapter 4, the SEY measurement setup which is built by myself are introduced in detail. In Chapter 5 transition metals and their coatings and non-evaporable getter (NEG) coatings have been studied. All the samples have been characterized by SEY measurements, their surface morphology was analysed with Scanning Electron Microscopy (SEM) and their chemistry was studied with X-ray Photoelectron Spectroscopy (XPS). Different surface treatments such as conditioning by electron beam, thermal treatment under vacuum on the sample surfaces have been investigated. For example, the maximum SEY (δmax) of as-received Ti, Zr, V and Hf were 2.30, 2.31, 1.72 and 2.45, respectively. After a dose of 7.9×10-3 C mm-2, δmax of Ti drops to 1.19. δmax for Zr, V and Hf drop to 1.27, 1.48 and 1.40 after doses of 6.4×10-3 Cmm-2, 1.3×10-3 and 5.2×10-3 Cmm-2, respectively. After heating to 350 ⁰C for 2.5 hours, the SEY of bulk Ti has dropped to 1.21 and 1.40, respectively. As the all bulk samples have a flat surface, there are no difference of morphology. So this reduction of SEY is believed to be a consequence of the growth of a thin graphitic film on the surface after electron bombardment and the removal of the contaminations on the surface after annealing.
Chapter 6 of this thesis is about the laser treated surface. Laser irradiation can transform highly reflective metals to black or dark coloured metal. From SEM results, metal surfaces modified by a nanosecond pulsed laser irradiation form a highly organised pyramid surface microstructures, which increase the surface roughness. Due to this reason, δmax of as-received laser treated surface could be lower than 1, which can avoid the electron cloud phenomenon. In this Chapter, the influence of different laser treatment parameters, such as power, hatch distance, different atmospheres on SEY has been investigated. Meanwhile, different surface treatments such as electron conditioning and thermal treatments are studied on the laser treated surface with the investigation of XPS. For example, the δmax of as-received type I with hatch distance 50, 60 and 80 μm in Air are 0.75, 0.75 and 0.80, respectively. After heating to 250 ºC for 2 hours, in all case the δmax drop to 0.59, 0.60, 0.62, respectively. The SEYs of all as-received samples are lower than 1 due to the increasing the roughness on the surface by the special pyramid structure. After thermal treatment, the SEY reduces even further. This is caused by removing the contaminations on the surfaces.
In conclusion, the present study has largely improved the knowledge of the electron cloud mitigation techniques by surface engineering of vacuum chambers. On the one hand, the surface treatments can modify the surface chemistry, such as the produce the graphic carbon layer on the surface by electron condition and the removal the contamination layer on the top of the surface by thermal treatment. On the other hand, the SEY could be critically low by engineering the surface roughness. Both methods allow reaching δmax less than unity. The efficiency of laser treated surface for e-cloud was demonstrated for a first time leading to a great interest to this new technology application for existing and future particle accelerators.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2016-01-01T00:00:00ZEffects of magnetic field on electron transport in semiconductor superlattices
https://dspace.lboro.ac.uk/2134/21922
Title: Effects of magnetic field on electron transport in semiconductor superlattices
Authors: Zhang, Liang
Abstract: Quantum superlattice with a narrow energy band is an artificial semiconductor structure demonstrating both nonlinear and active high-frequency electromagnetic properties. These types of superlattices are used as key elements in various miniature electronic devices including frequency multipliers and quantum cascade lasers. Interaction between terahertz radiation and magnetic field in semiconductor superlattices has been the subject of growing research interest, both theoretical and experimental. In this thesis, we study the nonlinear dynamics of electrons in minibands of the semiconductor superlattices subjected to a terahertz electric field and a magnetic field.
Electron transport in a semiconductor superlattice with an electric field and a tilted magnetic field has been studied using semiclassical equations. In particular, we consider how dynamics of electron in superlattices evolve with changing the strength and the tilt of a magnetic field. In order to investigate the influence of a tilted magnetic field on electron transport, we calculate the drift velocity for different values of the magnetic field. Studies have shown that the resonance of Bloch oscillations and cyclotron oscillations produces additional peaks in drift velocity. We also found out that appearance of these resonances can promote amplification of a small ac signal applied to the superlattice.
In the presence of the electromagnetic field, the superlattice is expected to demonstrate the Hall effect, which however should have a number of very specific features due to an excitation of Bloch oscillations and a significant electric anisotropy. Here, we theoretically study the Hall effect in a semiconductor superlattice both for the steady electron transport and for the transient response. We studied the coherent Hall effect in an extraordinary configuration where the electric field is applied in the transverse direction of the superlattice growth direction. By mapping the momentum dynamics to the pendulum equivalent, we distinguished the two regimes of the oscillations from the viewpoint of the effective potentials. We discuss the experimental manifestation of the Hall effect in a realistic superlattice. We also made the numerical simulations of the polarized THz field and the time-resolved internal electro-optic sampling (TEOS) signals where we found the unusual shaped waveforms of the THz signals.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2016-01-01T00:00:00ZEdge states, magnetisation and topological domain walls in graphene
https://dspace.lboro.ac.uk/2134/21801
Title: Edge states, magnetisation and topological domain walls in graphene
Authors: Liu, Yang
Abstract: We studied the edge states and their roles in conductivity
and magnetism of graphene nanoribbions and flakes. we studied the Aharonov-Bohm effect in graphene nanodisks and rings. We described the quantum oscillations of the magnetization of graphene flakes. we have examined the snake-like states of transport
electrons in the configurations of graphene ribbons with a domain wall in the centre.
Description: A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.2016-01-01T00:00:00Z