Simulation of ions confined by quadrupole electric fields

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dc.contributor.advisorThompson, Robert Ian
dc.contributor.authorCummings, Michael David
dc.date.accessioned2017-12-18T22:34:43Z
dc.date.available2017-12-18T22:34:43Z
dc.date.issued2012
dc.descriptionBibliography: p. 319-328en
dc.descriptionMany pages are in colour.en
dc.description.abstractComputer simulations are routinely used to develop physical insight into ionic systems confined by static and time-varying quadrupole electric fields. However, after nearly 30 years of numerical exploration, three questions remain: which numerical techniques produce accurate simulations for the least computational expense? How can thermal equilibrium initial conditions be generated? How should temperature be calculated? Trapped ion simulations generally employ molecular dynamics techniques, where ion trajectories are numerically calculated at discrete points in time. While many numerical methods have been applied to these systems, it is unclear which technique is fastest or what time-step is required. In this work, the computational speed of and time-step for 11 commonly used techniques are assessed through analysis of four numerical error com­ponents. The most rapid method and required step-size depend strongly on the system parameters, with any one of the Beeman, Gear6, 5th-order Adams-Bashforth-Moulton, or 4th-order Runge-Kutta algorithms proving most appropriate. The 11 algorithms are then applied to a realistic multi-ion system and verify that the four tests accurately predict the required step size. When equilibrium properties are desired, simulations should commence from initial conditions that conform closely to thermal equilibrium; however little has been pub­lished on initial condition generation and assessment for the multi-ion system. A method is presented for generating thermal equilibrium via laser cooling and recoil heating, a ramp-down stage, where the heating and cooling are gradually reduced, and an equili­bration phase where the ensemble is evolved under only the trapping forces. Furthermore, it is demonstrated that thermal equilibrium can be assessed using well-known tests of distribution normality. vVhen time-varying fields are present, temperature calculation becomes difficult, as the ion motion contains both thermal and nonthermal components. The literature de­scribes four temperature calculation procedures for multi-ion simulation; however nei­ther their accuracy nor mathematical underpinnings have been addressed. In this work, through detailed derivations, numerical calculations, and simulations, their accuracy is determined for a wide range of parameters. Furthermore, by extending an existing tem­perature calculation technique, a new method is created and is shown to be highly accu­rate while requiring low computational expense.
dc.format.extentxxvi, 462 leaves : ill. ; 30 cm.en
dc.identifier.citationCummings, M. D. (2012). Simulation of ions confined by quadrupole electric fields (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/4911en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/4911
dc.identifier.urihttp://hdl.handle.net/1880/105912
dc.language.isoeng
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.titleSimulation of ions confined by quadrupole electric fields
dc.typedoctoral thesis
thesis.degree.disciplinePhysics and Astronomy
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameDoctor of Philosophy (PhD)
ucalgary.item.requestcopytrue
ucalgary.thesis.accessionTheses Collection 58.002:Box 2105 627942975
ucalgary.thesis.notesUARCen
ucalgary.thesis.uarcreleaseyen
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