Simulation of ions confined by quadrupole electric fields
Date
2012
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Abstract
Computer 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.
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Bibliography: p. 319-328
Many pages are in colour.
Many pages are in colour.
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Citation
Cummings, 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/4911