Abstract
(Received 10 September 2013; revised manuscript received 13 June 2014; published 18 July 2014) Analytic expressions for the potentials and fields offlat and cylindrical plates, including the fringe fields, are given. The present analysis extends and simplifies the current expression for the fields of flat plates and develops expressions for the fringe fields of cylindrical plates in terms of polar coordinates. The development of a FORTRAN program to output the field strength at a given location within the Proton Electric Dipole Moment (Proton EDM) ring is then described. Fourth-order Runge-Kutta integration is used to investigate the effect of fringe fields on particle and spin dynamics with precision tracking in the proposed Proton EDM experiment.
Highlights
INTRODUCTIONThe hard-edge approximation that is often used accounts for the energy change of a particle through the fringe region and does not include the fringe fields themselves
Fringe fields are often neglected in analysis of electrostatic configurations
The equipotential surfaces of the cylindrical plates can be used to shape the end of the cylindrical plates of the Proton Electric Dipole Moment (EDM) experiment, similar to the Rogowski profile [4] used for flat plates
Summary
The hard-edge approximation that is often used accounts for the energy change of a particle through the fringe region and does not include the fringe fields themselves. This cannot be the full story since the hard-edge fields are not solutions to the Maxwell equations for the given system. We describe the implementation of the mathematical expressions of the fringe fields into a FORTRAN tracking program using fourth-order Runge-Kutta integration. We intend for this to become a valuable tool in accurately determining the effects of fringe fields on particle and spin dynamics in the fringe regions through precision tracking
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