Speaker
Description
Solving the electrostatic problems governing the potentials in ion traps is typically performed using numerical finite element methods. However, these simulations are slow due to the large number of mesh points needed to accurately approximate the potential. It has been recognised that translationally invariant [1] and axisymmetric [2] geometries can be solved analytically using the conformal mapping approach.
The solutions to Laplace's equation expressed in the complex plane are harmonic functions. Conformal maps are holomorphic functions which conserve this property. They can therefore be used to transform a solution from a simple geometry, such as a circle, to a more complicated geometry, such as an open polygon.
Historically, conformal maps have been used to calculate laminar airflow around a Joukowsky foil by transforming the solution obtained for a cylinder. Here, we employ the Schwarz-Christoffel transformation to calculate the electric potential and pseudopotential produced by arbitrary electrode configurations, to find optimal ion trap geometries with different boundary constraints.
[1] J. H. Wesenberg, PRA, 78, 063410 (2008).
[2] A. Valette and P. Indelicato, PRST, 13, 114001 (2010).
| Academic level | Postdoctoral researcher |
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