The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
Aalto

Exact Solutions for Some Spherical Electrostatic Scattering Problems

Mikko Pitkonen

Doctoral dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Faculty of Electronics, Communications and Automation for public examination and debate in Auditorium S3 at the Aalto University School of Science and Technology (Espoo, Finland) on the 10th of May 2010 at 12 noon.

Overview in PDF format (ISBN 978-952-60-3057-9)   [650 KB]
Dissertation is also available in print (ISBN 978-952-60-3056-2)

Abstract

The purpose of this thesis is to analyze some basic spherical structures in electrostatics using separable coordinate systems. The main emphasis is on a dielectric body immersed in a constant electric field. This setting gives rise to the concept of polarizability, which encapsulates the scattering properties of the dielectric body in a single matrix called a polarizability tensor. For simple structures, such as a sphere and ellipsoid, the polarizability tensor can be found in a closed-form. For more complicated geometries, where there is no separable coordinate system available, one usually must resort to numerical methods.

This thesis focuses on intersecting dielectric double spheres (both two- and three-dimensional). The coordinate system considered in three dimensions is a toroidal coordinate system (R-separable), which leads to an elegant numerical solution scheme (Neumann series) that can be implemented efficiently, for example, in a Java Applet. A special case of the toroidal coordinate system is the tangent sphere frame, representing spheres that intersect each other at a single point, in which the solution of the scattering problem is reduced to a second order linear ordinary differential equation with elementary coefficients. The two-dimensional double hemisphere (or double half-disk) is considered in the bipolar coordinate system, which leads to a closed form solution for the polarizability.

This thesis consists of an overview and of the following 4 publications:

  1. Mikko Pitkonen. 2006. Polarizability of the dielectric double-sphere. Journal of Mathematical Physics, volume 47, number 10, 102901, 10 pages.
  2. Mikko Pitkonen. 2007. An explicit solution for the electric potential of the asymmetric dielectric double sphere. Journal of Physics D: Applied Physics, volume 40, number 5, pages 1483-1488.
  3. Mikko Pitkonen. 2008. Polarizability of a pair of touching dielectric spheres. Journal of Applied Physics, volume 103, number 10, 104910, 7 pages.
  4. M. Pitkonen. A closed-form solution for the polarizability of a dielectric double half-cylinder. Journal of Electromagnetic Waves and Applications, accepted for publication.

Keywords: toroidal coordinate system, double sphere, polarizability, electrostatics, half-cylinder

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© 2010 Aalto University School of Science and Technology


Last update 2011-05-26