Exact solutions for some spherical electrostatic scattering problems

Mikko Pitkonen

    Research output: ThesisDoctoral ThesisCollection of Articles


    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.
    Translated title of the contributionExact solutions for some spherical electrostatic scattering problems
    Original languageEnglish
    QualificationDoctor's degree
    Awarding Institution
    • Aalto University
    • Sihvola, Ari, Supervising Professor
    • Sihvola, Ari, Thesis Advisor
    Print ISBNs978-952-60-3056-2
    Electronic ISBNs978-952-60-3057-9
    Publication statusPublished - 2010
    MoE publication typeG5 Doctoral dissertation (article)


    • toroidal coordinate system
    • double sphere
    • polarizability
    • electrostatics
    • half-cylinder


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