Resolving a distribution of charge into intrinsic multipole moments: A rankwise distributed multipole analysis

Abstract

We present a method for the rankwise distributed multipole analysis of an arbitrary distribution of charge and its surrounding field. Using the superposition principle, the electrostatic field created by a distribution of charge can be resolved recursively into the contributions of a set of intrinsic multipole moments "tied to" their rank-specific multipole centers. The positions of the multipole centers, which are fixed with respect to the distribution of charge, are determined from a term-by-term optimization of the Taylor's expansion of the electrostatic potential with respect to the charge coordinates. We describe the recursive construction of the intrinsic multipole moments and derive the algebraic expression of the multipole centers. The resulting distributed multipole expansion provides a conceptual framework for the analysis and modeling of the electrostatic field and of its associated distribution of charge.