A geometric analysis of the Maxwell field in a vicinity of a multipole particle and new special functions

TL;DR

This paper introduces a geometric method for solving Maxwell equations near a multipole particle, utilizing a new family of special functions to analyze field behavior and self-interaction effects.

Contribution

It presents a novel geometric approach and new special functions for solving Maxwell equations around moving multipole particles.

Findings

Series solution involving new special functions

Ability to analyze singular behavior near the particle

Application to self-interaction problems in electrodynamics

Abstract

A method of solving Maxwell equations in a vicinity of a multipole particle (moving along an arbitrary trajectory) is proposed. The method is based on a geometric construction of a trajectory-adapted coordinate system, which simplifies considerably the equations. The solution is given in terms of a series, where a new family of special functions arises in a natural way. Singular behaviour of the field near to the particle may be analyzed this way up to an arbitrary order. Application to the self-interaction problems in classical electrodynamics is discussed.