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We analyze the well posedness of certain field-only boundary integralequations (BIE) for frequency domain electromagnetic scattering from perfectlyconducting spheres. Starting from the observations that (1) the threecomponents of the scattered electric field $\mathbf{E}^s(\mathbf{x})$ and (2)scalar quantity $\mathbf{E}^s(\mathbf{x})\cdot\mathbf{x}$ are radiativesolutions of the Helmholtz equation, novel boundary integral equationformulations of electromagnetic scattering from perfectly conducting obstaclescan be derived using Green's identities applied to the aforementionedquantities and the boundary conditions on the surface of the scatterer. Theunknowns of these formulations are the normal derivatives of the threecomponents of the scattered electric field and the normal component of thescattered electric field on the surface of the scatterer, and thus theseformulations are referred to as field-only BIE. In this paper we use theCombined Field methodology of Burton and Miller within the field-only BIEapproach and we derive new boundary integral formulations that feature onlyHelmholtz boundary integral operators, which we subsequently show to be wellposed for all positive frequencies in the case of spherical scatterers. Relyingon the spectral properties of Helmholtz boundary integral operators inspherical geometries, we show that the combined field-only boundary integraloperators are diagonalizable in the case of spherical geometries and theireigenvalues are non zero for all frequencies. Furthermore, we show that forspherical geometries one of the field-only integral formulations considered inthis paper exhibits eigenvalues clustering at one -- a property similar tosecond kind integral equations.

Combined field-only boundary integral equations for PEC electromagnetic scattering problem in spherical geometries