Electrostatic solution and rayleigh approximation for small nonspherical particles in a spheroidal basis

The electrostatic approximation in the problem of diffraction of a plane wave by a group of coaxial small scatterers

“…Thus, in contrast to the methods from study [1], the MNFM applied to the electrostatic problem does not necessitate calculating integrals (with the help of standard techniques) for the estimation of the matrix elements of the algebraic sys tem to which the boundary value problem is reduced.…”

“…Let d denote the distance between the origins of the local coordinate frames and let z 0l denote the coordinate of the origin of the lth coordi nate frame in the common coordinate frame. As is known, the electrostatic field is expressed through potential Ψ according to the formula (1) , E = ∇Ψ KYURKCHAN, MANENKOV where Ψ satisfies the Laplace equation and the follow ing boundary conditions on surface S j of each particle:…”

“…f Z β δ max , which depends on the shape of the original sur face of the body. Below, we present a numerical algo rithm for the determination of δ max for so called Che byshev particles [1].…”

“…This problem can be regarded as an approximation in the investigation of diffraction of the electromagnetic field by a group of particles small in comparison to the wavelength. In study [1], where a similar problem is considered for a single particle, the authors apply the separation of variables method (SVM) and the extended boundary condition method (EVCM). It is interesting to compare these methods with the modi fied null field method (MNFM) and to generalize the problem to the case of a group of coaxial bodies.…”

Solution of the electrostatic problem for a non-confocal core-mantle spheroid

“…In our recent paper [1] we have developed a new approach to find the exact solution and the Rayleigh approximation for the spheroidal Chebyshev particles. In this work the approach is generalized for the case of non-confocal core-mantle spheroids.…”