Solutions of Laplace's equation in two dimensions with a curved longitudinal axis
Abstract
We derive a set of functions which satisfies Laplace's equation in two dimensions x and y, when the longitudinal or z axis has a constant but nonzero curvature. The functions generalize the Fourier harmonics of the standard twodimensional multipole expansion. Both the electrostatic scalar potential and the magnetic vector potential, and the electric and magnetic fields, are treated. Recursion relations are also supplied, in a form suitable for use in a computer program, to evaluate the multipoles to arbitrary order. A comparison with other work in the field is also presented.
 Publication:

Nuclear Instruments and Methods in Physics Research A
 Pub Date:
 September 1992
 DOI:
 10.1016/01689002(92)90414Y
 Bibcode:
 1992NIMPA.321..365M