In this paper, we describe a new class of fast solvers for separable elliptic
partial differential equations in cylindrical coordinates (r,θ,z) with
free-space radiation conditions. By combining integral equation methods in the
radial variable r with Fourier methods in θ and z, we show that
high-order accuracy can be achieved in both the governing potential and its
derivatives. A weak singularity arises in the Fourier transform with respect to
z that is handled with special purpose quadratures. We show how these solvers
can be applied to the evaluation of the Coulomb collision operator in kinetic
models of ionized gases.Comment: 20 pages, 5 figure