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In this paper, we describe a new class of fast solvers for separable ellipticpartial differential equations in cylindrical coordinates $(r,\theta,z)$ withfree-space radiation conditions. By combining integral equation methods in theradial variable $r$ with Fourier methods in $\theta$ and $z$, we show thathigh-order accuracy can be achieved in both the governing potential and itsderivatives. A weak singularity arises in the Fourier transform with respect to$z$ that is handled with special purpose quadratures. We show how these solverscan be applied to the evaluation of the Coulomb collision operator in kineticmodels of ionized gases.

Fast elliptic solvers in cylindrical coordinates and the Coulomb collision operator