Self-consistent numerical solution to Poisson's equation in an axisymmetric Malmberg-Penning trap

This paper summarizes a fast numerical technique for solving Poisson's equation in an axisymmetric Malmberg-Penning trap. The method assumes the charge density qn(r, z) and boundary potentials phi(r = R-w, z) are specified, and serves for the electrostatic potential phi(r, z) within the cylinder. The solution of Poisson's equation is often an important step in the numerical reconstruction of the nonneutral plasma density profile n(r, z) from the axially integrated measurements of the charge density profile, Q(r) = qA(h) integral dz n(r, z), where q is the charge and A(h) is the effective area of the collimator hole.