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Direct Numerical Solution of Poisson's Equation in Cylindrical (r, z) Coordinates

Authors: Edward H. Chao, Stephen F. Paul, Ronald C. Davidson, and Kevin S. Fine

A direct solver method is developed for solving Poisson's equation numerically for the electrostatic potential phi(r,z) in a cylindrical region (r < Rwall, 0 < z < L). The method assumes the charge density rho(r,z) and wall potential phi(r = R wall , z) are specified, and delta phi/delta z = 0 at the axial boundaries (z = 0, L).