Ion‐beam optics of a two‐stage electrostatic accelerator (i.e., the extraction‐accel‐decel column) is studied by three approaches: (i) a linear optics analytic solution based on the paraxial equations which account for lens effects and beam space charge, (ii) a nonlinear optics solution based on the Poisson‐Vlasov equations and including the two‐dimensional source‐plasma sheath, and (iii) a 60‐kV single‐beamlet experimental study. Principal results are that in certain operating modes, the minimum beam divergence in a two‐stage source is significantly less than in the conventional single‐stage source and that the optics of the two‐stage source is less sensitive to variation in extraction perveance about the divergence minimum. This is because the optimum extraction perveance in such modes of operation is relatively high, causing the crucial residual aberration fields near the first electrode to be smaller.