I'm trying to design an Einzel lens to focus an ion beam. The literature seems pretty consistent that the beam diverges in the first gap and converges in the second gap. (Gaps are between the three electrodes.) What I don't understand is that the potential is lowest at the centre of a cylindrical lens (highest closer to the central electrode). Why should the positive ions be attracted to a region of higher potential? I have written a simulation which solves for voltage (the laplace equation by the finite difference method), finds the electric field (as the gradient of voltage) and then calculates the particle trajectory. The simulation results show the beam bending towards the axis at the first gap and hardly any change at the second one. I'm obviously missing something here, can anyone point it out to me?