  Trapped ions offer long internal state (spin) coherence times and strong
inter-particle interactions mediated by the Coulomb force. This makes them
interesting candidates for quantum simulation of coupled lattices. To this end
it is desirable to be able to trap ions in arbitrary conformations with
precisely controlled local potentials. We provide a general method for
optimizing periodic planar radio-frequency electrodes for generating ion
trapping potentials with specified trap locations and curvatures above the
electrode plane. A linear-programming algorithm guarantees globally optimal
electrode shapes that require only a single radio-frequency voltage source for
operation. The optimization method produces final electrode shapes that are
smooth and exhibit low fragmentation. Such characteristics are desirable for
practical fabrication of surface-electrode trap lattices.
