We present designs for multipole ion traps based on a set of planar, annular, concentric electrodes which require only rf potentials to confine ions. We illustrate the desirable properties of the traps by considering a few simple cases of confined ions. We predict that mm-scale surface traps may have trap depths as high as tens of electron volts, or micromotion amplitudes in a 2-D ion crystal as low as tens of nanometers, when parameters of a magnitude common in the field are chosen. Several example traps are studied, and the scaling of those properties with voltage, frequency, and trap scale, for small numbers of ions, is derived. In addition, ions with very high charge-to-mass ratios may be confined in the trap, and species of very different charge-to-mass ratios may be simultaneously confined. Applications of these traps include quantum information science, frequency metrology, and cold ion-atom collisions.
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