  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.
