  Surface-electrode (SE) rf traps are a promising approach to manufacturing
complex ion-trap networks suitable for large-scale quantum information
processing. In this paper we present analytical methods for modeling SE traps
in the gapless plane approximation, and apply these methods to two particular
classes of SE traps. For the SE ring trap we derive analytical expressions for
the trap geometry and strength, and also calculate the depth in the absence of
control fields. For translationally symmetric multipole configurations (analogs
of the linear Paul trap), we derive analytical expressions for electrode
geometry and strength. Further, we provide arbitrarily good approximations of
the trap depth in the absence of static fields and identify the requirements
for obtaining maximal depth. Lastly, we show that the depth of SE multipoles
can be greatly influenced by control fields.
