In radiofrequency ion traps, electric fields are produced by applying time-varying potentials between machined metal electrodes. The electrode shape constitutes a boundary condition and defines the field shape. This paper presents a new approach to making ion traps in which the electrodes consist of two ceramic discs, the facing surfaces of which are lithographically imprinted with sets of concentric metal rings and overlaid with a resistive material. A radial potential function can be applied to the resistive material such that the potential between the plates is quadrupolar, and ions are trapped between the plates. The electric field is independent of geometry and can be optimized electronically. The trap can produce any trapping field geometry, including both a toroidal trapping geometry and the traditional Paul-trap field. Dimensionally smaller ion trajectories, as would be produced in a miniaturized ion trap, can be achieved by increasing the potential gradient on the resistive material and operating the trap at higher frequency, rather than by making any physical changes to the trap or the electrodes. Obstacles to miniaturization of ion traps, such as fabrication tolerances, surface smoothness, electrode alignment, limited access for ionization or ion injection, and small trapping volume are addressed using this design. analysis is accomplished using radiofrequency quadrupolar potentials in at least two dimensions. In the Paul trap, three hyperboloidal electrodes trap ions in all three dimensions. In the rectilinear and linear traps, DC potentials on end plates trap ions in the third dimension. In the toroidal ion trap, the two-dimensional trapping field forms a closed loop.In all ion trap variations, metal electrodes are used to produce the appropriate electric fields. For full-sized ion traps, modem machining equipment easily produces the hyperboloidal electrode surfaces of the quadrupole ion trap. For miniaturized traps, however, machining methods have been pushed to the limit, and simpler electrode geometries such as planar and cylindrical are required. For this reason, most miniaturized and microfabricated ion traps have utilized the cylindrical trap design [12,[16][17][18][19][20].The need for a portable mass spectrometer has largely driven efforts to produce miniaturized ion traps [21]. Although the mass analyzer is just one of several components of a complete mass spectrometer system, miniaturization of the mass analyzer can often reduce the size and weight of other components. For example, the amplitude of ion motion is reduced in a small ion trap, so the mean free path of ions can be smaller (or