An electrodynamic trap is proposed that stores cold neutral atoms or nonpolar molecules in their ground state as well as in excited states by means of the quadratic Stark effect. The trap uses an oscillating hexapole field and a superposed static homogeneous field. The dynamics of an atom in this trap can be described as a harmonic oscillation in a static pseudopotential. Stability criteria and sample parameters for a number of atomic species are given.
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