A simple method for studying motional stability in higher-order rf traps

The proposed numerical method finds an energetic stability domain for single-particle motions in a multipole rf trap. To show how the method works, the motional stability in a sextupole rf trap is investigated. The main idea in this method is to find the envelope of stable trajectories corresponding to particles launched from the trap centre, all of them having the same initial kinetic energy. We found that the confining power of the trap is diminished near some particular launching directions. It was proved that linear trajectories are possible in a sextupole trap. They belong either to the z-axis or to a conical surface passing through the trap centre. The motional stability, along these particular directions, and for the plane motion, was investigated. The energetic stability domain of a sextupole trap is given. Some general features of the multipole rf traps are discussed, and the relations giving the stability domain are generalized.