On the frequency-locked orbits of two particles in a Paul trap

Calculations are presented that show frequency-locking to be a prominent phenomenon in the dynamics of two ions in a Paul trap, provided that damping is linear and small. The frequency-locked attractors that exist when dissipation is present correspond to stable, periodic orbits of the underlying Hamiltonian system, which appear to be infinite in number. The accuracy of the calculations is illustrated by comparing an orbit observed in a Paul trap for microspheres with the solution of the equations of motion.