An ion conned within a Paul trap can be assimilated, in a good approximation, with a harmonic oscillator. A method which enables constructing of an invariant operator, based on the Lewis and Riesenfeld approach, is reported. The method is then applied to the case of an ion conned in a Paul trap, treated as a quantum harmonic oscillator. An invariant operator is associated to the system. The spectrum of the quasienergy operator nally results. The eigenvectors of the system are found using the Fock state basis.

Trapping of microparticles and aerosols is of great interest for physics and chemistry. We report microparticle trapping in case of multipole linear Paul trap geometries, operating under standard ambient temperature and pressure conditions. An 8- and 12-electrode linear trap geometries have been designed and tested with an aim to achieve trapping for larger number of particles and to study microparticle dynamical stability in electrodynamic fields. We report emergence of planar and volume ordered structures of microparticles, depending on the a.c. trapping frequency and particle specific charge ratio. The electric potential within the trap is mapped using the electrolytic tank method. Particle dynamics is simulated using a stochastic Langevin equation. We emphasize extended regions of stable trapping with respect to quadrupole traps, as well as good agreement between experiment and numerical simulations.