Cylindrical Penning traps with dynamic orthogonalized anharmonicity compensation for precision experiments

Harmonic potentials can be produced in cylindrical ion traps by means of dynamic orthogonalized anharmonicity compensation with use of two (or multiple) sets of compensation electrodes. One special example is for traps with multiple identical electrodes which are not only easy to construct and allow access to the center region of the trap for particle loading and releasing, laser beams, and microwaves, but also flexible in forming harmonic potential wells in many locations. The nested trap configuration and the side-by-side trap configuration are readily available in this special scheme. Analytical solutions for cylindrical traps with multiple sets of compensation potentials are presented. This work will be useful for studies involving Penning trap diagnostics, atomic and molecular interactions (including the production of antihydrogen atoms), accurate mass measurements of exotic particles, and precision measurements of the spin precession frequencies of trapped particles.