  Quadrupole ion traps can be transformed into nonlinear traps with integrable
motion by adding special electrostatic potentials. This can be done with both
stationary potentials (electrostatic plus a uniform magnetic field) and with
time-dependent electric potentials. These potentials are chosen such that the
single particle Hamilton-Jacobi equations of motion are separable in some
coordinate systems. The electrostatic potentials have several free adjustable
parameters allowing for a quadrupole trap to be transformed into, for example,
a double-well or a toroidal-well system. The particle motion remains regular,
non-chaotic, integrable in quadratures, and stable for a wide range of
parameters. We present two examples of how to realize such a system in case of
a time-independent (the Penning trap) as well as a time-dependent (the Paul
trap) configuration.
