Keplerian motion of particles with permanent electric dipole within cylindrical coaxial electrodes

A research on a possibility of trapping a particle with permanent electric dipole in an electrostatic field has been conducted. For cylindrical coaxial electrodes, Keplerian orbits for some particles were revealed. The exact criterion of successful trapping on a closed orbit within the electrodes is expressed in dimensionless parameters. For more complicated cases where the exact solution is unknown, a useful tool for numerical solution -- local field map interpolation with continuous first derivatives -- is constructed.