An electrostatic field with a square additive dependence on one of coordinates, also providing integrability of charged particle motion equations has been studied in the paper. The conditions of ion-motion finiteness were found for this field and in doing so it was shown the ion trap constructability. Potential parameter values providing a presence of sufficient workspace between two field-defining electrodes were revealed. An algorithm of optimal matching in beam characteristics and electrodes’ configuration was synthesized. To test the operability of the designed algorithm, three-dimensional equipotentials and a trajectory inside the ion-trap workspace were constructed. The ion trap designed in our studies can be put to experimental use as a mass spectrometer, extending the class of electrostatic ion traps presented by well-known Orbitrap and Cassini trap.