An orbital ion trap for electrostatic field ion trapping which includes an electrode structure defining an internal volume of the trap with at least some of electrode surfaces shaped to substantially follow equipotential lines of an ideal quadro-logarithmic electric potential around a longitudinal axis z. The ideal electric potential has an inner potential canyon, an outer potential canyon, and a low potential passage therebetween. The trap includes a trapping voltage supply which provides trapping voltages on the electrodes to generate a trapping electrostatic potential within the internal volume of the trap. The trapping electrostatic potential closely approximates at least a part of the ideal electric potential in at least a part of the internal volume of the trap.