An ion with mass m and charge q in a magnetic field performs a cyclotron motion as shown above. This motion provides a transverse confinement with respect to the magnetic field axis but no axial confinement. In order to prevent the ion from escaping along the magnetic field lines, an additional static electric (quadrupole) field can be superposed. This field can be created with an electrode configuration as shown above.
The ion motion in both electric and magnetic field remains simple. It consists of a superposition of three independent harmonic oscillations called axial oscillation, magnetron motion, and (reduced) cyclotron motion.