The works of Wolfgang Paul, which led to the Paul trap, are based on investigations of the properties of electric and magnetic so called multipoles. A common magnet has two poles and is called a dipole, one with four poles, a quadrupole, one with six, a hexapole etc. Paul has shown that a magnetic hexapole, used for instance in a hydrogen maser, focuses beams of atoms having a magnetic dipole moment.
    The electric quadrupole (fig. 7) works as a two-dimensional mass filter if a d.c. voltage in addition to an a.c. voltage is applied to the electrode pairs A-A. To the other electrode pair B-B the same voltages with opposite signs are applied. The Paul trap (fig. 4, 6, 8) now being used by many scientists for storing ions may be considered a three-dimensional version of the two-dimensional mass filter. The figures 7 and 8 are copied from the patent applications by Paul and his student Steinwedel submitted 1956 and 1960.

Hans Dehmelt‘s contributions are mainly connected with the development and use of the Penning trap. He invented ingenious methods of cooling, perturbing, storing (one single electron was trapped for more than 10 months), and communicating with the trapped particles, thus forcing them to reveal their properties. In the combined electric and magnetic field in the Penning trap charged particles describe a complicated motion (fig. 9), which consists of three independent oscillations; one axial, one cyclotron, and one magnetron oscillation, each one having a well defined frequency. The axial oscillation induces a signal in the end electrodes. This signal is sensitive to the total number of charged particles in the cloud. Figure 10 shows how it is possible to count electrons in the trap by studying the strength of the signal. By shining high frequency radiation into the trap it is possible to flip the electron dipole moment repeatedly (fig. 3). Furthermore, it is possible to “lift” the electron in the quantized cyclotron orbits which the electron actually occupies. With one single electron in the trap it has been possible to compare the resonance frequencies of these two events, the flip and the “lift”, thus deriving the so called g-factor. The g-factor, being a measure of the magnetism of the electron, has been determined with twelve significant digits and is now the most accurately known fundamental constant. One may use similar methods when comparing the masses of particles with a very high precision.