A Penning trap can be defined as the superposition of a homogeneous magnetic field and an electrostatic quadrupole field. The magnetic field B is used for radial confinement. The electric field prevents the ions from escaping along the magnetic field lines and hence leads to the axial confinement of a particle of charge q and mass m. Common property of all mass experiments with Penning trap spectrometers is the determination of the cyclotron frequency
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The motion in a Penning trap is not a simple cyclotron motion with angular frequency ω_c but a combination of three harmonic eigen motions, an axial oscillation (z) and two circular motions commonly referred to as magnetron (-) and cyclotron motion (+). There exist basic relations between the frequencies of these eigen motions and ω_c, which can be used for a precise determination of ω_c = (q / m) *B in a Penning trap. One of these relations is .
The ion motion can be driven by oscillating electric fields which in general results in a change of the amplitudes of the ion motions. An azimuthal quadrupole field allows the ion motion to be excited directly at ω_c = ω₊ + ω_- . The direct excitation at the "true" cyclotron frequency ω_c has the advantage that in the case of an ideal trap only ONE frequency measurement is needed for a mass determination, provided the magnetic field is known. This technique is used by ISOLTRAP for the mass determination of short-lived isotopes, as well as by other experiments.