Penningtrap

The Penning trap is a device that confines charged particles using a combination of a strong magnetic field and a static quadrupole electric potential. It can hold a single ion or small ion ensembles for long periods, enabling high-precision measurements and sensitive spectroscopy.

Construction and operation: The trap typically comprises hyperbolic or cylindrical electrodes inside a vacuum chamber. A uniform magnetic field B is applied along the trap axis, while a static electric potential creates a quadrupole field Φ(r,z) = (V0/2d^2)(z^2 − (r^2)/2). This configuration provides radial confinement by the magnetic field and axial confinement by the electric field.

Motion and stability: A trapped ion executes three independent motions: axial oscillation at frequency ω_z, a rapid modified cyclotron motion at ω_+, and a slow magnetron motion at ω_- in the radial plane. The frequencies satisfy ω_c = qB/m and ω_± = (ω_c/2) ± sqrt((ω_c^2/4) − (ω_z^2/2)). Stable trapping requires ω_c^2 > 2 ω_z^2.

Applications: Penning traps are central to high-precision mass spectrometry, determinations of fundamental constants, and precise g-factor measurements. They are used in antimatter research (storage of antiprotons and positrons) and in quantum information experiments. Detection relies on measuring image currents or coupled resonant circuits; cooling can be achieved by resistive, laser, or sympathetic methods. Ultra-high vacuum and field control are essential.