# Penning trap
A **Penning trap** is a device that confines charged particles using a combination of a static quadrupole electric field (electric field from four poles whose strength varies linearly from center) and a strong, uniform magnetic field. Because [Earnshaw's theorem](https://www.edgepedia.org/earnshaws-theorem) forbids stable trapping by an electrostatic or magnetostatic field alone, the two fields are combined: the magnetic field confines the particle radially and the electric quadrupole field confines it axially[1](https://pure.mpg.de/rest/items/item_3564332_2/component/file_3564333/content) • [2](https://depts.washington.edu/uwptms/research.html). In its simplest form the trap is a three-electrode device with two endcaps and a ring between them[2](https://depts.washington.edu/uwptms/research.html). Penning traps underpin precision measurements of particle masses and magnetic moments, including the work recognized by the 1989 [Nobel Prize in Physics](https://www.edgepedia.org/nobel-prize-in-physics), and have more recently been used to store and even transport antiprotons[3](https://www.livescience.com/16362-nobel-prize-physics-list.html) • [4](https://apnews.com/article/17369ec3439bf5263d82ca11f0124895).
| Key fact | Detail |
|---|---|
| Confinement | Static quadrupole electric field plus a uniform magnetic field; the magnetic field traps radially, the electric field axially[2](https://depts.washington.edu/uwptms/research.html) |
| Motions | Three independent harmonic modes: axial, modified cyclotron, and magnetron[5](https://base.web.cern.ch/base-experiment/) |
| Stability limit | The axial frequency must satisfy \( \omega_z \le \omega_c/\sqrt{2} \)[6](https://www.nature.com/articles/s41586-024-07111-x) |
| Nobel recognition | Hans G. Dehmelt and Wolfgang Paul shared the 1989 Nobel Prize in Physics "for the development of the ion trap technique"[3](https://www.livescience.com/16362-nobel-prize-physics-list.html) |
| Mass spectrometry | ISOLTRAP performed the first Penning-trap mass measurement of a radionuclide in 1987; relative precisions beyond \( \delta m/m = 10^{-8} \) are now routine[7](https://doi.org/10.1088/1361-6471/aa6752) • [8](https://www.annualreviews.org/content/journals/10.1146/annurev-nucl-102711-094939) |
| Antiproton physics | The BASE collaboration at CERN compared proton-antiproton magnetic moments and charge-to-mass ratios with 1.5 parts per billion and 16 parts per trillion precision using a four-Penning-trap system[9](https://home.web.cern.ch/science/experiments/base/) |
| Transport | In 2025 BASE-STEP moved 92 antiprotons in an 850 kg portable cryogenic trap at −269 °C across CERN's campus by truck[4](https://apnews.com/article/17369ec3439bf5263d82ca11f0124895) |
## How it works
**Fields and modes.** A charged particle in the trap undergoes simple harmonic motion along the trap axis under the electric field, circular [cyclotron motion](https://www.edgepedia.org/cyclotron-motion) from the magnetic field, and a slow magnetron drift caused by the crossed electric and magnetic fields[2](https://depts.washington.edu/uwptms/research.html). The radial motion is a superposition of modified-cyclotron and magnetron components with frequencies \( \omega_{\pm} = \omega_c/2 \pm \Omega \), where \( \Omega = \sqrt{\omega_c^2 - 2\omega_z^2}/2 \)[6](https://www.nature.com/articles/s41586-024-07111-x). The axial frequency is set by the applied voltage and the trap dimensions, and it can be tuned up to the stability limit \( \omega_z \le \omega_c/\sqrt{2} \)[6](https://www.nature.com/articles/s41586-024-07111-x).
**Reading out the particle.** The moving charge induces a tiny image current in the electrodes, which resonant detection circuits built from superconducting inductors and low-noise amplifiers convert into a measurable signal[5](https://base.web.cern.ch/base-experiment/) • [2](https://depts.washington.edu/uwptms/research.html). The true cyclotron frequency \( \nu_c \), which carries the charge-to-mass ratio \( 2\pi\nu_c = (q/m) \cdot B_0 \), is obtained from the invariance theorem
\[ \nu_c^2 = \nu_+^2 + \nu_z^2 + \nu_-^2 \]
which combines the three observable mode frequencies and is independent of the trap's electric field imperfections[5](https://base.web.cern.ch/base-experiment/).
**Precision requirements.** The electric field must be harmonic, so electrodes are machined to about 2.5 microns and compensation electrodes tune out residual anharmonicities. A large, stable magnetic field keeps the cyclotron orbit small and its frequency high; one research trap uses a 6 T superconducting magnet with a temporal stability of 1 part in \( 10^{12} \) per hour. Cooling the trap to liquid-helium temperature cryopumps the residual gas to an effective pressure below \( 10^{-18} \) torr and reduces thermal photon noise[2](https://depts.washington.edu/uwptms/research.html).
## History
The trap takes its name from the Penning discharge geometry of the Penning ion gauge, which interested Hans G. Dehmelt, a physicist at the University of Washington, already during his studies at [Göttingen](https://www.edgepedia.org/gottingen) and Duke. Work by Franken and Liebes on accidental electron trapping in 1955 showed him that in a pure electric quadrupole field the frequency shift would not depend on the particle's position in the trap, an advantage he decided to exploit. He built his first high-vacuum magnetron trap in 1959 and soon trapped electrons for about 10 seconds, detecting all three resonances[10](https://www.nobelprize.org/prizes/physics/1989/dehmelt/biographical/).
Dehmelt's later work with single trapped particles, including sideband cooling that held a single electron for ten months in a magnetic trap, led to the 1989 Nobel Prize in Physics, shared with [Wolfgang Paul](https://www.edgepedia.org/wolfgang-paul) "for the development of the ion trap technique"[11](https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.199007341) • [3](https://www.livescience.com/16362-nobel-prize-physics-list.html). [Mass spectrometry](https://www.edgepedia.org/mass-spectrometry) with Penning traps was started at the University of Washington by Dehmelt in the 1960s and has continued there since[2](https://depts.washington.edu/uwptms/research.html).
## Mass measurements of radionuclides
**ISOLTRAP.** The technique was first combined with short-lived radioactive nuclides at ISOLTRAP, the Penning-trap mass spectrometer at CERN's ISOLDE facility[8](https://www.annualreviews.org/content/journals/10.1146/annurev-nucl-102711-094939). The first Penning-trap mass measurement of a radionuclide was performed there in 1987[7](https://doi.org/10.1088/1361-6471/aa6752). In the precision trap, the mass \( m \) of an ion of charge \( q \) follows from the measured cyclotron frequency \( \nu_c = qB/(2\pi m) \), with the magnetic field \( B \) calibrated against a reference ion of known mass[12](https://cds.cern.ch/record/1233197/files/PhysRevC.80.044323.pdf?version=1) • [7](https://doi.org/10.1088/1361-6471/aa6752).
The method's value for nuclear physics comes from its combination of precision, speed, and sensitivity. Resolving powers exceeding \( \nu_c/\Delta\nu_c \) of 1 million and accuracies of typically \( \Delta m/m \approx 10^{-7} \) were demonstrated in early ISOLDE work[13](https://cds.cern.ch/record/5283?ln=en). At facilities throughout the field, relative masses are now determined to better than \( \delta m/m = 10^{-8} \), nuclides with half-lives of only a few milliseconds can be measured, and single ions captured at rates of about one per minute suffice, making short-lived isotopes accessible to measurement[8](https://www.annualreviews.org/content/journals/10.1146/annurev-nucl-102711-094939). Detection is commonly by the time-of-flight ion cyclotron resonance technique, in which ions are ejected toward a detector and the time of flight is recorded as the excitation frequency is scanned; the phase-imaging PI-ICR variant allows measurements with fewer ions and higher resolving power[12](https://cds.cern.ch/record/1233197/files/PhysRevC.80.044323.pdf?version=1) • [14](https://isoltrap.web.cern.ch/experiment.html).
## Precision tests with antiprotons
**The BASE experiment.** The Baryon Antibaryon Symmetry Experiment (BASE) at CERN's Antiproton Decelerator uses Penning traps to compare the magnetic moments and charge-to-mass ratios of protons and antiprotons, testing CPT symmetry, the principle that matter and antimatter should behave identically[9](https://home.web.cern.ch/science/experiments/base/) • [15](https://arxiv.org/abs/1604.08820). Its apparatus holds four traps: a reservoir trap that stores typically 50 to 100 antiprotons for months, a cooling trap, a precision trap with a homogeneous magnetic field, and an analysis trap where a strong magnetic bottle identifies the particle's spin state[9](https://home.web.cern.ch/science/experiments/base/) • [16](https://pmc.ncbi.nlm.nih.gov/articles/PMC10241734/). The reservoir trap has held antiprotons for a record 600 days, allowing operation even without accelerator beam[9](https://home.web.cern.ch/science/experiments/base/).
**Measuring a magnetic moment.** The magnetic moment in units of the nuclear magneton follows from measuring two frequencies of a single stored particle: the free cyclotron frequency \( 2\pi\nu_c = (q/m) \cdot B_0 \) and the Larmor spin-precession frequency \( 2\pi\nu_L = (g/2) \cdot (q/m) \cdot B_0 \)[5](https://base.web.cern.ch/base-experiment/). To detect the spin non-destructively, the continuous Stern-Gerlach effect superimposes a magnetic bottle \( B(z) = B_0 + B_2 z^2 \) that couples the spin magnetic moment to the axial oscillation frequency[5](https://base.web.cern.ch/base-experiment/).
A single trap with a strong magnetic bottle broadens the resonance lines and limits precision to roughly the parts-per-million level. The double-trap method separates the spin analysis in an inhomogeneous analysis trap from the frequency measurements in a precision trap whose field is more homogeneous by a factor of 75,000[5](https://base.web.cern.ch/base-experiment/). BASE extended this to a three-trap, two-particle scheme, using a hot particle at an effective temperature of 300 K for magnetic field measurements and a cold particle at 0.12 K for spin spectroscopy, shuttling both to the precision trap; avoiding time-consuming resistive cooling cycles enabled an antiproton magnetic moment measurement with parts-per-billion precision[17](https://base.web.cern.ch/antiproton-magnetic-moment). Combining proton and antiproton results, BASE has compared magnetic moments with 1.5 parts per billion and charge-to-mass ratios with 16 parts per trillion precision[9](https://home.web.cern.ch/science/experiments/base/).
## Transportable traps and quantum applications
Because a Penning trap needs only static fields, the whole apparatus can in principle be moved. The BASE-STEP project built a transportable antiproton trap compact enough to fit through ordinary laboratory doors and onto a truck. The aim is to deliver antiprotons to laboratories away from the magnetic interference of CERN's accelerators, where BASE spokesperson Stefan Ulmer expects measurements 100 to 1,000 times better[4](https://apnews.com/article/17369ec3439bf5263d82ca11f0124895).
Penning traps also serve quantum technology. A micro-fabricated Penning trap has been used to demonstrate quantum operations on a single \( ^9\mathrm{Be}^+ \) ion, with laser cooling and microwave control inside a cryogenic vacuum chamber[6](https://www.nature.com/articles/s41586-024-07111-x). In 2025 the BASE collaboration demonstrated the first coherent quantum transition spectroscopy with a single antiproton spin, reaching a coherence time of 50 seconds in what it describes as the first antimatter quantum bit, a system with the potential to improve magnetic moment precision at least 100-fold[9](https://home.web.cern.ch/science/experiments/base/).
## References
1. [Theory of Penning Trap Physics, Max Planck Society](https://pure.mpg.de/rest/items/item_3564332_2/component/file_3564333/content)
2. [High Precision Mass Spectrometry at the University of Washington](https://depts.washington.edu/uwptms/research.html)
3. [Nobel Prize in Physics: 1901–Present, Live Science](https://www.livescience.com/16362-nobel-prize-physics-list.html)
4. [Geneva's CERN hails delicate test on transporting antimatter as a scientific success, AP News](https://apnews.com/article/17369ec3439bf5263d82ca11f0124895)
5. [The BASE Experiment – Penning trap and image current detection, CERN](https://base.web.cern.ch/base-experiment/)
6. [Penning micro-trap for quantum computing, Nature (2024)](https://www.nature.com/articles/s41586-024-07111-x)
7. [Extending and refining the nuclear mass surface with ISOLTRAP, Journal of Physics G (2017)](https://doi.org/10.1088/1361-6471/aa6752)
8. [Penning-Trap Mass Measurements in Atomic and Nuclear Physics, Annual Review of Nuclear and Particle Science](https://www.annualreviews.org/content/journals/10.1146/annurev-nucl-102711-094939)
9. [BASE – Home, CERN](https://home.web.cern.ch/science/experiments/base/)
10. [Hans G. Dehmelt – Biographical, NobelPrize.org](https://www.nobelprize.org/prizes/physics/1989/dehmelt/biographical/)
11. [Experiments with an Isolated Subatomic Particle at Rest (Nobel Lecture), Angewandte Chemie (1990)](https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.199007341)
12. [High-precision Penning-trap mass measurements, Physical Review C 80, 044323 (2009)](https://cds.cern.ch/record/1233197/files/PhysRevC.80.044323.pdf?version=1)
13. [High-accuracy mass determination of unstable nuclei with a Penning trap mass spectrometer, CERN ISOLDE](https://cds.cern.ch/record/5283?ln=en)
14. [ISOLTRAP experiment, CERN](https://isoltrap.web.cern.ch/experiment.html)
15. [BASE – The Baryon Antibaryon Symmetry Experiment, arXiv:1604.08820](https://arxiv.org/abs/1604.08820)
16. [BASE – high-precision comparisons of the fundamental properties of protons and antiprotons, PMC](https://pmc.ncbi.nlm.nih.gov/articles/PMC10241734/)
17. [Antiproton Magnetic Moment – The BASE Experiment, CERN](https://base.web.cern.ch/antiproton-magnetic-moment)
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*Topic: Encyclopedia › Physical world and mathematics › Physics › Matter and radiation physics › Atomic and molecular physics › Laser cooling and trapping › Ion trapping and cooling*
*Initially written Sep 17, 2026 · Reviewed: Oct 15, 2026 · Edited: Oct 15, 2026 · Last review: Oct 15, 2026*
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