---
title: "How a rapidly reversing field can hold ions"
description: "Alternating quadrupoles confine ions. Excitation or an RF ramp sends them through an exit; independent standards connect arrival times with mass-to-charge."
canonical_url: "https://sandboxphysics.com/stories/instruments/paul-ion-trap-mass-spectrometer/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/instruments/paul-ion-trap-mass-spectrometer/"
last_modified: "2026-11-12"
---

[How physics instruments measure](https://sandboxphysics.com/stories/instruments/)

# How a rapidly reversing field can hold ions

An electric field can push an ion inward during one part of a cycle and outward during another, yet keep it within a small region. The timing and spatial shape matter: the ion changes position between those pushes. A Paul trap uses that motion to store ions, then sends selected ions towards a detector.

Sandbox Physics · 2026-11-12

## Four electrodes alternate the focusing directions

A linear Paul trap places four long electrodes around an axis. At one instant, the transverse electric field pushes a positive ion towards the axis in one direction and away in the other. The RF voltage reverses those roles. Within suitable voltage and frequency ranges, the transverse oscillation stays bounded. Static potentials at the ends provide axial confinement.

Averaging the field over a cycle misses the changing position of the ion. The force depends on the field where the ion actually is. Its rapid displacement interacts with the spatially varying field, producing a restoring effect on a slower timescale.

Hold the RF voltage fixed and the defocusing direction keeps pushing outward. The axial static well also comes with a tradeoff: it weakens transverse confinement. The radial RF field and the axial static field must work together to maintain stable motion.

$$
m\,\ddot{\mathbf r}=Q\,\mathbf E(\mathbf r,t)
$$

r is position, and the double dot denotes acceleration. An ion of mass m and charge Q responds to the field along its moving trajectory. With the same initial motion, its charge-to-mass ratio affects that response.

Sources: [1] [2]

## A fast ripple accompanies the slower oscillation

Slow the trajectory down and two rhythms appear. The ion oscillates relatively slowly within the trap, called secular motion. A faster micromotion follows the RF drive. Farther from the axis, the RF field is stronger and the micromotion generally becomes more pronounced.

When micromotion is small and the timescales are well separated, a smooth effective potential describes the slower motion. This picture explains confinement near the centre. Near an electrode edge or an exit slot, the changing field and the actual path still matter. A trapped ion also retains motion. Cooling needs an additional energy-transfer process, such as collisions that transfer energy to a colder buffer gas, or laser cooling.

Sources: [1] [2] [4]

## Another rhythm can drive an ion towards the exit

After storage, a weaker alternating excitation can be added across an electrode pair. An excitation that follows the secular motion can build up its amplitude over successive oscillations. This is the idea behind resonant ejection. Detuning the excitation usually makes that energy transfer less effective.

A slot in an electrode provides a way out. The ion must pass through it and then reach the collector to produce a detector pulse. Striking metal and leaving through another opening have different outcomes. Following those paths shows what the growing oscillation actually produces.

Sources: [2] [4]

## An RF amplitude ramp can release ions in sequence

Mass selection can also use the range of stable motion directly. With RF frequency fixed, increasing the voltage amplitude changes the conditions experienced by a stored ion. Different mass-to-charge ratios can lose stability at different stages and move outwards. This mass-selective instability scan and auxiliary resonant excitation are distinct operations to compare.

The Mathieu stability diagram explains the existence of these ranges for ideal periodic fields. A real scan also involves a changing voltage, finite electrodes and flight beyond the trap. The detector reports the final arrival time. A complete trajectory connects that arrival with the earlier motion.

Sources: [3] [2]

## Arrival times become a calibrated mass spectrum

The small electrical signal from an arriving ion needs to be read. One approach releases secondary particles at an impact surface. Further interactions in an electron multiplier amplify the signal into a measurable pulse. Electronics assigns an arrival time, producing a sequence of timestamps during the scan.

Send independently known ions through the same loading and scanning procedure and record their detector times. Other known ions, excluded from calibration, test the relation. An unknown arrival can then be compared with those references to obtain a mass-to-charge range.

Initial position and motion also affect ejection. Similar arrival times can come from different initial conditions, so calibration needs a specified preparation. When the evidence places an arrival only within an interval, retain that interval with its count. Touching or overlapping intervals do not resolve two separate peaks. Finer distinctions need a narrower response or further independent references.

A spectrum assembled this way has a physical origin for every observation: a count comes from a collector event, and its mass range comes from comparison with standards. Following storage, excitation, the exit and detection reveals how the whole instrument shapes the result.

Sources: [3] [4]

## [Follow storage, sideways ejection and mass intervals](https://sandboxphysics.com/labs/trapped-ion-sideband-spectroscopy/?instrument=ion-trap-mass-spectrum)

Compare auxiliary excitation with an RF amplitude scan, follow collector events through the slot and inspect the standards alongside the unknown samples.

Collision-free dilute ions in finite linear rods with side slots and idealized collector timing. The RF scan returns event-compatible intervals within its controlled preparation and calibration domain.

## Sources and further reading

1. [Wineland et al., Coherent Quantum State Manipulation of Trapped Atomic Ions (1998)](https://tf.nist.gov/general/pdf/1228.pdf)

   Reads printed pages 42–44, including Figure 1 and equations 1–2 on page 43, for the linear electrodes, axial static confinement and small-parameter secular/micromotion distinction. The central approximation is not extended over slotted electrodes; quantum-state performance is not adopted.

2. [Wolfgang Paul, Electromagnetic Traps for Charged and Neutral Particles, Nobel Lecture (1989)](https://www.nobelprize.org/uploads/2018/06/paul-lecture.pdf)

   Reads printed pages 603, 605, 609 and 612 for alternating quadrupoles, stable motion and resonant amplitude growth. Pages 609 and 612 concern a three-dimensional ring trap; separate linear-trap sources support the rods and side exit here. The full 22 pages are not claimed as read, and no figures are reproduced.

3. [Purdue University Aston Labs, Ion Trap Developments](https://integratedimaging.purdue.edu/research/ion-trap.html)

   Reads the explanation of mass-selective instability during an RF amplitude ramp and auxiliary-frequency scanning. The two ejection operations are distinguished. Tandem-MS data and commercial performance are not used as teaching measurements.

4. [Finnigan LXQ Hardware Manual, revision B (June 2006)](https://assets.thermofisher.com/TFS-Assets/CMD/manuals/Man-97055-97043-LXQ-Hardware-Man9705597043-B-EN.pdf)

   Reads printed pages 43–44 and 47–49, including Figure 17, for linear rods, slots, axial potentials, buffer gas and electron multiplication. Drawings and voltage tables are not copied; the Lab declares its own geometry and readout.

[How a vernier reads between millimetres](https://sandboxphysics.com/stories/instruments/length-metrology/) [Air helps hold up the object on a balance](https://sandboxphysics.com/stories/instruments/precision-balance/) [How Cavendish Measured the Attraction Between Spheres](https://sandboxphysics.com/stories/instruments/cavendish-balance/) [Which pressure does a liquid column measure?](https://sandboxphysics.com/stories/instruments/manometer/) [The cup absorbs heat too](https://sandboxphysics.com/stories/instruments/calorimeter/) [Rotational rheometers need both torque and speed](https://sandboxphysics.com/stories/instruments/rotational-rheometer/) [Why the air beyond a pipe changes its resonance](https://sandboxphysics.com/stories/instruments/resonance-tube/) [How a seismometer reads the ground through motion inside its case](https://sandboxphysics.com/stories/instruments/seismometer/) [Why does a meter change the circuit?](https://sandboxphysics.com/stories/instruments/electrical-meters/) [How a null detector reveals a resistance](https://sandboxphysics.com/stories/instruments/resistance-bridges/) [Why a capacitor can behave like an inductor](https://sandboxphysics.com/stories/instruments/lcr-impedance/) [Where does the slow wave on an oscilloscope come from?](https://sandboxphysics.com/stories/instruments/digital-oscilloscope/) [How a lock-in amplifier finds a signal buried in noise](https://sandboxphysics.com/stories/instruments/lock-in-amplifier/) [Where a small peak in a spectrum can come from](https://sandboxphysics.com/stories/instruments/spectrum-analyzer/) [How a network analyzer separates the cable from the device](https://sandboxphysics.com/stories/instruments/vector-network-analyzer/) [When a slower quartz crystal can measure added mass](https://sandboxphysics.com/stories/instruments/quartz-microbalance/) [How an echelle spectrograph gives overlapping colors a second direction](https://sandboxphysics.com/stories/instruments/echelle-spectrograph/) [How total brightness reveals many infrared colors](https://sandboxphysics.com/stories/instruments/ftir-spectrometer/) [Measuring a Solution’s Concentration with Light](https://sandboxphysics.com/stories/instruments/uv-vis-spectrophotometer/) [How an ellipsometer reads thin-film thickness from reflected light](https://sandboxphysics.com/stories/instruments/spectroscopic-ellipsometer/) [How a polarimeter reveals mixed polarization](https://sandboxphysics.com/stories/instruments/mueller-polarimeter/) [How individual photons reveal a fluorescence lifetime](https://sandboxphysics.com/stories/instruments/tcspc-fluorescence-lifetime/) [Brillouin Microscopy Listens to Sound with Light](https://sandboxphysics.com/stories/instruments/brillouin-microscope/) [How a white sphere compares a lamp’s total output](https://sandboxphysics.com/stories/instruments/integrating-sphere-radiometer/) [How powder rings reveal atomic spacing](https://sandboxphysics.com/stories/instruments/powder-xray-diffractometer/) [How Small-Angle X-ray Scattering Reads a Particle Halo](https://sandboxphysics.com/stories/instruments/small-angle-xray-scattering/) [Why X-ray fluorescence depends on sample thickness](https://sandboxphysics.com/stories/instruments/xray-fluorescence-spectrometer/) [Why an AFM makes a bump look wider](https://sandboxphysics.com/stories/instruments/atomic-force-microscope/) [How a small indentation separates hardness from elasticity](https://sandboxphysics.com/stories/instruments/nanoindenter/) [How Differential Scanning Calorimetry Reads a Melting Peak](https://sandboxphysics.com/stories/instruments/differential-scanning-calorimeter/) [How thermogravimetry separates mass loss from the gas around it](https://sandboxphysics.com/stories/instruments/thermogravimetric-analyzer/) [How a diamond anvil cell reads pressure in ruby light](https://sandboxphysics.com/stories/instruments/diamond-anvil-cell/) [How diamond fluorescence reveals a magnetic-field direction](https://sandboxphysics.com/stories/instruments/nv-center-magnetometer/) [Reading a magnetic field in the rhythm of atoms](https://sandboxphysics.com/stories/instruments/optically-pumped-magnetometer/) [Keeping a laser in time with atoms](https://sandboxphysics.com/stories/instruments/optical-lattice-clock/) [Why a Kibble balance needs two experiments](https://sandboxphysics.com/stories/instruments/kibble-balance/) [How a dilution refrigerator keeps carrying heat away](https://sandboxphysics.com/stories/instruments/dilution-refrigerator/) [Why a bigger vacuum pump may barely help the sample](https://sandboxphysics.com/stories/instruments/ultra-high-vacuum-system/) [How microwaves read a superconducting qubit](https://sandboxphysics.com/stories/instruments/superconducting-qubit-readout/) [How current leaves a voltage across a thin sheet](https://sandboxphysics.com/stories/instruments/four-probe-hall/) [How an ion flight becomes a mass spectrum](https://sandboxphysics.com/stories/instruments/time-of-flight-mass-spectrometer/) [How four straight rods select ion mass](https://sandboxphysics.com/stories/instruments/quadrupole-mass-filter/) [How a cyclotron keeps a proton on the accelerating beat](https://sandboxphysics.com/stories/instruments/cyclotron-synchrocyclotron/) [Why the drift tubes in an RF linac get longer](https://sandboxphysics.com/stories/instruments/radio-frequency-linac/) [The directions hidden inside a small beam spot](https://sandboxphysics.com/stories/instruments/beam-diagnostics/) [How defocusing magnets help a beam stay in a ring](https://sandboxphysics.com/stories/instruments/synchrotron-storage-ring/) [Why a collider cannot keep every collision](https://sandboxphysics.com/stories/instruments/collider-trigger-daq/) [Getting synchrotron light onto a sample](https://sandboxphysics.com/stories/instruments/synchrotron-beamline/) [How a free-electron laser gathers electrons into a brighter beam](https://sandboxphysics.com/stories/instruments/xray-free-electron-laser/) [Following energy exchange with neutron flight times](https://sandboxphysics.com/stories/instruments/pulsed-neutron-time-of-flight/)

## Keep reading

How physics instruments measure · Reading path

### How physics instruments measure

1. [Article **How a vernier reads between millimetres**](https://sandboxphysics.com/stories/instruments/length-metrology/)
2. [Article **Air helps hold up the object on a balance**](https://sandboxphysics.com/stories/instruments/precision-balance/)
3. [Article **How Cavendish Measured the Attraction Between Spheres**](https://sandboxphysics.com/stories/instruments/cavendish-balance/)
4. [Article **Which pressure does a liquid column measure?**](https://sandboxphysics.com/stories/instruments/manometer/)
5. [Article **The cup absorbs heat too**](https://sandboxphysics.com/stories/instruments/calorimeter/)
6. [Article **Rotational rheometers need both torque and speed**](https://sandboxphysics.com/stories/instruments/rotational-rheometer/)
7. [Article **Why the air beyond a pipe changes its resonance**](https://sandboxphysics.com/stories/instruments/resonance-tube/)
8. [Article **How a seismometer reads the ground through motion inside its case**](https://sandboxphysics.com/stories/instruments/seismometer/)
9. [Article **Why does a meter change the circuit?**](https://sandboxphysics.com/stories/instruments/electrical-meters/)
10. [Article **How a null detector reveals a resistance**](https://sandboxphysics.com/stories/instruments/resistance-bridges/)
11. [Article **Why a capacitor can behave like an inductor**](https://sandboxphysics.com/stories/instruments/lcr-impedance/)
12. [Article **Where does the slow wave on an oscilloscope come from?**](https://sandboxphysics.com/stories/instruments/digital-oscilloscope/)
13. [Article **How a lock-in amplifier finds a signal buried in noise**](https://sandboxphysics.com/stories/instruments/lock-in-amplifier/)
14. [Article **Where a small peak in a spectrum can come from**](https://sandboxphysics.com/stories/instruments/spectrum-analyzer/)
15. [Article **How a network analyzer separates the cable from the device**](https://sandboxphysics.com/stories/instruments/vector-network-analyzer/)
16. [Article **When a slower quartz crystal can measure added mass**](https://sandboxphysics.com/stories/instruments/quartz-microbalance/)
17. [Article **How an echelle spectrograph gives overlapping colors a second direction**](https://sandboxphysics.com/stories/instruments/echelle-spectrograph/)
18. [Article **How total brightness reveals many infrared colors**](https://sandboxphysics.com/stories/instruments/ftir-spectrometer/)
19. [Article **Measuring a Solution’s Concentration with Light**](https://sandboxphysics.com/stories/instruments/uv-vis-spectrophotometer/)
20. [Article **How an ellipsometer reads thin-film thickness from reflected light**](https://sandboxphysics.com/stories/instruments/spectroscopic-ellipsometer/)
21. [Article **How a polarimeter reveals mixed polarization**](https://sandboxphysics.com/stories/instruments/mueller-polarimeter/)
22. [Article **How individual photons reveal a fluorescence lifetime**](https://sandboxphysics.com/stories/instruments/tcspc-fluorescence-lifetime/)
23. [Article **Brillouin Microscopy Listens to Sound with Light**](https://sandboxphysics.com/stories/instruments/brillouin-microscope/)
24. [Article **How a white sphere compares a lamp’s total output**](https://sandboxphysics.com/stories/instruments/integrating-sphere-radiometer/)
25. [Article **How powder rings reveal atomic spacing**](https://sandboxphysics.com/stories/instruments/powder-xray-diffractometer/)
26. [Article **How Small-Angle X-ray Scattering Reads a Particle Halo**](https://sandboxphysics.com/stories/instruments/small-angle-xray-scattering/)
27. [Article **Why X-ray fluorescence depends on sample thickness**](https://sandboxphysics.com/stories/instruments/xray-fluorescence-spectrometer/)
28. [Article **Why an AFM makes a bump look wider**](https://sandboxphysics.com/stories/instruments/atomic-force-microscope/)
29. [Article **How a small indentation separates hardness from elasticity**](https://sandboxphysics.com/stories/instruments/nanoindenter/)
30. [Article **How Differential Scanning Calorimetry Reads a Melting Peak**](https://sandboxphysics.com/stories/instruments/differential-scanning-calorimeter/)
31. [Article **How thermogravimetry separates mass loss from the gas around it**](https://sandboxphysics.com/stories/instruments/thermogravimetric-analyzer/)
32. [Article **How a diamond anvil cell reads pressure in ruby light**](https://sandboxphysics.com/stories/instruments/diamond-anvil-cell/)
33. [Article **How diamond fluorescence reveals a magnetic-field direction**](https://sandboxphysics.com/stories/instruments/nv-center-magnetometer/)
34. [Article **Reading a magnetic field in the rhythm of atoms**](https://sandboxphysics.com/stories/instruments/optically-pumped-magnetometer/)
35. [Article **Keeping a laser in time with atoms**](https://sandboxphysics.com/stories/instruments/optical-lattice-clock/)
36. [Article **Why a Kibble balance needs two experiments**](https://sandboxphysics.com/stories/instruments/kibble-balance/)
37. [Article **How a dilution refrigerator keeps carrying heat away**](https://sandboxphysics.com/stories/instruments/dilution-refrigerator/)
38. [Article **Why a bigger vacuum pump may barely help the sample**](https://sandboxphysics.com/stories/instruments/ultra-high-vacuum-system/)
39. [Article **How microwaves read a superconducting qubit**](https://sandboxphysics.com/stories/instruments/superconducting-qubit-readout/)
40. [Article **How current leaves a voltage across a thin sheet**](https://sandboxphysics.com/stories/instruments/four-probe-hall/)
41. [Article **How an ion flight becomes a mass spectrum**](https://sandboxphysics.com/stories/instruments/time-of-flight-mass-spectrometer/)
42. [Article **How four straight rods select ion mass**](https://sandboxphysics.com/stories/instruments/quadrupole-mass-filter/)
43. [You are here **How a rapidly reversing field can hold ions**](https://sandboxphysics.com/stories/instruments/paul-ion-trap-mass-spectrometer/)
44. [Article **How a cyclotron keeps a proton on the accelerating beat**](https://sandboxphysics.com/stories/instruments/cyclotron-synchrocyclotron/)
45. [Article **Why the drift tubes in an RF linac get longer**](https://sandboxphysics.com/stories/instruments/radio-frequency-linac/)
46. [Article **The directions hidden inside a small beam spot**](https://sandboxphysics.com/stories/instruments/beam-diagnostics/)
47. [Article **How defocusing magnets help a beam stay in a ring**](https://sandboxphysics.com/stories/instruments/synchrotron-storage-ring/)
48. [Article **Why a collider cannot keep every collision**](https://sandboxphysics.com/stories/instruments/collider-trigger-daq/)
49. [Article **Getting synchrotron light onto a sample**](https://sandboxphysics.com/stories/instruments/synchrotron-beamline/)
50. [Article **How a free-electron laser gathers electrons into a brighter beam**](https://sandboxphysics.com/stories/instruments/xray-free-electron-laser/)
51. [Article **Following energy exchange with neutron flight times**](https://sandboxphysics.com/stories/instruments/pulsed-neutron-time-of-flight/)

1 more group

### Other articles that use the same experiments

Each experiment from this article that another series also uses, followed by the articles there.

1. [Lab **Trapped-Ion Sideband Spectroscopy**](https://sandboxphysics.com/labs/trapped-ion-sideband-spectroscopy/)
2. [Article **How Ramsey and ion traps gave atoms more time**](https://sandboxphysics.com/stories/quantum-evidence/ramsey-ion-traps-measurement/)
3. [Article **How a changing electric field holds an ion**](https://sandboxphysics.com/stories/quantum-evidence/paul-trap-dynamic-stability-micromotion/)
4. [Article **Reading the sidebands in the first ion ground-state cooling experiment**](https://sandboxphysics.com/stories/quantum-evidence/sideband-asymmetry-ground-state-cooling/)
5. [Article **Let a second ion read out a narrow transition**](https://sandboxphysics.com/stories/quantum-evidence/quantum-logic-spectroscopy-shared-motion/)
6. [Article **How to measure one quantum system and keep it available**](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/)