---
title: "Why the drift tubes in an RF linac get longer"
description: "Metal drift tubes shelter ions from reversing fields. Growing tube lengths and a chosen RF phase help faster particles gain energy and arrive together."
canonical_url: "https://sandboxphysics.com/stories/instruments/radio-frequency-linac/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/instruments/radio-frequency-linac/"
last_modified: "2026-11-12"
---

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

# Why the drift tubes in an RF linac get longer

As an ion gets faster, the next drift tube must usually get longer. The extra length keeps it sheltered while the electric field changes, so it reaches the next gap when the field can push it forward again. Keeping a whole group together requires a further choice: which part of that repeating push should they meet?

Sandbox Physics · 2026-11-12

## A metal tube provides a place to wait

A positive ion speeds up in a forward electric field. An RF field, however, repeatedly reverses direction. The push that helps now can pull backward a little later. If the ion remains exposed for equal portions of both directions, energy gained during one part can be taken back during the other.

A drift tube shelters the ion during an unhelpful part of the cycle. In the ideal shielding approximation, there is no accelerating axial field inside the metal tube. The ion coasts through at its existing speed, then emerges into an exposed gap where the field can do work. Tube length controls the waiting time; gaps supply the energy.

Phase describes where an arrival falls within the repeating field cycle. Shift the arrival by half a cycle and a forward push becomes a backward pull. Two ions can therefore encounter the same peak voltage and still leave with very different energies, simply because they arrived at different times.

Sources: [1] [2]

## Higher speed needs a longer sheltered journey

In an Alvarez drift-tube arrangement, neighbouring gaps share the same field phase, called zero mode. A chosen design particle is timed to travel between neighbouring gap centres in one full RF period. It has moved to another gap, but the field has returned to the same part of its cycle.

That reference particle becomes faster after each useful crossing. It covers more distance during the next period, so the later tubes grow longer. Their extra length does not provide extra accelerating work. It keeps the faster particle inside the shield until the next suitable moment to emerge.

A different drift-tube arrangement can put neighbouring gaps in opposite phases and use a half-period timing rule. Those rules cannot be interchanged. Multiplying an entrance speed by a period starts a spacing estimate. The finished design follows the changing speed through each finite gap.

Sources: [1] [2]

## Early and late particles need the right feedback

There is one design particle but a source supplies an ensemble. Some ions leave earlier; others start with more energy. Even a well-timed reference does not ensure that nearby particles stay close to it. Their small timing errors can shrink or grow as energy gain changes their subsequent speed.

Consider a forward field that is becoming stronger. An early particle receives a smaller push and then travels a little more slowly. A late one receives a larger push and travels a little faster. This feedback can tighten their arrival times. Longitudinal bunching means bringing particles closer together along their direction of travel.

On the falling side of the field, the mean gain can be similar while the feedback reverses: early particles become faster and late ones slower. Arrival times spread apart. Equal average exit energy therefore does not establish equal bunch quality. The range of initial errors and the remaining flight distance also limit how far the restoring argument applies.

Sources: [1]

## Even a narrow gap takes time to cross

The field keeps changing while an ion crosses a gap. It may weaken, or even reverse, before the crossing finishes. Actual work accumulates along the moving trajectory. Peak voltage alone cannot say how much energy every ion receives from each gap.

For a uniform gap with nearly constant crossing speed, a transit-time factor describes the difference between this accumulated action and an ideal instantaneous encounter. Slow ions, wide gaps and higher frequencies let the field rotate further during a crossing. When acceleration changes the speed appreciably, that change must be solved along with the flight.

Measurements can follow concrete events: two timing pickups within one shielded tube provide a flight time over a known distance. With a separately known ion species, that speed gives kinetic energy. Comparing the energies in neighbouring tubes tests the work done in the intervening gap. Distances, clocks and pickup responses each need calibration.

The terminal arrival distribution shows how tightly the detected ensemble reaches the exit. A narrow pulse does not by itself demonstrate cooling: a larger energy spread can accompany a smaller timing spread. Both coordinates belong in longitudinal phase space. Acceleration and bunching can be explained without claiming lower temperature or successful transmission of every incoming particle.

Sources: [3] [1]

## [Compare gap timing and the outgoing ensemble](https://sandboxphysics.com/labs/radio-frequency-linac/)

Shorten the drift tubes, then compare phases with similar mean energy gains and different arrival spreads.

Uses prescribed uniform axial fields and dilute ions of a known species. It does not solve cavity electrodynamics, transverse focusing or space charge; time bunching does not establish cooling.

## Sources and further reading

1. [Maurizio Vretenar, Linear accelerators, CERN Accelerator School (arXiv:1303.6766)](https://arxiv.org/abs/1303.6766)

   Reads PDF pages 3–5, 10 and 16–17 for longitudinal acceleration, zero-mode versus opposite-phase timing, synchronous phase and longitudinal phase space. Pages 5 and 17 were also inspected visually. Other pages are not claimed as read; facility parameters are not simulated observations.

2. [Frank Gerigk, RF basics I and II, CERN Accelerator School (arXiv:1111.4897)](https://arxiv.org/abs/1111.4897)

   Reads PDF pages 1–3, with visual inspection of pages 1 and 3. Uses the field-phase and structural distinction between Widerøe and Alvarez drift-tube arrangements; the half-period rule is not applied to same-phase gaps.

3. [Erk Jensen, Cavity basics, CERN Accelerator School (arXiv:1201.3202)](https://arxiv.org/abs/1201.3202)

   Reads and visually inspects PDF pages 12–13, corresponding to CERN printed pages 270–271, equations 24–27. Uses the moving-path voltage integral and transit-time definition; a signed uniform-gap approximation is distinguished from the complex-voltage magnitude.

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## 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. [Article **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. [You are here **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/)