---
title: "Radio-Frequency Linear Accelerator Interactive Lab | Sandbox Physics"
description: "Why do longer drift tubes help faster particles keep the beat? A drift tube shields the particle while the field turns back toward acceleration."
canonical_url: "https://sandboxphysics.com/labs/radio-frequency-linac/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/radio-frequency-linac/"
last_modified: "2026-11-12"
---

# Radio-Frequency Linear Accelerator

**Why do longer drift tubes help faster particles keep the beat?** A drift tube shields the particle while the field turns back toward acceleration. Faster particles travel farther during each cycle, so later tubes must be longer. Timing can tighten when early particles gain less energy and late particles gain more; the opposite field slope makes the arrival spread grow.

Drag the tube-length adjuster and follow ions through an alternating field. Compare bunches with similar energy gain but different arrival spread, retaining gap events and energy observations.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

Three to five shielded drift tubes use Alvarez zero mode: all prescribed uniform axial gap fields share one 5-MHz phase. The known design reference is a singly charged 40-u ion at 2000 eV; tube lengths are designed once from its trajectory. Finite-gap work and time are continuous, not instantaneous kicks. Thirty-two independent dilute exposures are separated by 100 RF cycles. Replay folds out known whole programme cycles, overlays ideal forward paths on the common programme clock and slows them two million times. Axial coordinates retain metres; radial cutaways and ion markers are enlarged. Cavity electrodynamics, transverse focusing, space charge, wall losses and real detector bandwidth are omitted. Timing pickups and probe response are ideal teaching assumptions. Independent voltage, position and clock standards, a species certificate and heldout checks support raw-only reconstruction with first-order shared-reference and observation-cell covariance. Flight-energy readout is restricted to 100–10000 eV for the known species. Unresolved phase retains supported flight energy. Useful counts describe only a fixed design energy/phase window, including ambiguous membership. Observed arrival spread has no instrumental deconvolution and does not establish cooling or total transmission efficiency. Each capture has an independent virtual clock origin and UTC validity anchor; controls/reset preserve saved history.

Observed run

Timing pickups give the energy points. The phase plot is centred on the design phase; dashed guides mark its useful window. Gap work comes from adjacent flight energies.

Grey bars show source arrivals; cyan bars show detected exits. Each uses its own observed mean, without per-ion launch alignment. Bins span at least one calibrated clock tick.

Individual events and finite-gap checks

Scroll sideways, or focus the table and use the arrow keys, to read every column.

| Exposure | Tube | Energy / eV | Standard uncertainty / eV | Gap work / eV | Field check |
| --- | --- | --- | --- | --- | --- |

Raw counter/ADC observations and independent standards

Each run is a new virtual acquisition with its own clock origin and UTC validity anchor. Parent links preserve comparison history, not continuous occupancy of one instrument. JSON includes separately labelled ideal forward diagnostics; CSV retains only raw observations. Imported unknown data are never regenerated from settings.

Import JSON / CSV

Scroll sideways, or focus the table and use the arrow keys, to read every column.

| Channel | Role | Reference value | Standard uncertainty | Raw code | Actual clock interval |
| --- | --- | --- | --- | --- | --- |

Scroll sideways, or focus the table and use the arrow keys, to read every column.

| Exposure | Gate start / tick | Gate end / tick | Channel | Event / tick |
| --- | --- | --- | --- | --- |

## Cross each gap at a useful time

**Background** An RF electric field keeps reversing. Metal drift tubes shield the ions; the exposed gaps between tubes let the field do work.

**Why it matters** Energy gain changes the arrival time at the next gap. A successful mean acceleration does not guarantee that the whole source ensemble stays together.

- **Focus question**: Why must tube lengths grow with speed, and why must the field phase also be chosen?
- **One-sentence intuition**: Zero-mode gaps share one phase. The reference crosses successive gap centres one full RF period apart. On a rising accelerating field, earlier particles gain less and later particles gain more, allowing arrival times to tighten.

### Core mathematical model

#### Work through a finite gap

$$
\Delta K=q\int_{z_a}^{z_b}E_z\!\left(z,t(z)\right)\,dz
$$

Positive ions travel forward along the axis. The field changes continuously during their crossing, so peak gap voltage need not equal the actual energy increment per charge.

#### Zero-mode synchronism

$$
\Delta t_{\mathrm{centres}}=1/f,\qquad d\simeq v/f
$$

Reference flight time between neighbouring gap centres is one full period. The length estimate assumes a narrow gap and little speed change. Actual tube lengths come from the finite-gap reference trajectory, not the half-period rule for opposite-phase gaps.

#### Flight-energy observation

$$
v=\frac{\Delta z}{\Delta t},\qquad K=\tfrac12 mv^2
$$

The two timing planes lie within one shielded tube. Distance and time have independent standards and heldout checks; an independent species certificate supplies mass and charge. Energy conversion stays inside the declared nonrelativistic domain.

#### Weak-field transit-time factor

$$
T=\frac{\sin(\pi f g/v)}{\pi f g/v}
$$

This signed factor multiplies the peak voltage and centre-phase cosine only for a uniform gap with nearly constant crossing velocity. Actual trajectories use the continuous gap solution. A negative factor also changes the phase interpretation.

### Common difficulties

#### Does a longer tube provide more accelerating work?

**Typical misconception** The ion accelerates throughout the metal tube.

**Better mental model** An ideal tube shields its interior field. The ion drifts there while the field reverses; exposed gaps do the work. Tube length controls arrival time.

#### Does a shorter pulse prove cooling?

**Typical misconception** Narrow arrival times guarantee a narrower energy distribution.

**Better mental model** Longitudinal bunching exchanges timing and energy spread. Both coordinates matter; this apparatus does not infer temperature or cooling rate.

### Run the experiment

1. 01

   #### Shorten the tubes

   Hold the gold adjuster and drag left, or focus the canvas and press the left arrow.

   **What to observe:** The ions reach subsequent gaps earlier and can encounter a decelerating field. The live geometry and observations change before release.

2. 02

   #### Compare similar energy gains

   Compare “Catch the rising field” with “Same gain, growing timing spread”.

   **What to observe:** Their mean energies can be similar while their arrival spreads differ. The field slope changes how timing errors feed back through energy gain.

3. 03

   #### Widen the gap

   Choose “A gap takes time to cross” and open the event and finite-gap checks.

   **What to observe:** The field rotates further during each crossing. Work cannot be obtained by simply adding peak voltages. Measured after-minus-before flight energies still test the continuous model.

4. 04

   #### Keep a run before changing it

   Acquire a run, change phase and select the earlier run; export and reimport its raw CSV.

   **What to observe:** Earlier counter events, encoder codes and standards remain unchanged. The apparatus retains the current setup, while the selected data are reconstructed from their own original channels.

Physical conclusion

Compare local energy, RF phase and exit arrival spread together. Bunching can increase energy spread; a narrower pulse alone does not establish cooling.

## Related experiments and articles

How physics instruments measure · Reading path

### How physics instruments measure

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Why the drift tubes in an RF linac get longer**](https://sandboxphysics.com/stories/instruments/radio-frequency-linac/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)