---
title: "Time-of-Flight Mass Spectrometer Interactive Lab | Sandbox Physics"
description: "How do arrival times separate an ion beam by mass-to-charge ratio? Ions with the same charge gain the same energy across a voltage drop."
canonical_url: "https://sandboxphysics.com/labs/time-of-flight-mass-spectrometer/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/time-of-flight-mass-spectrometer/"
last_modified: "2026-11-12"
---

IN41 · Timing an ion flight

# Time-of-Flight Mass Spectrometer

**How do arrival times separate an ion beam by mass-to-charge ratio?** Ions with the same charge gain the same energy across a voltage drop. Lighter ions travel faster. Known reference ions calibrate the start delay and time scale before arrival times become mass-to-charge values. Charge state needs separate information.

Follow finite ion flights through straight and reflected paths. Use independent references to reconstruct mass-to-charge peaks and widths.

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

Model assumptions

Positive ions cross a finite uniform extraction gap, a field-free drift and a finite single-stage electrostatic mirror. Source positions and signed launch velocities have distributions. Apertures, electrodes, the mirror barrier and detector acceptance can remove ions. Mass references, blanks, efficiency checks and unknown events are separate acquisitions. Only detected arrivals enter the raw record; independent calibration sets the time and mass-to-charge axes. Resolving power uses observed peak widths. One peak can contain different species with the same mass-to-charge ratio. Fringing fields, space charge, collisions and fragmentation are omitted. Strong beams, failed references and clipped gates preserve raw data and withhold inference. Transverse dimensions and ions are enlarged; playback is slowed.

### Detected mass-to-charge spectrum

Detected events **$0$**

Supported peaks **$0$**

First peak **$0$**

First-peak resolving power **$0$**

$\mu=(m/u)/z\quad(\mathrm{Da}/e)$

Detected counts are preserved. A single broad band can contain unresolved components; one mass-to-charge peak does not determine charge state.

Raw clocks, calibration and limits

### Saved unknown arrival times

$(t_{\mathrm{arrival}}-t_{\mathrm{trigger}})/\mathrm{\mu s}$

$F_s=1.00\,\mathrm{GHz},\quad \eta_{\mathrm{ref}}=0.65$

$\Delta\mu_{\mathrm{FWHM}}$

Values after ± are standard uncertainties. Shared reference errors propagate together; the common clock scale cancels from mass-to-charge. Width uncertainty uses 256 resampled pulse blocks plus bin resolution. An unresolved mean clock-cell correction is retained instead of averaging it away. Approximate compatibility intervals are conditional on the retained band and stationary independent pulses, with no certified coverage claim.

Known mass standards fit time delay and scale; independent held-out standards test them. Blanks estimate background, and separate measured charge/count references check efficiency. A frozen calibration precedes all held-out and unknown events.

Replay a complete JSON or CSV archive

Each acquisition is a separate virtual experiment with its own counter origin and UTC anchor; comparison histories can overlap in simulated physical time. Whole records include every pulse gate and voltage readback, all reference and unknown event ticks, uncertainties and lineage. Unsupported conditions retain raw events and withhold mass and width results.

Physics tutorial

## Time the whole ion flight

**Background** Electric fields accelerate ions into a field-free tube. Equal charges gain similar energies, so light ions arrive before heavy ones.

**Why it matters** Source positions, launch velocities and electronic delays broaden or shift the arrivals. Reference peaks establish the mass-to-charge scale.

Start with the essentials

- **Focus question**: How can arrival times reveal an ion beam’s mass-to-charge ratios?
- **One-sentence intuition**: Keep detected arrival times and calibrate them independently. Peak position gives mass-to-charge ratio; observed width measures resolving power.

### Core mathematical model

#### The extraction gap takes time too

$$
m\dot{\mathbf v}=q\mathbf E,\quad t_{\mathrm{flight}}=t_{\mathrm{gap}}+t_{\mathrm{drift}}+t_{\mathrm{mirror}}
$$

Every physical segment contributes to the recorded time. Mirror operation includes deceleration, reversal and the return flight.

#### Reference ions establish the time scale

$$
t=\beta+\alpha\sqrt{\frac{\mu}{V}},\qquad \mu=\frac{m/u}{z}
$$

Known reference ratios fit the delay and scale. Separate held-out references test that relation before unknown events use the frozen calibration and measured voltage.

#### Resolving power comes from the observed width

$$
R=\frac{\mu_{\mathrm{peak}}}{\Delta\mu_{\mathrm{FWHM}}}
$$

Full width at half maximum is estimated from detected events. An unresolved broad band remains an unresolved result.

### Common difficulties

#### Acceleration has a finite duration

**Typical misconception** Tube length divided by final speed gives the entire flight time.

**Better mental model** Ions also cross an extraction gap. Starting position and velocity change both that time and the exit energy.

#### Detected counts and source abundance

**Typical misconception** Peak area directly counts all ions emitted by the source.

**Better mental model** Apertures, detection efficiency, gates and deadtime remove events. Separate charge references check efficiency; unknown incident counts are absent from the raw record.

### Run the experiment

1. 01

   #### Start with two peaks

   Select Two neighbouring peaks, then drag the gold voltage knob.

   **What to observe:** Ion speeds change before release. A new acquisition supplies new reference and arrival records.

2. 02

   #### Give energetic ions a longer route

   Compare A wide starting region, Refocus with an ion mirror and An untuned mirror.

   **What to observe:** Faster ions penetrate deeper and spend longer in the mirror. A suitable field narrows arrival differences; mistuning broadens them.

3. 03

   #### Interpret a single peak

   Select Different ions, same ratio and open the raw times and calibration.

   **What to observe:** Different masses and charge states can share one mass-to-charge ratio and one arrival peak.

4. 04

   #### Keep a record and reset

   Acquire, export JSON or CSV, then reset the controls.

   **What to observe:** Reset appends a default acquisition. Existing events, standards and exports stay unchanged. An excessive beam retains raw events and withholds inference.

Physical conclusion

Every segment affects the flight clock. Independent references and saved events turn that clock into a mass-to-charge measurement.

## 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 **How an ion flight becomes a mass spectrum**](https://sandboxphysics.com/stories/instruments/time-of-flight-mass-spectrometer/)

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)