---
title: "Quadrupole Mass Filter Interactive Lab | Sandbox Physics"
description: "How can four straight rods separate ions of different masses? Rapidly reversing rod voltages alternately gather and spread ions sideways."
canonical_url: "https://sandboxphysics.com/labs/quadrupole-mass-filter/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/quadrupole-mass-filter/"
last_modified: "2026-11-12"
---

IN42 · Select mass through alternating focus

# Quadrupole Mass Filter

**How can four straight rods separate ions of different masses?** Rapidly reversing rod voltages alternately gather and spread ions sideways. Different mass-to-charge ratios respond differently. Combining a constant voltage with the alternating drive selects a narrow range that reaches the collector before striking a rod.

Follow ions through an alternating electric field. Change the voltage ratio and rod length, watch rod impacts and collector hits, then infer two mass-to-charge ratios from the actual transmitted counts.

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

Model assumptions

Synthetic positive singly charged beam containing two unknown mass-to-charge populations. Ideal hyperbolic electrodes have a 3 mm field radius and a 2 MHz drive. Axial speed is constant at the declared injection energy. Finite rods and a housing of twice the field radius absorb ions; the collector radius is 0.8 times the field radius. Integrated terminal events determine transmission, with unit detector efficiency and zero dark counts. Unlimited-time Mathieu stability is a separate reference. Independent voltage and clock standards, two known ion species and a withheld third species calibrate the mass axis. The sample is assumed to contain exactly two species; unresolved peaks or failed checks withhold mass conversion. Voltages are rod-to-ground DC and zero-to-peak RF, unlike the pair-to-pair convention in Paul’s lecture. End fields, collisions, space charge, fragmentation and electronics transients are omitted. Truncated fields and constant axial speed form a long-rod near-axis teaching approximation. Transverse geometry is enlarged fourfold relative to axial length. Motion is slowed for replay.

Ideal hyperbolic electrode cutaway; ion markers enlarged. Transverse distances are enlarged fourfold. Two independent stored launches align at entry and share physical elapsed time, slowed 150,000 times.

Display scan

Import raw scan

### Collector hits from finite flight events

$V_{\rm RF}/\mathrm V$ · $N_{\rm hit}$

### Unlimited-time reference for a singly charged test ion $m=28\,\mathrm u$

Blue: both transverse directions bounded; dark: unstable; gray: marginal. The marker uses this scan’s recorded voltages. This reference does not decide detector hits.

$q$ · $a$

Raw gates, standards and uncertainty

Each voltage and clock channel has two fitted standards and one withheld check. Two known ion scans set the mass axis; a third checks it. Counts are sums of unit-efficiency collector hits from a synthetic two-species beam. Injection and loss paths are simulation diagnostics. Reference values and uncertainties are synthetic teaching inputs.

First eight scan gates; complete events and standards are exported

| RF code | DC code | Gate start tick | Gate stop tick | Hits |
| --- | --- | --- | --- | --- |

Field model and source convention

$$
\begin{gathered}a=\frac{8QU}{mr_0^2\Omega^2}\\q=\frac{4QV}{mr_0^2\Omega^2}\end{gathered}
$$

Voltages are rod-to-ground, with RF measured zero to peak. Paul’s 1989 lecture uses the voltage between opposite rod pairs and has coefficients half as large. Both conventions describe the same field after conversion.

The exact ideal transverse field is cut off at each end; axial speed stays constant. End fringes, collisions, space charge, fragmentation and electronics settling are omitted. The finite beam can hit physical hyperbolic surfaces or the separate exit aperture even when the unlimited-time reference is bounded.

Physics tutorial

## Reach the end before hitting a rod

**Background** A positive ion enters between four rods. The field focuses one transverse direction and defocuses the other. Their roles reverse when the voltage changes sign.

**Why it matters** The detector collects ions that reach the end. Scanning the voltages turns differences in transverse motion into a mass-to-charge spectrum.

Start with the essentials

- **Focus question**: How can four straight rods separate ions of different masses?
- **One-sentence intuition**: The same alternating field drives different mass-to-charge ratios differently; the aperture and transit time decide transmission.

### Core mathematical model

#### Quadrupole potential

$$
\Phi=\frac{U+V\cos(\Omega t+\phi)}{r_0^2}(x^2-y^2)
$$

The transverse forces have opposite directions. DC and zero-to-peak RF voltages are rod-to-ground; angular frequency is in radians per second and positions in metres.

#### Field strength and inertia

$$
\begin{gathered}a=\frac{8QU}{mr_0^2\Omega^2}\\q=\frac{4QV}{mr_0^2\Omega^2}\end{gathered}
$$

These dimensionless parameters combine the electric drive and ion mass-to-charge ratio. A fixed voltage ratio traces a straight line through this plane.

#### RF cycles during flight

$$
N_{\rm RF}=fL\sqrt{\frac{m}{2E_z}}
$$

Shorter rods or greater axial energy give fewer cycles. An unstable trajectory can leave a short device before it grows enough to hit a rod.

### Common difficulties

#### Stability and transmission

**Typical misconception** Every ion passes when the operating point is stable.

**Better mental model** Bounded motion can still intersect a rod if the initial displacement or angle is too large.

#### Naming a peak

**Typical misconception** A peak uniquely identifies a molecule.

**Better mental model** Known-ion standards provide mass-to-charge ratio. Charge state, fragmentation and other chemistry are needed for identification.

### Run the experiment

1. 01

   #### Turn the RF feed knob

   Hold the gold feed knob and drag horizontally, or focus the canvas and use arrow keys.

   **What to observe:** The actual drive and current trajectories change while the pointer remains held.

2. 02

   #### Shorten the filter

   Choose “Short rods” and compare the count spectrum.

   **What to observe:** Ions that would strike a longer rod can reach the end first. Previously separate peaks may merge.

3. 03

   #### Remove one voltage

   Compare “RF without DC” and “DC without RF”.

   **What to observe:** RF alone gives a broad high-pass response. DC alone continually defocuses one direction.

4. 04

   #### Save a scan

   Keep the scan, change a setting, then select and export the saved record.

   **What to observe:** Launches, drive readbacks, gates, counts and independent standards retain their original values.

Physical conclusion

Compare unlimited-time stability with actual impacts and detector counts, then calibrate the axis using known ions.

## 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 four straight rods select ion mass**](https://sandboxphysics.com/stories/instruments/quadrupole-mass-filter/)

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)