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.

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.

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 misconceptionEvery ion passes when the operating point is stable.

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

Naming a peak

Typical misconceptionA peak uniquely identifies a molecule.

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

Run the experiment

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.
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.
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.
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.

Quadrupole Mass Filter

Collector hits from finite flight events

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

Reach the end before hitting a rod

Core mathematical model

Quadrupole potential

Field strength and inertia

RF cycles during flight

Common difficulties

Stability and transmission

Naming a peak

Run the experiment

Turn the RF feed knob

Shorten the filter

Remove one voltage

Save a scan

Related experiments and articles

How physics instruments measure

Collector hits from finite flight events

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

Core mathematical model

Quadrupole potential

Field strength and inertia

RF cycles during flight

Common difficulties

Stability and transmission

Naming a peak

Run the experiment

Turn the RF feed knob

Shorten the filter

Remove one voltage

Save a scan

Related experiments and articles

How physics instruments measure

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