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.

Separate ions by arrival time

Extraction voltage

V/\mathrm{V}

2000

Drift length

L/\mathrm m

0.8

Full source width

w/\mathrm{\mu m}

40

Mirror field (engages mirror)

E_r/E_{r,0}

1

Mean ions per pulse

\lambda

0.3

Drag the gold voltage, source-width or mirror knob. The live flight changes before release; use Acquire to keep new observations.

Source and model assumptions

Axial velocity standard deviation

\sigma_v/(\mathrm{m/s})

200

The source occupies a uniform finite axial width. Signed launch velocities follow a Gaussian truncated at three standard deviations. A finite uniform extraction gap, free drift and a single uniform-field mirror determine every arrival. The mirror reverses axial velocity; finite apertures, barrier height and detector acceptance remove ions.

The detector has a prescribed ten-nanosecond nonparalyzable deadtime and independent single-ion response. Separate destructive charge exposures and MCP references measure downstream efficiency from the extraction exit at their reference loading. Unknown incident counts and species are absent from inference. Fringing fields, collisions, space charge and fragmentation are omitted.

Geometry is open for inspection. Transverse dimensions are enlarged tenfold relative to longitudinal scale; representative ions are enlarged and flight playback is slowed. Stored events use physical seconds and integer clock ticks.

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.

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 misconceptionTube length divided by final speed gives the entire flight time.

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

Detected counts and source abundance

Typical misconceptionPeak area directly counts all ions emitted by the source.

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

Run the experiment

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.
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.
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.
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.

Time-of-Flight Mass Spectrometer

Detected mass-to-charge spectrum

Saved unknown arrival times

Time the whole ion flight

Core mathematical model

The extraction gap takes time too

Reference ions establish the time scale

Resolving power comes from the observed width

Common difficulties

Acceleration has a finite duration

Detected counts and source abundance

Run the experiment

Start with two peaks

Give energetic ions a longer route

Interpret a single peak

Keep a record and reset

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