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Inspect the ¹³³Xe ground and isomeric states in the chart, including excitation energy and uncertainty. An isomer is a relatively long-lived excited nuclear state. In MR-TOF, ions repeatedly travel between electrostatic mirrors: change the lap count, peak width and relative populations. In TOF-ICR, a radiofrequency excitation is scanned across the cyclotron resonance; compare the mixed signal with a one-species fit and the residuals (observed minus fitted values). In PI-ICR, ion-motion phases are imaged on a detector; change the accumulation time to see angles wrap through a full turn. Peak separation, statistical precision and model bias describe different limitations.

Play while the beam is off. Best scores are kept in your browser only.

⏳ Which lives longer?

Two nuclei from NUBASE2020 — pick the one with the longer half-life. Keep the streak going!

🎯 Find the cyclotron resonance (TOF-ICR)

Set the excitation frequency ν_rf, shoot ions and find the minimum of the time of flight. ¹³³Cs⁺ in a 7 T trap: ν_c = qB/(2πm) ≈ 808 795.01 Hz. Fewer shots and a closer guess give more points.

💡 What do these controls mean?

Choose an ion, positive charge z, B and excitation time. Rectangular means one RF pulse; Ramsey means two separated pulses. More ions per shot reduces simulated counting noise.

Move νrf away from resonance and take shots to build the curve. Theory overlays the model. Points/pixels changes detector drawing only. Longer excitation narrows the ideal resonance.

💡 Physics hints
  • At ν_rf = ν_c the quadrupole drive converts the slow magnetron motion completely into fast reduced-cyclotron motion. On the way to the detector the radial energy E_r ∝ ω₊²r² is turned into axial energy in the magnetic-field gradient, so resonant ions fly faster: the resonance is a MINIMUM of the time of flight.
  • Line width: FWHM ≈ 0.8/T_rf for a rectangular pulse. Longer excitation → narrower dip → more precise ν_c (statistical precision ∝ 1/(T_rf·√N)).
  • Rectangular excitation has side minima (a sinc²-like pattern). Ramsey excitation (two short pulses with a waiting time) gives a ~40 % narrower central fringe and stronger side fringes — do not mistake a side fringe for the centre.
  • From frequency to mass: m = qB/(2πν_c) (B is calibrated with a reference ion). An error of 0.1 Hz at 808 kHz is δm/m ≈ 1.2×10⁻⁷ ≈ 15 keV for A = 133.

TOF-ICR: overlapping resonances and fit bias

Compare individual resonances with a mixed sample. A single-species fit can give a precise-looking centre that differs from the target ion’s resonance.

💡 What do these controls mean?

Start with ion mass, positive charge, B and trap voltage/size. ν₊, ν₋ and νz are modified-cyclotron, magnetron and axial frequencies; νc = ν₊ + ν₋ in this ideal model.

Use the existing presets first, then change one parameter at a time and compare the readouts. Radii/phases set initial motion, excitation settings set the applied pulse, and Speed sets playback. Fancier can use separate trap-1/trap-2 calibration; enable it explicitly in the calibration panel.

Interpretation

Loading evaluated nuclear data…
Advanced parameters and assumptions

Masses: AME2020 ground state + NUBASE2020 excitation energy. # marks extrapolated properties. Unknown uncertainty is not zero; unavailable covariance uses an explicit diagonal approximation. Ionization and molecular binding energies are omitted.

Teaching response: t(F) = t_offset + t_scale / √(1 + κF). F is the dimensionless mode-conversion fraction, 0–1. Defaults: t_offset = 62 µs, t_scale = 193 µs, κ = 1.876; 8% unconverted background, event widths σ = 7 and 9 µs. Mixture means are population-weighted; displayed component event densities include population weights. Noise is illustrative. Local Δχ² = 1 fit intervals exclude mixture bias.

NUBASE2020 · AME2020 · Kretzschmar: Ramsey excitation

🌀 Resolve the isomer (PI-ICR)

Phase-imaging: after the accumulation time t_acc the cyclotron phase of each ion is projected onto a position-sensitive detector. Ground state and isomer differ in mass by Eₓ/c², so their spots move apart by Δφ = 2π Δν_c t_acc. Find a t_acc that separates them.

💡 What do these controls mean?

Search an ion or enable multiple ions. Other states includes catalogue records beyond the default ground/isomer list. Mass table chooses the evaluated source; B sets the field. Accumulation time sets phase growth; longer time can also wrap the separation around 360°.

Radius is the detector-ring radius; spot width uses the displayed 0.1 mm unit. Ratio and contamination set populations. σ is the spot-width separation target, not mass uncertainty. Phase offsets move reference/ion origins; the clock rounds requested time to achievable time. Detector practice adds an angular floor and centroid counts; the seed repeats noise. Open the phase/timing guide for details. U₀ and d set the ideal trap frequencies.

Reference phase and timing

These are counterclockwise offsets of the projected detector patterns, in the magnetron-reference frame. The first entered ion, or the ground state in single-pair mode, sets the reference frequencies. With overlap enabled, the requested time advances to the next solution of νc t + (δ₊ − δ₋)/360° = integer. The default clock rounds this ideal time to 4 ns, following the PyMassScanner timing convention; the remaining mismatch is shown rather than hidden. Ideal timing gives exact overlap. Plots, turn counts, uncertainty, comparisons and exports use the actual time. The common origin rotates all spots without changing separations.

α₋ = α₀ + δ₋; α₊ = α₀ + δ₊ + 360°νc t; νc = ν₊ + ν₋.

PI-ICR phase and overlap method

Detector and practice

The first species is the reference. Total turns = νc t; Δ turns = (νc − νc,ref)t. Residual angles are wrapped to [−180°, 180°). The first opposite-position time is 1/(2|Δνc|); equal frequencies never separate. This time is pair-specific, and applying it rounds to the 0.01 ms control grid. All turn counts here use known simulation frequencies.

Accumulation-time comparison

Known simulation frequencies determine the full turn count. Additional times reveal phase wrapping; this view does not determine an unknown experimental turn count.

Counterclockwise angles. The common origin rotates all spots without changing relative separations. The detector drawing radius is 21.00 mm; it expands to 32.00 mm when the spot radius exceeds 20.00 mm. This drawing does not model detector acceptance losses.

σ means one event’s angular standard deviation. The search checks every ion pair on a 0.01 ms grid up to 5000 ms, including phase wrapping; it is not a fitted confidence level.

Outer-spot σ controls event blur and phase resolution. Centre-spot σ controls only the central detector cloud; increasing it does not broaden the orbiting species.

σ is the angular standard deviation of individual events. 2.355σ approximates one Gaussian peak’s full width at half maximum (FWHM); it is not a confidence level or the combined uncertainty of two centroids. Presets and the custom box set the same target used by the shortest-time search and comparison line.

💡 Physics hints

Relative to the common origin, νc = (φ + 2πn)/(2πt), with phase φ in radians and complete turns n. The simulator knows n; experiments must determine it separately. For rest-energy increase E at fixed charge: |Δνc|/νc = E/(mion c² + E). At small angles σφ ≈ σx,y/r; r is editable, initially 10.00 mm. R = 2πνc t/(2.355 σφ) is a FWHM resolution guide, not mass uncertainty. Longer times can make wrapped spots overlap again.

The ideal trap has fast radial motion ν₊, slow magnetron motion ν₋ and axial oscillation νz. Here Φ = U₀(z² − r²/2)/(2d²), νc = qB/(2πmion), νz = √(qU₀/(mion d²))/(2π), ν± = [νc ± √(νc² − 2νz²)]/2. Confinement requires νc² > 2νz². Ideal identities: ν₊ + ν₋ = νc and ν₊² + ν₋² + νz² = νc². First order: ν₋ ≈ U₀/(4πBd²).

What angle corresponds to 1 keV?

This is +1 keV of rest energy (mass), not kinetic energy: δm = 1 keV/c² = 0.00000107354410 u. With the same charge and B, δνc = −νc δm/(mion + δm) and δφ = 360° δνc t. Negative means lagging the reference in this counterclockwise convention. The result depends on the first ion and the current accumulation time; it is a hypothetical increment, not a measured isomer energy.

🪞 Separate the isobars (MR-TOF)

Ions bounce between two electrostatic mirrors; every lap adds flight time, so the time difference between two isobars grows while the peaks only broaden slowly. Start with the initial bunch width from the cooler-buncher, then add laps until the peaks separate.

💡 What do these controls mean?

Select an ion pair or enable manual input. Ratio sets their relative abundance; Counts sets simulated events. Laps sets the number of mirror round trips.

Δt₀ is the starting time width, Δt/lap the added broadening per lap, t/lap the round-trip time, and t₀ the initial flight time. Use the units shown. More laps may separate peaks but also broaden them. Sum adds the peaks; log R changes the resolving-power scale.

💡 Physics hints

t(N) = t₀ + N·T_lap ∝ √m, Δt = t·Δm/(2m), FWHM² = Δt₀² + (N·δ)², R = t/(2·FWHM). Separation when Δt ≥ FWHM, i.e. R ≥ m/Δm. A short initial bunch matters most at few laps; per-lap broadening limits R at many laps.

MR-TOF: separate species and isomers

Choose up to three ion species. Compare individual peaks with their combined spectrum, then see how separation changes with lap count.

💡 What do these controls mean?

Start with ion mass, positive charge, B and trap voltage/size. ν₊, ν₋ and νz are modified-cyclotron, magnetron and axial frequencies; νc = ν₊ + ν₋ in this ideal model.

Use the existing presets first, then change one parameter at a time and compare the readouts. Radii/phases set initial motion, excitation settings set the applied pulse, and Speed sets playback. Fancier can use separate trap-1/trap-2 calibration; enable it explicitly in the calibration panel.

Interpretation

Loading evaluated nuclear data…
Advanced parameters and assumptions

Masses: AME2020 ground state + NUBASE2020 excitation energy. # marks extrapolated properties. Unknown uncertainty is not zero; unavailable covariance uses an explicit diagonal approximation. Ionization and molecular binding energies are omitted.

Flight time scales exactly as √(mion/q); fixed electronic delay is added afterwards. Width is phenomenological: FWHM² = initial width² + (laps × broadening)². Populations are detected fractions; displayed survival does not simulate decay products.

NUBASE2020 · AME2020

🧲 Keep the ions (linear Paul trap / RFQ mass filter)

Ions move in the rapidly switching quadrupole field of four rods. Only ions whose working point (q, a) lies inside the stability region stay inside r₀; the others oscillate with growing amplitude and hit a rod (spark). Set U and V so that only the target mass passes.

💡 What do these controls mean?

Choose ions and a target; Custom accepts a comma-separated list such as 100Sn, 99In, 133Cs+2. A is mass number, V the RF voltage, U the DC voltage, r₀ the electrode radius, and Ω/2π the RF frequency.

Emittance sets the initial spread relative to r₀. Cycles sets residence in RF periods, Speed only playback. A seed repeats the same simulated initial ensemble. Stability cutoffs describe an ideal Mathieu model; transmission is a trajectory result for that ensemble.

V is the zero-to-peak RF voltage; U is the DC voltage. This collisionless transverse model illustrates finite-time transmission. Axial transport, buffer gas, space charge and fringe fields are omitted. Mathieu equation

Trap design, inverse calculations and derivations

RFQ rod potentials are ±(U−V cos Ωt). V is the zero-to-peak amplitude of one rod pair relative to ground; the differential amplitude is 2V. The cooling panel uses differential V_RF, so equal numerical voltages are not interchangeable.

Φ=(U−V cos Ωt)(x²−y²)/r₀² → Eₓ=−2(U−V cos Ωt)x/r₀², Eᵧ=+2(U−V cos Ωt)y/r₀².
τ=Ωt/2 → x″+(a−2q cos 2τ)x=0, y″+(−a+2q cos 2τ)y=0.
a=8QU/(mr₀²Ω²), q=4QV/(mr₀²Ω²), a/q=2U/V.
νx,y=βx,y f_RF/2; ν≈f_RF√(a+q²/2)/2 in the adiabatic approximation only.

Inverse design uses the selected target ion, radius and RF frequency. Preview before applying; any edit invalidates the previous preview. Nominal depth QqV/4 is for U=0 at r=r₀ in the ideal adiabatic model, rather than a measured rod-surface barrier. Mass cutoffs describe the infinite-time first stability region; finite-residence transmission may differ. NIST DLMF

Operating line and mass cutoffs

Ideal Mathieu cutoffs are not measured transmission efficiencies. V is zero-to-peak RF amplitude; the RF peak-to-peak voltage is 2V. Cutoffs scale with charge; values here are m/z in u/e.

💡 Physics hints

RF cycles is a residence-time setting, not a rod length: N cycles at frequency f MHz give t = N/f microseconds. At the defaults, 60 cycles at 1.00 MHz mean 60.00 µs. A physical filter length would also require the axial speed, L = v_z t; axial motion is not simulated here. r₀ is the distance from the axis to the electrode surface, initially 10.00 mm. V is the zero-to-peak RF voltage; U is the DC voltage and Ω = 2πf. Charge z is the number of elementary positive charges; m/z is mass per charge. Dimensionless a and q locate an ion in the Mathieu stability diagram, and the operating line is a/q = 2U/V. LMCO and HMCO are the ideal lower and upper mass-per-charge boundaries, not transmission efficiencies. The initial spread sets the launch-position disk radius as a percentage of r₀; launch velocities also use this teaching spread and are not a measured beam emittance. Animation speed changes playback, not a, q or the cutoffs. Seed repeats the same random launch sequence. Green stability means bounded motion for the ideal infinite-time equation; surviving a finite time alone does not prove stability.

🧪 Periodic table & origin of the elements

Colour the table by chemical block, by astrophysical origin (several sources per element), by state or as a property heat map; then play the origin highlight game.

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🧩 Magic numbers & elements

Quick questions about the nuclear landscape.

🦓 Trap zoo

How different devices hold or guide ions — animated sketches, not to scale.

Animated sketches, not to scale. Red/blue = electrode polarity (switching with the RF where relevant); the coloured trail is one ion or atom.

Hyperbolic Penning trapStrong axial magnetic field + weak electric quadrupole. Three eigenmotions: fast cyclotron ν₊, slow magnetron ν₋, axial ν_z; ν₊ + ν₋ = ν_c = qB/(2πm) gives the mass.
Cylindrical Penning trapSame principle with stacked open cylinders: easy injection and ejection; correction electrodes make the potential harmonic. Used for purification and precision traps (e.g. JYFLTRAP).
Paul (RF) trapOnly an oscillating (RF) electric quadrupole: the force switches faster than the ion can escape and averages to a confining pseudopotential (Mathieu stability).
Linear Paul trap / RFQFour rods with RF give radial confinement (cross-section shown); DC end electrodes trap axially. With buffer gas it cools and bunches beams — the cooler-buncher before every trap.
MR-TOF mass spectrometerTwo electrostatic mirrors fold a flight path of kilometres into a metre: TOF ∝ √(m/q), resolving power above 10⁵ within milliseconds; also a fast isobar separator.
Storage ringDipole magnets bend and quadrupoles focus the circulating ions; the revolution frequency gives m/q (isochronous or Schottky mass spectrometry), even for a single ion.
Electron-beam ion trap (EBIT)A dense electron beam ionises ions step by step and holds them radially by its space charge; drift-tube potentials trap them axially — source of highly charged ions.
OrbitrapIons orbit a spindle electrode inside a barrel and oscillate along it with ω_z = √(k·q/m); the Fourier transform of the image current gives the mass spectrum.
Magneto-optical trap (MOT)Six red-detuned laser beams slow neutral atoms by Doppler cooling; an anti-Helmholtz quadrupole field makes the scattering force push them to the centre — clouds at µK temperatures.
Optical tweezer / dipole trapA tightly focused far-detuned laser beam induces a dipole that is pulled into the intensity maximum (optical dipole force): single atoms held at the focus, arrays for quantum simulation.