Games
Try a measurement walkthrough
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
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.
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
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.
🌀 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₋.
Detector and practice
Comma-separated: 84Rb · Rb-84 · 133Cs+2 or 133Cs2+ (charge) · 45mSc, 45Scm or 45Sc* (isomer, Eₓ from NUBASE2020; m2 = second isomer) · 12C16O2 or 12C11 (molecules, clusters) · 87Rb:0.3 (relative intensity). Ion mass = atomic mass − q·mₑ (electron binding energies neglected).
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.
🌀 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₋.
Detector and practice
Comma-separated: 84Rb · Rb-84 · 133Cs+2 or 133Cs2+ (charge) · 45mSc, 45Scm or 45Sc* (isomer, Eₓ from NUBASE2020; m2 = second isomer) · 12C16O2 or 12C11 (molecules, clusters) · 87Rb:0.3 (relative intensity). Ion mass = atomic mass − q·mₑ (electron binding energies neglected).
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
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.
🧲 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.
❄️ Laser cooling — Optical molasses — cool the cloud
Red-detuned laser light slows atoms and ions: a moving particle sees the beam it flies into Doppler-shifted towards resonance and scatters more photons from it. Each absorption gives a kick ħk against the motion; random spontaneous emission heats. The balance is the Doppler temperature.
Two counter-propagating beams along x. Tune the detuning and intensity, start the laser and try to reach the Doppler limit ħΓ/2k_B as fast as possible.
Goal: T < 1.2 × Doppler limit
📐 Principles (physics in detail)
Scattering rate. A two-level atom with linewidth Γ in a beam of saturation s₀ = I/I_sat scatters R = (Γ/2)·s₀/(1 + s₀ + (2Δ/Γ)²) photons per second; Δ = δ − k·v is the detuning seen by an atom moving with velocity v (Doppler shift k·v, k = 2π/λ).
Radiation pressure. Each absorbed photon gives a momentum kick ħk along the beam; spontaneous emission goes in a random direction, so on average only absorption pushes. Force from one beam: F = ħk·R.
Molasses force. With two counter-propagating red-detuned beams (δ < 0) an atom moving to the right is closer to resonance with the beam coming from the right and scatters more from it: F(v) = ħk[R(δ − kv) − R(δ + kv)] ≈ −β·v for |kv| ≪ Γ, with β = −8ħk²δs₀/(Γ(1 + s₀ + (2δ/Γ)²)²). The red curve in the plot is this F(v); it acts only within the capture velocity ≈ (Γ/2k)√(1+s₀).
Heating. Every scattered photon adds two random recoil kicks (absorption from either beam and emission), giving momentum diffusion D₀ = ħ²k²R_tot(1+η)/2, where η is the fraction of emission projected on the axis (1 for the textbook 1D model, 1/3 for isotropic 3D emission).
Doppler temperature. Damping and heating balance at k_BT = D₀/β = ħΓ(1+η)(1 + s₀ + (2δ/Γ)²)/(16|δ|/Γ). The minimum, at δ = −(Γ/2)√(1+s₀) and s₀ → 0, is the Doppler limit T_D = ħΓ/2k_B (η = 1). Recoil sets a lower floor T_r = ħ²k²/(m k_B); narrow lines (Γ comparable to the recoil frequency) break the semiclassical model.
Simulation. Each time step draws Poisson-distributed photon numbers from each beam for every atom and adds ±ħk/m per absorption and a random emission kick, so the temperature curve shows real shot noise around the analytic value. Blue detuning (δ > 0) turns the force into anti-damping and heats the cloud.
💡 Hints
Best Doppler temperature: δ = −Γ/2 at low intensity. Higher s₀ cools faster but power-broadens: T ∝ (1 + s₀ + (2δ/Γ)²)/(2|δ|/Γ).
If atoms are faster than the capture velocity ≈ Γ/2k they barely interact: start colder or use a larger detuning first.
Two-level model: no hyperfine structure, dark states or micromotion. Ions such as Ca⁺ need a repumper; values are teaching estimates, not an experiment.
📚 Sources
💡 Parameter guide, physical basics and experiments
The 3D motion and cooling curves use the same clock. Spatial trajectories are projected onto the screen; rotating the camera does not change the ions. Dynamics use ideal fields, classical ions and independent two-level beams.
Each beam scatters at R = (Γ/2)s/[1+s+(2(δ−kv)/Γ)²]. Absorption gives ±ℏk momentum; spontaneous emission gives random 3D recoil. Axis temperatures use velocity variance after removing centre-of-mass drift, Tᵢ=m Var(vᵢ)/kB; mean temperature averages the axes. Micromotion and collective motion can enter this diagnostic; it is not automatically an equilibrium temperature.
| Parameter / quantity | Meaning, effect and use |
|---|---|
| Species / transition | Mass sets recoil and trap frequencies. Wavelength sets photon momentum; linewidth sets scattering and Doppler scales. The simplified beams omit repumper dynamics. |
| Detuning δ/Γ | Negative detuning usually damps velocity; positive detuning heats. Start at −0.5, then compare +0.5. Γ is the angular decay rate: Γ = 2π × linewidth in MHz. |
| Saturation s | Larger s increases scattering but also recoil and power broadening; it does not guarantee a colder cloud. Original/analytic panels use per-beam s; the 3D panel divides its intensity scale by six per active beam. |
| Initial temperature | Sets the initial Gaussian velocity variance, not the final equilibrium. A small sample need not equal the requested temperature exactly. Use a fixed seed when comparing conditions. |
| Particle count | More particles smooth statistical noise, but Coulomb pair computation grows as N². Begin with 8–12; use a small count for the actual RF model. |
| Emission recoil / photon model | Random photon emission heats while red-detuned absorption cools. Isotropic emission spreads recoil over three axes. The desktop mean-force option removes this diffusion and cannot predict a Doppler equilibrium. |
| Magnetic field B (T) | Penning only. Larger B raises the cyclotron frequency and changes the magnetron frequency and cooling window. Require ωc² > 2ωz². Fine decimal entry is a numerical setting, not field accuracy. |
| U₀ and characteristic length d | Analytic Penning model: ωz² = Q U₀/(m d²), so larger U₀ or smaller d tightens axial confinement but can destroy radial stability. The 3D model takes axial frequency directly. |
| Axial frequency νz (kHz) | Confines z. In a Paul trap its DC field defocuses x/y; in a Penning trap it changes both radial modes. Recheck stability after increasing it. |
| RF frequency and Mathieu q | Paul only. The time-averaged radial frequency obeys ωr² ≈ Ω²q²/8 − ωz²/2. Increasing q tightens confinement but increases micromotion. The displayed stability check is a secular/first-band guide, not a complete Floquet map. |
| Time-averaged versus actual RF | The averaged potential removes fast micromotion. Actual RF integrates the oscillating quadrupole and includes micromotion in kinetic temperature. Compare at the same seed and duration. Penning has no RF quadrupole in this model. |
| Radial beam offset yb (µm) | Penning: offset creates an intensity-gradient torque. Zero offset cools cyclotron motion but can heat magnetron motion. Suggest offset searches the analytic small-amplitude window; numerical 3D results need not have the same optimum. |
| Beam waist w (µm) | Gaussian intensity is proportional to exp[−2(y−yb)²/w²]. A narrower beam strengthens gradients but covers less of the orbit. Analytic rates are local approximations; use amplitude much smaller than w. |
| Beam tilt θ | Analytic Penning: increasing tilt supplies an axial cooling component while reducing the radial component. The fancier 3D Penning model instead has one radial +x beam and two axial ±z beams; it is a different beam geometry. |
| Initial r₊, r₋ and z amplitudes | Analytic Penning starts the three envelopes at this amplitude. Large values can leave the linear cooling regime. Start with 20 µm and a 100 µm waist. Inspect time shows later amplitudes; it does not change the initial value. |
| Initial cloud σ / relaxation | 3D: σ is the Gaussian width on each spatial axis. A random interacting cloud can release electrostatic energy and warm initially. Paul Relax initial positions prepares an approximate local configuration before the clock starts; it is not simulated cooling or a proven global minimum. |
| Coulomb repulsion | Repulsion redistributes energy and may create ordered structures. The force is softened at 0.3 µm to avoid a singular close encounter. Shape alone is not proof of a crystal phase. Penning begins with repulsion off for a clear single-particle comparison. |
| Observation duration / inspect time | Duration sets the physical end time; playback speed changes presentation. Analytic Show this time jumps to the chosen envelope time. Reset restarts at t=0. All 3D projections and temperatures share one clock. |
| Radial/axial ranges, zoom and camera | Ranges are half-widths in µm. Fixed limits reveal shrinkage; fit reveals detail. Zoom and camera never alter the physics. A clipped orbit is marked; clipping is distinct from an ion crossing the model aperture. |
| Random seed | Same seed plus identical settings and numerical steps repeats the stochastic run. Different seeds change photon histories. Compare trends over several seeds before interpreting small differences. |
| βrω₋ < F′ < βrω₊ | βr is the radial friction coefficient (N·s/m); F′ is the transverse force gradient (N/m). For βr>0, F′/(2πβr) must lie between ν₋ and ν₊. Negative amplitude rates cool; positive rates heat. The logarithmic frequency axis makes both boundaries visible. |
| PNG / CSV / settings | PNG saves the views; CSV saves physical traces and a parameter header. Browsers normally save to their configured download folder; choose your preferred local folder. Desktop exports include particle coordinates, inputs, structure diagnostics and PNG/PDF/SVG. No data are uploaded. |
| Centre view on cloud | Subtracts the cloud mean position from the drawing only. Combine with Fit whole view to resolve a cold cloud that has drifted off the trap centre. Coordinates are then relative to the cloud centre; exported physics and temperature remain unchanged. |
Suggested sequence: (1) compare red and blue detuning in optical molasses; (2) compare zero and suggested offset in analytic Penning, show 50 ms and fit the orbit; (3) choose Paul or Penning in the fancier panel and compare all three axes; (4) compare averaged and actual RF for Paul; (5) save CSV after fixing parameters and seed. Penning confinement has no positive-definite static 3D electric-potential minimum, so Paul static relaxation must not be applied to Penning.
Leibfried et al. (2003) · Hendricks et al., Penning cooling · Ca⁺ transition measurement
🌀 Laser cooling — One ion in a Penning trap
A radial beam cools the cyclotron motion but heats the magnetron motion (its energy is negative). Shift the beam off centre so the intensity gradient pushes the magnetron orbit inwards; tilt it to cool the axial motion too.
Goal: all three amplitudes below 10 µm within 100 ms
Compare beam offset 0 with Suggest offset: the indicator enters the green window and the magnetron rate changes from positive to negative. Keep a fixed range to compare cooling; Fit current orbit magnifies the current motion. Inspect time changes the observation point without refitting.
📐 Principles (physics in detail)
Penning-trap motions. An ion in B and a quadrupole potential U₀ has three eigenmotions: modified cyclotron ω₊, magnetron ω₋ and axial ω_z, with ω₊ + ω₋ = ω_c = qB/m and ω₊ω₋ = ω_z²/2.
Magnetron problem. The magnetron motion has negative total energy (potential hill dominates), so a friction force that removes kinetic energy increases its radius: a centred radial laser cools ω₊ but heats ω₋.
Itano–Wineland solution. Offset the beam by y_b so that the intensity gradient gives a force gradient F′ = ∂F/∂y. The radial amplitude rates become γ₊ = (F′ − β_rω₊)/(2mΔω) and γ₋ = (β_rω₋ − F′)/(2mΔω) with Δω = ω₊ − ω₋. Both are negative (cooling) only inside the window β_rω₋ < F′ < β_rω₊ — shown as the green bar. Their sum is fixed: γ₊ + γ₋ = −β_r/(2m).
Axial cooling. Tilting the beam by θ out of the radial plane gives axial damping γ_z = −β sin²θ/(2m) and reduces the radial share to β_r = β cos²θ.
Equilibrium. Recoil diffusion D limits the amplitudes to A_eq = √(D/(−2γ)); amplitudes evolve as A(t)² = A₀²e^{2γt} + D(e^{2γt} − 1)/(2γ), drawn in the log–log plot. Sources: Itano & Wineland PRA 25, 35 (1982); Hendricks et al. arXiv:0709.3817.
💡 Hints
Penning trap: the radial damping β_r is shared as γ₊ + γ₋ = −β_r/2m; the beam offset moves damping from the cyclotron to the magnetron mode.
Two-level model: no hyperfine structure, dark states or micromotion. Ions such as Ca⁺ need a repumper; values are teaching estimates, not an experiment.
💡 Parameter guide, physical basics and experiments
The 3D motion and cooling curves use the same clock. Spatial trajectories are projected onto the screen; rotating the camera does not change the ions. Dynamics use ideal fields, classical ions and independent two-level beams.
Each beam scatters at R = (Γ/2)s/[1+s+(2(δ−kv)/Γ)²]. Absorption gives ±ℏk momentum; spontaneous emission gives random 3D recoil. Axis temperatures use velocity variance after removing centre-of-mass drift, Tᵢ=m Var(vᵢ)/kB; mean temperature averages the axes. Micromotion and collective motion can enter this diagnostic; it is not automatically an equilibrium temperature.
| Parameter / quantity | Meaning, effect and use |
|---|---|
| Species / transition | Mass sets recoil and trap frequencies. Wavelength sets photon momentum; linewidth sets scattering and Doppler scales. The simplified beams omit repumper dynamics. |
| Detuning δ/Γ | Negative detuning usually damps velocity; positive detuning heats. Start at −0.5, then compare +0.5. Γ is the angular decay rate: Γ = 2π × linewidth in MHz. |
| Saturation s | Larger s increases scattering but also recoil and power broadening; it does not guarantee a colder cloud. Original/analytic panels use per-beam s; the 3D panel divides its intensity scale by six per active beam. |
| Initial temperature | Sets the initial Gaussian velocity variance, not the final equilibrium. A small sample need not equal the requested temperature exactly. Use a fixed seed when comparing conditions. |
| Particle count | More particles smooth statistical noise, but Coulomb pair computation grows as N². Begin with 8–12; use a small count for the actual RF model. |
| Emission recoil / photon model | Random photon emission heats while red-detuned absorption cools. Isotropic emission spreads recoil over three axes. The desktop mean-force option removes this diffusion and cannot predict a Doppler equilibrium. |
| Magnetic field B (T) | Penning only. Larger B raises the cyclotron frequency and changes the magnetron frequency and cooling window. Require ωc² > 2ωz². Fine decimal entry is a numerical setting, not field accuracy. |
| U₀ and characteristic length d | Analytic Penning model: ωz² = Q U₀/(m d²), so larger U₀ or smaller d tightens axial confinement but can destroy radial stability. The 3D model takes axial frequency directly. |
| Axial frequency νz (kHz) | Confines z. In a Paul trap its DC field defocuses x/y; in a Penning trap it changes both radial modes. Recheck stability after increasing it. |
| RF frequency and Mathieu q | Paul only. The time-averaged radial frequency obeys ωr² ≈ Ω²q²/8 − ωz²/2. Increasing q tightens confinement but increases micromotion. The displayed stability check is a secular/first-band guide, not a complete Floquet map. |
| Time-averaged versus actual RF | The averaged potential removes fast micromotion. Actual RF integrates the oscillating quadrupole and includes micromotion in kinetic temperature. Compare at the same seed and duration. Penning has no RF quadrupole in this model. |
| Radial beam offset yb (µm) | Penning: offset creates an intensity-gradient torque. Zero offset cools cyclotron motion but can heat magnetron motion. Suggest offset searches the analytic small-amplitude window; numerical 3D results need not have the same optimum. |
| Beam waist w (µm) | Gaussian intensity is proportional to exp[−2(y−yb)²/w²]. A narrower beam strengthens gradients but covers less of the orbit. Analytic rates are local approximations; use amplitude much smaller than w. |
| Beam tilt θ | Analytic Penning: increasing tilt supplies an axial cooling component while reducing the radial component. The fancier 3D Penning model instead has one radial +x beam and two axial ±z beams; it is a different beam geometry. |
| Initial r₊, r₋ and z amplitudes | Analytic Penning starts the three envelopes at this amplitude. Large values can leave the linear cooling regime. Start with 20 µm and a 100 µm waist. Inspect time shows later amplitudes; it does not change the initial value. |
| Initial cloud σ / relaxation | 3D: σ is the Gaussian width on each spatial axis. A random interacting cloud can release electrostatic energy and warm initially. Paul Relax initial positions prepares an approximate local configuration before the clock starts; it is not simulated cooling or a proven global minimum. |
| Coulomb repulsion | Repulsion redistributes energy and may create ordered structures. The force is softened at 0.3 µm to avoid a singular close encounter. Shape alone is not proof of a crystal phase. Penning begins with repulsion off for a clear single-particle comparison. |
| Observation duration / inspect time | Duration sets the physical end time; playback speed changes presentation. Analytic Show this time jumps to the chosen envelope time. Reset restarts at t=0. All 3D projections and temperatures share one clock. |
| Radial/axial ranges, zoom and camera | Ranges are half-widths in µm. Fixed limits reveal shrinkage; fit reveals detail. Zoom and camera never alter the physics. A clipped orbit is marked; clipping is distinct from an ion crossing the model aperture. |
| Random seed | Same seed plus identical settings and numerical steps repeats the stochastic run. Different seeds change photon histories. Compare trends over several seeds before interpreting small differences. |
| βrω₋ < F′ < βrω₊ | βr is the radial friction coefficient (N·s/m); F′ is the transverse force gradient (N/m). For βr>0, F′/(2πβr) must lie between ν₋ and ν₊. Negative amplitude rates cool; positive rates heat. The logarithmic frequency axis makes both boundaries visible. |
| PNG / CSV / settings | PNG saves the views; CSV saves physical traces and a parameter header. Browsers normally save to their configured download folder; choose your preferred local folder. Desktop exports include particle coordinates, inputs, structure diagnostics and PNG/PDF/SVG. No data are uploaded. |
| Centre view on cloud | Subtracts the cloud mean position from the drawing only. Combine with Fit whole view to resolve a cold cloud that has drifted off the trap centre. Coordinates are then relative to the cloud centre; exported physics and temperature remain unchanged. |
Suggested sequence: (1) compare red and blue detuning in optical molasses; (2) compare zero and suggested offset in analytic Penning, show 50 ms and fit the orbit; (3) choose Paul or Penning in the fancier panel and compare all three axes; (4) compare averaged and actual RF for Paul; (5) save CSV after fixing parameters and seed. Penning confinement has no positive-definite static 3D electric-potential minimum, so Paul static relaxation must not be applied to Penning.
Leibfried et al. (2003) · Hendricks et al., Penning cooling · Ca⁺ transition measurement
Orbits use the physical ν₊, ν₋ and νz phases at the displayed time; the trail covers the last six cyclotron periods. Playback uses an accelerated logarithmic clock and fast motion can visually alias. Drag the 3D view to rotate; wheel to zoom.
❄ Fancier simulation: 3D laser cooling in Paul / Penning traps
Compare the actual RF drive with the time-averaged potential. Watch micromotion, ion repulsion, red-detuned cooling and blue-detuned heating. All views share one simulation clock.
Trap design and inputs
Axial frequency is calculated from endcap voltage, geometry and ion mass. Enter physical voltages normally; advanced mode sets Mathieu q directly. Species changes preserve voltages: check stability again. V_RF is the differential zero-to-peak amplitude between rod pairs.
Equations, variables and stability
Φ = (U_dc − V_RF cos Ωt)(x² − y²)/(2r₀²) + κ U_end (z² − (x²+y²)/2)/z₀².
q = 2 Q V_RF/(m r₀² Ω²); aₓ,ᵧ = 4Q(±U_dc/r₀² − κ U_end/z₀²)/(mΩ²); ωz² = 2QκU_end/(mz₀²); νx,y = βx,y Ω/(4π).
Penning: Φ = U₀(z² − ρ²/2)/(2d²), ωz² = QU₀/(md²), ωc = QB/m, ω± = (ωc ± √(ωc²−2ωz²))/2. d² = (z₀²+r₀²/2)/2 for ideal hyperbolic electrodes. Real plate electrodes require a calibrated field coefficient; plate spacing alone does not establish this ideal potential. Geometry and display range are different quantities. NIST Mathieu stability · Brown & Gabrielse
3D view: drag to rotate, wheel to zoom (use View zoom on touch screens); Fit restores the scale. Video records a 2–30 second clip under the current conditions. Short runs slow their display while recording; the physical clock remains explicit. Figures and video include a condition summary; save full conditions as JSON and numbers as CSV. Choose your preferred folder in the browser’s save dialog.
Initial phase-space area and ion-ball size
εₓ = √(Var(x)Var(vₓ) − Cov(x,vₓ)²), in µm·m/s. An uncorrelated Gaussian start has ε ≈ σₓ√(kBT/m). Set T from ε uses this relation and disables initial-position relaxation. Finite samples differ from the requested target; the status shows actual initial and current ε. Temperature uses the velocity sample variances after centre-of-mass subtraction; mean is the average of x/y/z. Initial T is a distribution target, so a small sample differs. Potential-energy release and micromotion can cause transient heating; curves are not forced to decrease. The Doppler line is a reference scale rather than a prediction for every condition. This is a phase-space area, rather than beam emittance in mm·mrad, which requires a longitudinal velocity. Ball radius changes the drawn marker only; it is not the ion’s physical radius.
Model, controls and sources
Defaults: ⁴⁰Ca⁺, 397 nm, Γ/2π=23.05 MHz. Run cooling, then compare blue heating or the RF preset. Changing physical parameters resets the trajectory; zoom changes only the drawing. Temperature uses velocity variance after subtracting centre-of-mass drift. Actual-RF temperature includes micromotion and is not a pure secular temperature.
Classical point ions, ideal fields, independent two-level beams and stochastic recoil; Coulomb softening 0.3 µm, adjustable rod radius/aperture. At least 40 integration steps per RF period. Multilevel repumping dynamics are omitted; this teaching model is not experimental or crystal-phase evidence. Leibfried et al., RMP 75, 281 (2003) · Ca⁺ transition source
Ion masses: AME2020 atomic mass minus electron mass; ionization binding corrections are omitted. Voltage mode keeps voltages and geometry when changing species; q and motional frequencies change with mass. The JSON conditions record the mass. AME2020
💡 Parameter guide, physical basics and experiments
The 3D motion and cooling curves use the same clock. Spatial trajectories are projected onto the screen; rotating the camera does not change the ions. Dynamics use ideal fields, classical ions and independent two-level beams.
Each beam scatters at R = (Γ/2)s/[1+s+(2(δ−kv)/Γ)²]. Absorption gives ±ℏk momentum; spontaneous emission gives random 3D recoil. Axis temperatures use velocity variance after removing centre-of-mass drift, Tᵢ=m Var(vᵢ)/kB; mean temperature averages the axes. Micromotion and collective motion can enter this diagnostic; it is not automatically an equilibrium temperature.
| Parameter / quantity | Meaning, effect and use |
|---|---|
| Species / transition | Mass sets recoil and trap frequencies. Wavelength sets photon momentum; linewidth sets scattering and Doppler scales. The simplified beams omit repumper dynamics. |
| Detuning δ/Γ | Negative detuning usually damps velocity; positive detuning heats. Start at −0.5, then compare +0.5. Γ is the angular decay rate: Γ = 2π × linewidth in MHz. |
| Saturation s | Larger s increases scattering but also recoil and power broadening; it does not guarantee a colder cloud. Original/analytic panels use per-beam s; the 3D panel divides its intensity scale by six per active beam. |
| Initial temperature | Sets the initial Gaussian velocity variance, not the final equilibrium. A small sample need not equal the requested temperature exactly. Use a fixed seed when comparing conditions. |
| Particle count | More particles smooth statistical noise, but Coulomb pair computation grows as N². Begin with 8–12; use a small count for the actual RF model. |
| Emission recoil / photon model | Random photon emission heats while red-detuned absorption cools. Isotropic emission spreads recoil over three axes. The desktop mean-force option removes this diffusion and cannot predict a Doppler equilibrium. |
| Magnetic field B (T) | Penning only. Larger B raises the cyclotron frequency and changes the magnetron frequency and cooling window. Require ωc² > 2ωz². Fine decimal entry is a numerical setting, not field accuracy. |
| U₀ and characteristic length d | Analytic Penning model: ωz² = Q U₀/(m d²), so larger U₀ or smaller d tightens axial confinement but can destroy radial stability. The 3D model takes axial frequency directly. |
| Axial frequency νz (kHz) | Confines z. In a Paul trap its DC field defocuses x/y; in a Penning trap it changes both radial modes. Recheck stability after increasing it. |
| RF frequency and Mathieu q | Paul only. The time-averaged radial frequency obeys ωr² ≈ Ω²q²/8 − ωz²/2. Increasing q tightens confinement but increases micromotion. The displayed stability check is a secular/first-band guide, not a complete Floquet map. |
| Time-averaged versus actual RF | The averaged potential removes fast micromotion. Actual RF integrates the oscillating quadrupole and includes micromotion in kinetic temperature. Compare at the same seed and duration. Penning has no RF quadrupole in this model. |
| Radial beam offset yb (µm) | Penning: offset creates an intensity-gradient torque. Zero offset cools cyclotron motion but can heat magnetron motion. Suggest offset searches the analytic small-amplitude window; numerical 3D results need not have the same optimum. |
| Beam waist w (µm) | Gaussian intensity is proportional to exp[−2(y−yb)²/w²]. A narrower beam strengthens gradients but covers less of the orbit. Analytic rates are local approximations; use amplitude much smaller than w. |
| Beam tilt θ | Analytic Penning: increasing tilt supplies an axial cooling component while reducing the radial component. The fancier 3D Penning model instead has one radial +x beam and two axial ±z beams; it is a different beam geometry. |
| Initial r₊, r₋ and z amplitudes | Analytic Penning starts the three envelopes at this amplitude. Large values can leave the linear cooling regime. Start with 20 µm and a 100 µm waist. Inspect time shows later amplitudes; it does not change the initial value. |
| Initial cloud σ / relaxation | 3D: σ is the Gaussian width on each spatial axis. A random interacting cloud can release electrostatic energy and warm initially. Paul Relax initial positions prepares an approximate local configuration before the clock starts; it is not simulated cooling or a proven global minimum. |
| Coulomb repulsion | Repulsion redistributes energy and may create ordered structures. The force is softened at 0.3 µm to avoid a singular close encounter. Shape alone is not proof of a crystal phase. Penning begins with repulsion off for a clear single-particle comparison. |
| Observation duration / inspect time | Duration sets the physical end time; playback speed changes presentation. Analytic Show this time jumps to the chosen envelope time. Reset restarts at t=0. All 3D projections and temperatures share one clock. |
| Radial/axial ranges, zoom and camera | Ranges are half-widths in µm. Fixed limits reveal shrinkage; fit reveals detail. Zoom and camera never alter the physics. A clipped orbit is marked; clipping is distinct from an ion crossing the model aperture. |
| Random seed | Same seed plus identical settings and numerical steps repeats the stochastic run. Different seeds change photon histories. Compare trends over several seeds before interpreting small differences. |
| βrω₋ < F′ < βrω₊ | βr is the radial friction coefficient (N·s/m); F′ is the transverse force gradient (N/m). For βr>0, F′/(2πβr) must lie between ν₋ and ν₊. Negative amplitude rates cool; positive rates heat. The logarithmic frequency axis makes both boundaries visible. |
| PNG / CSV / settings | PNG saves the views; CSV saves physical traces and a parameter header. Browsers normally save to their configured download folder; choose your preferred local folder. Desktop exports include particle coordinates, inputs, structure diagnostics and PNG/PDF/SVG. No data are uploaded. |
| Centre view on cloud | Subtracts the cloud mean position from the drawing only. Combine with Fit whole view to resolve a cold cloud that has drifted off the trap centre. Coordinates are then relative to the cloud centre; exported physics and temperature remain unchanged. |
Suggested sequence: (1) compare red and blue detuning in optical molasses; (2) compare zero and suggested offset in analytic Penning, show 50 ms and fit the orbit; (3) choose Paul or Penning in the fancier panel and compare all three axes; (4) compare averaged and actual RF for Paul; (5) save CSV after fixing parameters and seed. Penning confinement has no positive-definite static 3D electric-potential minimum, so Paul static relaxation must not be applied to Penning.
Leibfried et al. (2003) · Hendricks et al., Penning cooling · Ca⁺ transition measurement
❄ 3D optical molasses: cooling and cloud expansion
Six counterpropagating Gaussian beams act on independent neutral atoms. Molasses damps velocity without a restoring force; a MOT combines a quadrupole magnetic field and circular polarization to restore displaced atoms. Compare temperature, bulk drift and cloud size separately.
Browser semiclassical teaching model: ideal F=0 → F′=1, instantaneous steady scattering, shared-saturation approximation and isotropic spontaneous-emission diffusion. Alkali entries are effective-line examples; their real hyperfine structure, repumping, polarization-gradient, sub-Doppler and gray-molasses dynamics are omitted.
Transition data and approximations
Γ/2π is given in MHz; the kernel uses Γ (rad/s), λ (m) and atomic mass (kg). Recoil-resolved transitions are rejected rather than treated as valid diffusion cooling.
Beams, magnetic field and initial cloud
Integration, duration and loss criterion
Stochastic diffusion integration with additional damping, restoring-force, beam-transit and Zeeman-change timestep limits. Optical cycles, internal-state transients and individual sparse photon events are not resolved; photon counts are expectations. Playback speed never changes the physical timestep. Work is capped at 20 million particle steps; halve the timestep to check convergence. The loss radius is a user-defined diagnostic boundary, not a MOT wall; survivor temperature uses only atoms still inside it.
View and value inspection
Drag the 3D plot to rotate and use the wheel to zoom. Hover over a point or curve for values; click to pin them in the textbox. View changes keep the physics; physical edits stop and reset the run. Hidden method tabs pause immediately without background simulation.
PNG and PDF use the same selected views; the PDF contains a high-resolution image. JSON saves conditions, view, actual timestep and statistics; restore starts from the same seed rather than resuming the random state midway. CSV saves the sampled history and particle snapshot. Recorded video has a separate save link below its browser preview; choose your folder in the system save dialog.
Physics, equations, limits and sources
Rᵢ = (Γ/2) Σ_q sᵢ |εᵢ,q|² / [1 + Σⱼ sⱼ + 4(Δᵢ,q/Γ)²], Δᵢ,q = δ − kᵢ·v − q μ_eff |B|/ℏ. F = Σᵢ ℏ kᵢ Rᵢ. B = (−b x/2, −b y/2, b z).
Circular polarization is projected onto the local magnetic-field direction; strong and transverse axes have opposite helicities. Absorption shot noise and isotropic spontaneous emission give Var(dvⱼ)/dt = vᵣ²(Rⱼ,+ + Rⱼ,− + R_total/3). Tⱼ = m Σ(vⱼ−v̄ⱼ)²/[(N−1)k_B]; centroid drift is excluded. Recoil off is a deterministic comparison, not a physical cooling limit. The Doppler scale ℏΓ/(2k_B) is a reference; finite beams, saturation, magnetic fields, gravity and escape alter equilibrium and capture.
This program does not call PyLCP; its heuristic equation supplies the formula reference. At high velocity or saturation this approximation differs from full rate equations or optical Bloch equations. Multiple scattering, collisions, dark states, coherence, dipole forces, magnetic-dipole forces and multilevel repumping are omitted.
Eckel et al., PyLCP, Computer Physics Communications 270 (2022) 108166 · Eq. 35 · Author paper (NIST) · PyLCP documentation · Alkali transition data · AME2020
❄ Magneto-optical trap: six-beam 3D capture and cooling
Six counterpropagating Gaussian beams act on independent neutral atoms. Molasses damps velocity without a restoring force; a MOT combines a quadrupole magnetic field and circular polarization to restore displaced atoms. Compare temperature, bulk drift and cloud size separately.
Browser semiclassical teaching model: ideal F=0 → F′=1, instantaneous steady scattering, shared-saturation approximation and isotropic spontaneous-emission diffusion. Alkali entries are effective-line examples; their real hyperfine structure, repumping, polarization-gradient, sub-Doppler and gray-molasses dynamics are omitted.
Transition data and approximations
Γ/2π is given in MHz; the kernel uses Γ (rad/s), λ (m) and atomic mass (kg). Recoil-resolved transitions are rejected rather than treated as valid diffusion cooling.
Beams, magnetic field and initial cloud
Integration, duration and loss criterion
Stochastic diffusion integration with additional damping, restoring-force, beam-transit and Zeeman-change timestep limits. Optical cycles, internal-state transients and individual sparse photon events are not resolved; photon counts are expectations. Playback speed never changes the physical timestep. Work is capped at 20 million particle steps; halve the timestep to check convergence. The loss radius is a user-defined diagnostic boundary, not a MOT wall; survivor temperature uses only atoms still inside it.
View and value inspection
Drag the 3D plot to rotate and use the wheel to zoom. Hover over a point or curve for values; click to pin them in the textbox. View changes keep the physics; physical edits stop and reset the run. Hidden method tabs pause immediately without background simulation.
PNG and PDF use the same selected views; the PDF contains a high-resolution image. JSON saves conditions, view, actual timestep and statistics; restore starts from the same seed rather than resuming the random state midway. CSV saves the sampled history and particle snapshot. Recorded video has a separate save link below its browser preview; choose your folder in the system save dialog.
Physics, equations, limits and sources
Rᵢ = (Γ/2) Σ_q sᵢ |εᵢ,q|² / [1 + Σⱼ sⱼ + 4(Δᵢ,q/Γ)²], Δᵢ,q = δ − kᵢ·v − q μ_eff |B|/ℏ. F = Σᵢ ℏ kᵢ Rᵢ. B = (−b x/2, −b y/2, b z).
Circular polarization is projected onto the local magnetic-field direction; strong and transverse axes have opposite helicities. Absorption shot noise and isotropic spontaneous emission give Var(dvⱼ)/dt = vᵣ²(Rⱼ,+ + Rⱼ,− + R_total/3). Tⱼ = m Σ(vⱼ−v̄ⱼ)²/[(N−1)k_B]; centroid drift is excluded. Recoil off is a deterministic comparison, not a physical cooling limit. The Doppler scale ℏΓ/(2k_B) is a reference; finite beams, saturation, magnetic fields, gravity and escape alter equilibrium and capture.
This program does not call PyLCP; its heuristic equation supplies the formula reference. At high velocity or saturation this approximation differs from full rate equations or optical Bloch equations. Multiple scattering, collisions, dark states, coherence, dipole forces, magnetic-dipole forces and multilevel repumping are omitted.
Eckel et al., PyLCP, Computer Physics Communications 270 (2022) 108166 · Eq. 35 · Author paper (NIST) · PyLCP documentation · Alkali transition data · AME2020
🧪 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.
…
🧩 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.