Jeux
Suivre les étapes d’une mesure
Examinez dans la carte les états fondamental et isomérique de ¹³³Xe, leurs énergies d’excitation et incertitudes. Un isomère est un état nucléaire excité relativement durable. En MR-TOF, les ions circulent entre deux miroirs électrostatiques : modifiez les tours, les largeurs de pics et les populations. En TOF-ICR, comparez la réponse mélangée, l’ajustement à une espèce et les résidus, observation moins ajustement. En PI-ICR, changez le temps d’accumulation pour observer l’enroulement des phases. Séparation, précision statistique et biais du modèle sont des limites distinctes.
Jouez pendant les pauses du faisceau. Les meilleurs scores sont conservés uniquement dans votre navigateur.
Parcours de spectroscopie
Huit défis : trouver une source, vérifier une règle de sélection, interpréter un déplacement isotopique et suivre une transition gamma.
Exercices pédagogiques avec des nombres fictifs. Aucune donnée isotopique mesurée ni aucun résultat expérimental n’est généré.
Chargement des exercices…
⏳ Qui vit le plus longtemps ?
Deux noyaux de NUBASE2020 : choisissez la demi-vie la plus longue et poursuivez la série.
🎯 Trouver la résonance cyclotron (TOF-ICR)
Réglez ν_rf, tirez des ions et cherchez le minimum du temps de vol. Pour ¹³³Cs⁺ à 7 T, νc = qB/(2πm) ≈ 808795.01 Hz. Moins de tirs et une meilleure estimation donnent davantage de 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.
💡 Repères physiques
- À ν_rf = νc, l’excitation quadrupolaire convertit le magnétron lent en cyclotron modifié rapide. Le gradient magnétique convertit l’énergie radiale en énergie axiale ; les ions résonants arrivent plus vite. La résonance est un minimum du temps de vol.
- Largeur FWHM ≈ 0.8/T_rf pour une impulsion rectangulaire. Une excitation plus longue rétrécit le creux ; la précision statistique suit 1/(T_rf·√N).
- L’impulsion rectangulaire possède des lobes secondaires de type sinc². Ramsey donne une frange centrale environ 40 % plus étroite et des franges latérales plus fortes. Ne confondez pas une frange latérale et le centre.
- Masse : m = qB/(2πνc), avec B étalonné par une référence. Une erreur de 0.1 Hz à 808 kHz vaut δm/m ≈ 1.2×10⁻⁷, soit environ 15 keV à A = 133.
TOF-ICR : résonances superposées et biais d’ajustement
Comparez les résonances individuelles au mélange. L’ajustement d’une seule espèce peut sembler précis tout en étant décalé de la cible.
一部の科学的な説明は英語で表示されます。
💡 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.
Interprétation
Paramètres avancés et hypothèses
Masses : fondamental AME2020 et excitation NUBASE2020. # indique une extrapolation. Une erreur inconnue ne vaut pas zéro ; la covariance indisponible est remplacée explicitement par une approximation diagonale. Ionisation et liaison moléculaire sont omises.
Réponse pédagogique : t(F) = t_offset + t_scale / √(1 + κF), F fraction de conversion entre 0 et 1. Valeurs initiales : 62 µs, 193 µs, κ = 1.876 ; fond non converti de 8 %, largeurs σ = 7 et 9 µs. Moyennes et densités sont pondérées par les populations. Le bruit est illustratif ; les intervalles locaux Δχ² = 1 n’incluent pas le biais du mélange.
TOF-ICR : résonances superposées et biais d’ajustement
Comparez les résonances individuelles au mélange. L’ajustement d’une seule espèce peut sembler précis tout en étant décalé de la cible.
一部の科学的な説明は英語で表示されます。
💡 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.
Interprétation
Paramètres avancés et hypothèses
Masses : fondamental AME2020 et excitation NUBASE2020. # indique une extrapolation. Une erreur inconnue ne vaut pas zéro ; la covariance indisponible est remplacée explicitement par une approximation diagonale. Ionisation et liaison moléculaire sont omises.
Réponse pédagogique : t(F) = t_offset + t_scale / √(1 + κF), F fraction de conversion entre 0 et 1. Valeurs initiales : 62 µs, 193 µs, κ = 1.876 ; fond non converti de 8 %, largeurs σ = 7 et 9 µs. Moyennes et densités sont pondérées par les populations. Le bruit est illustratif ; les intervalles locaux Δχ² = 1 n’incluent pas le biais du mélange.
🌀 Séparer l’isomère par PI-ICR
Après t_acc, la phase cyclotron de chaque ion est projetée sur un détecteur de position. Fondamental et isomère diffèrent de Eₓ/c² ; leurs taches se séparent de Δφ = 2π Δνc t_acc. Cherchez un temps qui les sépare.
💡 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.
Phase de référence et synchronisation
Décalages antihoraires des figures du détecteur dans le repère magnétron. Le premier ion, ou le fondamental d’une paire, fixe les fréquences de référence. Avec superposition, le temps avance à la solution suivante de νc t + (δ₊ − δ₋)/360° = entier. L’horloge initiale arrondit à 4 ns selon PyMassScanner et affiche l’écart restant. Le temps idéal donne une superposition exacte. Graphiques, tours, incertitudes et exports utilisent le temps réalisé. L’origine commune tourne toutes les taches sans changer les séparations.
α₋ = α₀ + δ₋; α₊ = α₀ + δ₊ + 360°νc t; νc = ν₊ + ν₋.
Détecteur et entraînement
Séparez par des virgules : 84Rb · Rb-84 · 133Cs+2 ou 133Cs2+ pour la charge ; 45mSc, 45Scm ou 45Sc* pour un isomère, Eₓ de NUBASE2020, m2 pour le deuxième ; 12C16O2 ou 12C11 pour les molécules et agrégats ; 87Rb:0.3 pour l’intensité relative. Masse ionique = masse atomique − q·mₑ, liaisons électroniques négligées.
La première espèce est la référence. Tours totaux = νc t ; Δ tours = (νc − νc,ref)t. Les angles résiduels sont repliés sur [−180°, 180°). Le premier temps opposé vaut 1/(2|Δνc|) ; des fréquences égales ne se séparent jamais. Ce temps dépend de la paire et est arrondi au pas de 0.01 ms. Les fréquences de simulation sont connues.
Comparer les temps d’accumulation
Les fréquences connues de simulation donnent le nombre entier de tours. Les temps supplémentaires révèlent le repliement des phases ; ils ne déterminent pas un nombre expérimental inconnu.
Angles antihoraires. L’origine commune tourne toutes les taches sans changer leurs séparations. Le dessin utilise un rayon de 21.00 mm, porté à 32.00 mm si une tache dépasse 20.00 mm. Il ne modélise pas les pertes d’acceptance du détecteur.
σ est l’écart-type angulaire d’un événement. La recherche teste toutes les paires par pas de 0.01 ms jusqu’à 5000 ms, repliement compris ; ce n’est pas un niveau de confiance ajusté.
Le σ extérieur règle le flou et la résolution de phase. Le σ central ne modifie que la tache centrale, pas les espèces en orbite.
σ est l’écart-type angulaire des événements individuels. 2.355σ approche la FWHM d’un pic gaussien ; ce n’est ni un niveau de confiance ni l’erreur combinée de deux centroïdes. Le préréglage et la saisie manuelle contrôlent la même cible pour la recherche et la comparaison.
💡 Repères physiques
Par rapport à l’origine commune, νc = (φ + 2πn)/(2πt), φ en radians et n tours complets. La simulation connaît n ; l’expérience doit le déterminer. Pour une énergie de repos supplémentaire E à charge fixe : |Δνc|/νc = E/(mion c² + E). Aux petits angles, σφ ≈ σx,y/r ; r est modifiable, initialement 10.00 mm. R = 2πνc t/(2.355 σφ) est un repère FWHM, pas une erreur de masse. Un temps plus long peut superposer à nouveau les taches.
Le piège idéal combine cyclotron rapide ν₊, magnétron lent ν₋ et axial νz. Φ = U₀(z² − r²/2)/(2d²), νc = qB/(2πmion), νz = √(qU₀/(mion d²))/(2π), ν± = [νc ± √(νc² − 2νz²)]/2. Il faut νc² > 2νz². Identités : ν₊ + ν₋ = νc et ν₊² + ν₋² + νz² = νc² ; au premier ordre, ν₋ ≈ U₀/(4πBd²).
Quel angle correspond à 1 keV ?
Il s’agit de +1 keV d’énergie de repos, pas cinétique : δm = 1 keV/c² = 0.00000107354410 u. À charge et B fixes, δνc = −νc δm/(mion + δm), δφ = 360° δνc t. Négatif signifie en retard dans la convention antihoraire. Cela dépend du premier ion et du temps ; c’est un incrément hypothétique, pas une excitation mesurée.
🌀 Séparer l’isomère par PI-ICR
Après t_acc, la phase cyclotron de chaque ion est projetée sur un détecteur de position. Fondamental et isomère diffèrent de Eₓ/c² ; leurs taches se séparent de Δφ = 2π Δνc t_acc. Cherchez un temps qui les sépare.
💡 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.
Phase de référence et synchronisation
Décalages antihoraires des figures du détecteur dans le repère magnétron. Le premier ion, ou le fondamental d’une paire, fixe les fréquences de référence. Avec superposition, le temps avance à la solution suivante de νc t + (δ₊ − δ₋)/360° = entier. L’horloge initiale arrondit à 4 ns selon PyMassScanner et affiche l’écart restant. Le temps idéal donne une superposition exacte. Graphiques, tours, incertitudes et exports utilisent le temps réalisé. L’origine commune tourne toutes les taches sans changer les séparations.
α₋ = α₀ + δ₋; α₊ = α₀ + δ₊ + 360°νc t; νc = ν₊ + ν₋.
Détecteur et entraînement
Séparez par des virgules : 84Rb · Rb-84 · 133Cs+2 ou 133Cs2+ pour la charge ; 45mSc, 45Scm ou 45Sc* pour un isomère, Eₓ de NUBASE2020, m2 pour le deuxième ; 12C16O2 ou 12C11 pour les molécules et agrégats ; 87Rb:0.3 pour l’intensité relative. Masse ionique = masse atomique − q·mₑ, liaisons électroniques négligées.
La première espèce est la référence. Tours totaux = νc t ; Δ tours = (νc − νc,ref)t. Les angles résiduels sont repliés sur [−180°, 180°). Le premier temps opposé vaut 1/(2|Δνc|) ; des fréquences égales ne se séparent jamais. Ce temps dépend de la paire et est arrondi au pas de 0.01 ms. Les fréquences de simulation sont connues.
Comparer les temps d’accumulation
Les fréquences connues de simulation donnent le nombre entier de tours. Les temps supplémentaires révèlent le repliement des phases ; ils ne déterminent pas un nombre expérimental inconnu.
Angles antihoraires. L’origine commune tourne toutes les taches sans changer leurs séparations. Le dessin utilise un rayon de 21.00 mm, porté à 32.00 mm si une tache dépasse 20.00 mm. Il ne modélise pas les pertes d’acceptance du détecteur.
σ est l’écart-type angulaire d’un événement. La recherche teste toutes les paires par pas de 0.01 ms jusqu’à 5000 ms, repliement compris ; ce n’est pas un niveau de confiance ajusté.
Le σ extérieur règle le flou et la résolution de phase. Le σ central ne modifie que la tache centrale, pas les espèces en orbite.
σ est l’écart-type angulaire des événements individuels. 2.355σ approche la FWHM d’un pic gaussien ; ce n’est ni un niveau de confiance ni l’erreur combinée de deux centroïdes. Le préréglage et la saisie manuelle contrôlent la même cible pour la recherche et la comparaison.
💡 Repères physiques
Par rapport à l’origine commune, νc = (φ + 2πn)/(2πt), φ en radians et n tours complets. La simulation connaît n ; l’expérience doit le déterminer. Pour une énergie de repos supplémentaire E à charge fixe : |Δνc|/νc = E/(mion c² + E). Aux petits angles, σφ ≈ σx,y/r ; r est modifiable, initialement 10.00 mm. R = 2πνc t/(2.355 σφ) est un repère FWHM, pas une erreur de masse. Un temps plus long peut superposer à nouveau les taches.
Le piège idéal combine cyclotron rapide ν₊, magnétron lent ν₋ et axial νz. Φ = U₀(z² − r²/2)/(2d²), νc = qB/(2πmion), νz = √(qU₀/(mion d²))/(2π), ν± = [νc ± √(νc² − 2νz²)]/2. Il faut νc² > 2νz². Identités : ν₊ + ν₋ = νc et ν₊² + ν₋² + νz² = νc² ; au premier ordre, ν₋ ≈ U₀/(4πBd²).
Quel angle correspond à 1 keV ?
Il s’agit de +1 keV d’énergie de repos, pas cinétique : δm = 1 keV/c² = 0.00000107354410 u. À charge et B fixes, δνc = −νc δm/(mion + δm), δφ = 360° δνc t. Négatif signifie en retard dans la convention antihoraire. Cela dépend du premier ion et du temps ; c’est un incrément hypothétique, pas une excitation mesurée.
🪞 Séparer les isobares par MR-TOF
Les ions se réfléchissent entre deux miroirs électrostatiques. Chaque tour augmente le temps de vol et la séparation temporelle des isobares, tout en élargissant les pics. Commencez avec la largeur du paquet initial puis ajoutez des tours.
💡 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.
💡 Repères physiques
t(N) = t₀ + N·T_lap ∝ √m, Δt = t·Δm/(2m), FWHM² = Δt₀² + (N·δ)², R = t/(2·FWHM). Séparation si Δt ≥ FWHM, soit R ≥ m/Δm. La largeur initiale domine aux faibles tours ; l’élargissement par tour limite R aux grands nombres de tours.
MR-TOF : séparer espèces et isomères
Choisissez jusqu’à trois espèces. Comparez leurs pics au spectre combiné et examinez l’effet du nombre de tours.
一部の科学的な説明は英語で表示されます。
💡 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.
Interprétation
Paramètres avancés et hypothèses
Masses : fondamental AME2020 et excitation NUBASE2020. # indique une extrapolation. Une erreur inconnue ne vaut pas zéro ; la covariance indisponible est remplacée explicitement par une approximation diagonale. Ionisation et liaison moléculaire sont omises.
Le temps de vol suit exactement √(mion/q), puis on ajoute le retard électronique. La largeur est phénoménologique : FWHM² = largeur initiale² + (tours × élargissement)². Les populations sont les fractions détectées ; la survie affichée ne simule pas les produits de désintégration.
🧲 Garder les ions : piège de Paul linéaire / filtre RFQ
Les ions traversent le champ quadrupolaire alternatif de quatre électrodes. Seuls les points (q,a) stables restent dans r₀ ; les autres croissent et frappent une barre. Réglez U et V pour transmettre seulement la masse visée.
💡 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 est l’amplitude RF zéro-crête ; U la tension continue. Ce modèle transverse sans collision illustre la transmission en durée finie. Transport axial, gaz tampon, charge d’espace et champs de bord sont omis. Équation de Mathieu
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
Droite de fonctionnement et limites de masse
Les limites idéales de Mathieu ne sont pas des efficacités de transmission mesurées. V est l’amplitude RF zéro-crête ; crête-à-crête = 2V. Les limites dépendent de la charge ; les valeurs sont m/z en u/e.
💡 Repères physiques
Les cycles règlent le séjour, pas la longueur : N cycles à f MHz donnent t = N/f µs. Ainsi 60 cycles à 1 MHz valent 60 µs. Une longueur exigerait la vitesse axiale L = vz t, non simulée. r₀ est la distance axe–électrode, initialement 10 mm ; V est zéro-crête, U continu, Ω = 2πf. z compte les charges positives, m/z la masse par charge. Les paramètres de Mathieu a,q suivent a/q = 2U/V. LMCO/HMCO sont des limites idéales, pas des efficacités mesurées. La dispersion initiale fixe le disque de départ et les vitesses du modèle, pas une émittance mesurée. La vitesse d’animation n’altère ni a,q ni les limites ; la graine répète les lancements. Survivre un temps fini ne prouve pas la stabilité infinie.
❄️ Refroidissement laser — Mélasse optique : refroidir le nuage
Un laser décalé vers le rouge freine les atomes et ions : la particule voit le faisceau opposé à son mouvement rapproché de la résonance. Chaque absorption transfère ħk ; l’émission spontanée aléatoire réchauffe. Leur équilibre fixe la température Doppler.
Deux faisceaux opposés selon x. Réglez désaccord et intensité, allumez le laser et approchez la limite ħΓ/2k_B.
Objectif : T < 1.2 × limite Doppler
📐 Principes physiques détaillés
Diffusion : R = (Γ/2)s₀/(1+s₀+(2Δ/Γ)²), Δ = δ − k·v, k = 2π/λ. Γ est la largeur angulaire et s₀ la saturation.
Pression lumineuse : chaque absorption donne ħk selon le faisceau. L’émission spontanée est aléatoire. La force moyenne d’un faisceau vaut F = ħk R.
Deux faisceaux rouges opposés donnent F(v) = ħk[R(δ−kv)−R(δ+kv)] ≈ −βv pour |kv| ≪ Γ, β = −8ħk²δs₀/[Γ(1+s₀+(2δ/Γ)²)²]. La capture est limitée à environ (Γ/2k)√(1+s₀).
Le recul produit la diffusion D₀ = ħ²k² R_tot(1+η)/2, avec η = 1 en 1D et 1/3 pour une émission 3D isotrope projetée sur l’axe.
L’équilibre donne k_BT = D₀/β = ħΓ(1+η)(1+s₀+(2δ/Γ)²)/(16|δ|/Γ). À faible saturation et η=1, T_D = ħΓ/2k_B. T_r = ħ²k²/(m k_B) ; une raie étroite exige un traitement du recul.
La simulation tire les nombres de photons selon Poisson et applique les impulsions d’absorption et d’émission. La température fluctue donc autour de la valeur analytique. δ > 0 produit un anti-amortissement.
💡 Conseils
À faible intensité, le minimum Doppler est à δ = −Γ/2. Augmenter s₀ accélère le refroidissement mais élargit la raie : T ∝ (1 + s₀ + (2δ/Γ)²)/(2|δ|/Γ).
Au-delà de la vitesse de capture ≈ Γ/2k, l’interaction est faible. Commencez plus froid ou avec un désaccord plus grand.
Modèle à deux niveaux, sans structure hyperfine, état noir ou micromouvement. Ca⁺ nécessite un repompage. Les résultats sont des estimations pédagogiques, pas une expérience.
📚 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
🌀 Refroidissement laser — Un ion dans un piège de Penning
Un faisceau radial refroidit le cyclotron mais peut agrandir le magnétron d’énergie négative. Décalez le faisceau pour centrer l’orbite et inclinez-le pour refroidir aussi l’axe.
Objectif : trois amplitudes sous 10 µm avant 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.
📐 Principes physiques détaillés
Mouvements propres : ω₊ + ω₋ = ωc = qB/m et ω₊ω₋ = ωz²/2 pour le piège quadrupolaire idéal.
Le magnétron possède une énergie totale négative : une friction qui retire l’énergie cinétique agrandit son rayon. Un faisceau radial centré refroidit ω₊ mais chauffe ω₋.
Itano–Wineland : le décalage y_b donne F′ = ∂F/∂y ; γ₊ = (F′−β_rω₊)/(2mΔω), γ₋ = (β_rω₋−F′)/(2mΔω), Δω = ω₊−ω₋. Les deux taux sont négatifs si β_rω₋ < F′ < β_rω₊. Leur somme vaut −β_r/(2m).
Incliner de θ hors du plan radial donne γz = −β sin²θ/(2m) et β_r = β cos²θ.
Le recul limite A_eq = √(D/(−2γ)). L’amplitude suit A(t)² = A₀² exp(2γt) + D[exp(2γt)−1]/(2γ). Sources : Itano et Wineland, PRA 25, 35 (1982) ; Hendricks et al., arXiv:0709.3817.
💡 Conseils
Dans Penning, γ₊ + γ₋ = −β_r/2m ; décaler le faisceau redistribue l’amortissement du cyclotron vers le magnétron.
Modèle à deux niveaux, sans structure hyperfine, état noir ou micromouvement. Ca⁺ nécessite un repompage. Les résultats sont des estimations pédagogiques, pas une expérience.
💡 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.
…
🧩 Nombres magiques et éléments
Questions sur le paysage nucléaire.
🦓 Panorama des pièges
Schémas animés de dispositifs qui stockent ou guident les ions, sans échelle.
Animated sketches, not to scale. Red/blue = electrode polarity (switching with the RF where relevant); the coloured trail is one ion or atom.