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Sandbox Physics

Neutrinos · D10 · From ionization to an image

Liquid Argon Time Projection Chamber

Follow charged-particle deposits inside a liquid-argon chamber. Drift their electrons to three wire orientations, freeze the readout, then recover slice centroids from those same projections.

Interactive modelLiquid Argon Time Projection Chamber
Electron drift speed—\text{—}
Charge retained—\text{—}
Recovered slices—\text{—}

ONE DEPOSIT · THREE PROJECTIONS

The chamber writes in charge and time.

U 60∘60^\circ

V −60∘-60^\circ

W 0∘0^\circ

Simulated charge after ideal deconvolution; U and V are not raw induction currents. Colors use a common logarithmic display scale. Linear signed pixel charges remain in the exported record; three maps do not mean three times the collected charge.

—\text{—}

Recover the charge centroids

A point is one time-slice charge centroid, not an identified particle. Coincident branches merge; a centroid may lie between tracks. Dots outside the chamber expose a wrong assumed clock or speed and are not clipped into the physical volume.

Exact transport, slice values & model assumptions
Initial free charge—\text{—}
Expected surviving charge—\text{—}
Maximum transverse spread—\text{—}

The active region is 2.4 m deep, 1.8 m high and 2.8 m long. Wire spacing is 25 mm and time bins are 16.875 microseconds. The readout starts 100 microseconds before the event. Three idealized orientations share the same effective anode and arrival time; actual separated-plane transit is omitted. Display markers are enlarged. Drift at 87 K follows the ICARUS low-field parameterization used in LArSoft, restricted to 300–600 V/cm.

Charge maps integrate Gaussian diffusion and an 8 microsecond electronics response, then add independent zero-mean Gaussian pixel noise. Source ionization fluctuations, field-dependent recombination, space charge, scintillation transport, wire weighting fields, interplane transit, induction deconvolution, dead channels and detailed showers are omitted. The three topologies are prescribed geometry, not neutrino interaction or particle-type simulations.

Recovery keeps pixels above three noise standard deviations or 20 electron equivalents and requires at least 1000 electron equivalents per plane per slice (or 20 noise scales). Thresholds, finite bins and overlapping deposits bias centroids; the algorithm does not infer individual correspondence or a confidence region. CSV includes every observed and expected pixel, source deposit and the current recovered centroids.

CONTINUE EXPLORING

From flavor to evidence

Propagation predicts a flavor probability. Which parts of the experiment turn an interaction into a usable record?

Physics tutorial

Time supplies the missing coordinate.

BackgroundICARUS developed large liquid-argon time projection chambers; MicroBooNE and ProtoDUNE extended their measurement and calibration. A neutrino is not a luminous incoming track: charged secondary particles deposit energy, producing ionization and scintillation.

Why it mattersThree wire orientations supply transverse projections. Arrival time supplies distance from the anode only if the event start and drift speed are known. This Lab isolates that measurement chain.

Start with the essentials

Focus question
Can the same wire images imply different depths when the clock or speed calibration changes?
One-sentence intuition
The recorded image stays fixed while an assumed clock shifts every recovered depth. More projections cannot replace a missing event start time.

Core mathematical model

Coordinate and field convention

E=Ex^,ve=−vdx^,t−t0=xvd\mathbf E=E\hat{\mathbf x},\quad\mathbf v_e=-v_d\hat{\mathbf x},\quad t-t_0=\frac{x}{v_d}

The anode is at zero and the cathode at 2400 mm. The positive field points towards the cathode; electrons drift in the opposite direction. All three wire orientations use an effective common anode time.

Charge generation and attachment

Q0=0.65 ΔE23.6 eV,Q(t)=Q0e−t/τQ_0=\frac{0.65\,\Delta E}{23.6\,\mathrm{eV}},\qquad Q(t)=Q_0e^{-t/\tau}

Constant stopping power is 2.1 MeV/cm and recombination survival is fixed at 0.65. These are prescribed teaching deposits, not a field-dependent calorimetric calibration. Lifetime describes attachment during drift; it does not slow the surviving electrons.

Diffusion and electronics

σT2=2DTt,σt2=2DLtvd2+(8 μs)2\sigma_T^2=2D_Tt,\qquad\sigma_t^2=\frac{2D_Lt}{v_d^2}+(8\,\mathrm{\mu s})^2

At multiplier one, transverse and longitudinal diffusion coefficients are 12 and 4 square centimeters per second. They are illustrative constants, not field-dependent measurements. The electronics add a fixed Gaussian temporal response. Charge is integrated over finite bins.

Three charge projections

wk=ysin⁡θk+zcos⁡θk,θk∈{−60∘,0,60∘}w_k=y\sin\theta_k+z\cos\theta_k,\qquad\theta_k\in\{-60^\circ,0,60^\circ\}

Wire coordinate is perpendicular to the wire direction. The 25 mm pitch is intentionally coarse. Positive signal maps approximate charge after ideal deconvolution; actual induction signals are bipolar and have a field response omitted here.

Recover a slice, not every particle

x^=vcal(t−t0,cal),(y^,z^)=arg⁡min⁡y,z∑k(wˉk−ysin⁡θk−zcos⁡θk)2\hat x=v_{\mathrm{cal}}(t-t_{0,\mathrm{cal}}),\qquad (\hat y,\hat z)=\arg\min_{y,z}\sum_k(\bar w_k-y\sin\theta_k-z\cos\theta_k)^2

Above-threshold charge gives one centroid per plane and time slice. At least two distinct orientations are needed. Two projections fit exactly; a third checks consistency. Overlapping branches are merged into a centroid and may fail that check. The residual is not a confidence interval.

Common difficulties

A readout projection is not a photograph

Typical misconceptionEach positive wire image is the raw current on an induction plane.

Better mental modelU and V are idealized charge projections after deconvolution. This model omits weighting-field induction, wire transparency and raw bipolar pulse shapes.

Truth and recovered centroids have different jobs

Typical misconceptionThe 3D deposit is reconstructed from the measured pixels.

Better mental modelThe apparatus shows the labeled prescribed source and its transport. The separate recovery plot uses only observed image bins and assumed calibration. Its optional dashed truth reference is not an inversion input.

Run the experiment

  1. 01

    Watch the electrons arrive

    Acquire a straight deposit, select Side, then scrub from zero to complete arrival.

    What to observe: Electrons drift towards the anode while the original charged-particle deposit stays in place. Gold points mark charge already collected. Marker radii are enlarged; time playback is stretched.
  2. 02

    Read three views of one record

    Inspect U, V and W images. Select a time slice by click or arrow keys.

    What to observe: The three images contain projections of the same transported charge. Their bright features differ with wire orientation, rather than representing three separate events.
  3. 03

    Remove the clock

    Switch off Known event start, then restore it and change the assumed trigger offset.

    What to observe: Without the event start, absolute depth is undetermined. Changing an assumed start shifts reconstructed depth while leaving every measured pixel unchanged.
  4. 04

    Change purity and geometry

    Try Impure argon and Branched deposit; remove one or two projections.

    What to observe: Attachment reduces surviving charge. Multiple tracks sharing a time slice can produce a center of charge between tracks; it must not be called an individually recovered trajectory.