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Neutrinos · D10 · From ionization to an image

Liquid Argon Time Projection Chamber

How does a liquid argon detector use timing to get a track’s third dimension? By timing the drift. Ionization electrons drift toward the wire planes at a known speed, so the time from the start of the event to their arrival tells you how far they traveled: the depth. If the start time or the drift speed is wrong, every depth comes out wrong, and adding more wire views cannot fix that.

Charged particles leave a trail of ionization in a liquid-argon chamber. Drift the freed electrons to wire planes with three orientations, freeze the readout, and then recover the center of charge in each time slice from those same projections.

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

One charge deposit in three projections

The chamber records charge against arrival 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.

The charge maps include Gaussian diffusion and an 8 microsecond electronics response, plus independent zero-mean Gaussian noise in each pixel. The model leaves out ionization fluctuations at the source, field-dependent recombination, space charge, scintillation transport, wire weighting fields, transit between planes, induction deconvolution, dead channels and detailed showers. The three track shapes are set geometrically; they do not simulate neutrino interactions or particle types.

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.

Physics tutorial

Time supplies the missing coordinate.

BackgroundICARUS developed large liquid-argon time projection chambers, and MicroBooNE and ProtoDUNE extended how they are measured and calibrated. The incoming neutrino leaves no glowing track of its own. The charged particles it produces deposit energy in the argon, which creates ionization and scintillation light.

Why it mattersThe three wire orientations give projections across the chamber. The arrival time gives the distance from the anode, but only if you know when the event started and how fast the electrons drift. This Lab looks at that chain of measurements on its own.

Start with the essentials

Focus question
Can the same wire images imply different depths when the clock or speed calibration changes?
One-sentence intuition
Changing the assumed clock moves every recovered depth while the recorded images stay the same, and more projections cannot make up for an unknown event start time.

Core mathematical model

Coordinates and field direction

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 sits at zero and the cathode at 2400 mm. The field points toward the cathode, so electrons drift the other way. All three wire orientations share one effective arrival time at the anode.

Charge produced and lost to 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}

The stopping power is a constant 2.1 MeV/cm, and a fixed fraction of 0.65 of the charge survives recombination. These are prescribed teaching deposits, not a field-dependent calorimetric calibration. The lifetime describes charge lost to attachment during the drift; it does not slow down the electrons that survive.

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

With the multiplier at one, the transverse and longitudinal diffusion coefficients are 12 and 4 square centimeters per second. These are illustrative constants, not field-dependent measurements. The electronics add a fixed Gaussian spread in time, and charge is summed 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\}

Each wire coordinate is measured perpendicular to the wires. The 25 mm pitch is deliberately coarse. The positive signal maps approximate the charge after ideal deconvolution. Real induction signals are bipolar and carry a field response, which is left out here.

Recover one point per time 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

Charge above threshold gives one centroid per plane in each time slice. You need at least two distinct orientations: two projections fit exactly, and a third checks whether they agree. Overlapping branches merge into one 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 show idealized charge projections after deconvolution. The model leaves out weighting-field induction, wire transparency and the raw bipolar pulse shapes.

The true deposit and the recovered centroids are separate

Typical misconceptionThe three-dimensional deposit in the chamber view is reconstructed from the measured pixels.

Better mental modelThe chamber view shows the prescribed source, labeled as such, and how its charge drifts. The separate recovery plot uses only the observed image bins and the assumed calibration. Its optional dashed truth line is there for comparison and is not fed into the reconstruction.

Run the experiment

  1. 01

    Watch the electrons arrive

    Acquire a straight deposit, select Side, then move the playback time from zero until all the charge has arrived.

    What to observe: The electrons drift toward the anode, and the original charged-particle deposit stays where it was. Gold points mark charge that has already been collected. The markers are drawn larger than life, and playback is slowed down.
  2. 02

    Read three views of one record

    Look at the U, V and W images. Pick a time slice by clicking or with the arrow keys.

    What to observe: All three images are projections of the same drifting charge. Their bright features look different because the wires point in different directions, not because they show three separate events.
  3. 03

    Remove the clock

    Switch off Known event start, then switch it back on and change the assumed trigger offset.

    What to observe: Without the event start, the absolute depth cannot be determined. Changing the assumed start moves the reconstructed depth, but every measured pixel stays the same.
  4. 04

    Change purity and geometry

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

    What to observe: Attachment leaves less charge to collect. When several tracks share a time slice, the recovered center of charge can fall between them, and it should not be called an individually recovered track.

Related experiments and articles

Continue exploring

How detectors see a neutrino

A neutrino leaves only light, charge or a pair of signals close in time. How does each detector turn that into a direction, an energy or a source?

  1. LabReactor Antineutrino CoincidenceSelect prompt and delayed signals against accidental pairs.
  2. LabCherenkov Light & Detector RingsTurn charged-particle geometry into a recorded light pattern.
  3. You are hereLiquid Argon Time Projection ChamberTurn electron arrival times and wire projections into calibrated slice centroids.
  4. LabIceCube: From Sensor Hits to a TrackInfer a track direction from the recorded sensor times.
  5. LabSupernova Neutrino Burst ObservatoryScan a frozen burst record, then inspect one interaction at the optical timescale.
  6. LabNeutrino Sky Search ObservatorySearch frozen neutrino directions and compare a local hotspot with paired finite-grid background trials.

Neutrinos · Reading path

Make a source and test its journey

Articles on this path that use this experiment, followed by the other experiments they suggest.

  1. ArticleDUNE: what detailed argon images and a long baseline can answer
  2. LabLong-Baseline CP Observatory
  3. LabNeutrino Flavor Propagation

Neutrinos · Reading path

Follow the measurement chain

Articles on this path that use this experiment, followed by the other experiments they suggest.

  1. ArticleWater, scintillator and argon: what does each detector see?
  2. LabCherenkov Light & Detector Rings
  3. LabReactor Antineutrino Coincidence
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