Water Cherenkov Detector

What is modelled

Light travels more slowly in water than in empty space, at about three quarters of its vacuum speed. A fast charged particle can outrun it, and then it leaves a cone of light behind it, like the bow wave of a boat or the boom of an aircraft. The cone has a fixed angle that depends only on the speed of the particle and the refractive index, so the angle measures the speed. The number of photons grows with the square of the sine of that angle. A particle slower than light in the medium makes no light at all, which is why a heavy particle needs much more energy than an electron to make a ring. Detectors such as Super-Kamiokande look at the ring on thousands of light sensors on the walls and use its shape to tell electrons from muons.

Equations

• Threshold: β > 1 / n, kinetic energy Tthr = m c2 (1 / √(1 − 1 / n2) − 1).
• Cone angle cosθc = 1 / (n β), at most 41.2 degrees in water.
• Frank-Tamm: d2N / (dx dλ) = 2 π α sin2θc / λ2, about 330 photons per centimetre between 300 and 600 nm.
• Ring radius on an end cap at distance D: r = D tanθc.

Checks run in the page

• The threshold energy by a search against its formula.
• The cone angle from a numerical wavelet construction.
• The photon yield with a colour-dependent index against the constant-index formula.
• The ring radius and the barrel hit position from traced photons.

Honest simplifications

A constant energy loss of 2 MeV per centimetre, a straight track with no scattering, no light absorption or scattering in the water, no showers from electrons, a simple dispersion law for the index and a single number for sensor coverage and efficiency. A real detector needs a full simulation of the particle and the light, so the counts here are only an order of magnitude.

• Press Muon just above threshold and see how little light and how short a track a slow muon makes.
• Press Electron at 30 MeV and compare its ring with the 1 GeV muon.
• Lower the refractive index with the slider and watch the thresholds on the last graph move up.