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Beam and chamber
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The science
How a cloud chamber shows a particle
A charged particle crossing a gas ionises atoms along its path. In a chamber filled with supersaturated vapour, each ion becomes the seed of a tiny droplet, so the track appears as a thin line of fog that lasts for a moment. The density of droplets follows the ionisation, which for a fast particle is given by the Bethe-Bloch formula -dE/dx = K z² (Z/A) (1/β²) [ ½ ln(2 mec² β²γ² Tmax / I²) - β² ] with K = 0.307 MeV cm²/mol and mean excitation energy I of the gas. The loss falls as 1/β² at low speed, has a minimum near βγ ≈ 3.5 (a "minimum-ionising" muon in air loses about 1.8 MeV cm²/g, roughly 2.2 keV per cm at 1 atm) and rises slowly again; slow particles end in a dense Bragg peak, so an alpha track is short (about 4 cm in air) and thick.
Curvature in a magnetic field
The Lorentz force bends the path into a helix about the field. The radius of the circle in the plane perpendicular to B is r = p⊥ / (0.2998 q B) in metres for p in GeV/c and B in tesla, so momentum can be read directly from the track curvature and the sign of the charge from the sense of the turn. Low-energy electrons spiral because they lose momentum as they go; a dip angle makes the helix drift along the field (visible in 3D).
Honest simplifications
The simulation integrates the path with the true Lorentz rotation, Bethe-Bloch energy loss (smoothly continued to the Bragg peak, no shell or density corrections, no effective-charge reduction for slow alphas) and Highland multiple scattering. Electrons lose energy by ionisation only, with no bremsstrahlung, no delta-ray branches and no showers; the cosmic-ray mix and its spectra are illustrative, not measured fluxes. Droplet growth, gas turbulence and the chamber's sensitive time are not modelled.
Model checks (run in the page): the integrated range of a 5.49 MeV alpha in air against the Bragg-Kleeman rule; the muon stopping power at the Bethe minimum against the tabulated value; and a measured track radius from a three-point circle fit against p/(0.2998 q B).