# Cherenkov Radiation & Mach Cone

When a charged particle exceeds the phase speed of light c/n in a medium, it emits a coherent blue shock-cone. Slide the speed and index to see the cone form, vanish below threshold, and match the acoustic Mach cone.

> Canonical page: https://elysiatools.com/en/visualizations/cherenkov-radiation

- **Category:** Physics

## Overview

Interactive Cherenkov radiation visualization. When a charged particle moves through a dielectric medium faster than the phase speed of light c/n, the spherical wavefronts it emits can no longer keep up and pile up into a coherent blue shock-cone — the electromagnetic analogue of a sonic boom. The cone half-angle satisfies cos θ = 1/(n·β) where β = v/c, and radiation exists only above the threshold n·β > 1 (i.e. v > c/n). Three visualization panels: (1) Main animated scene of a charged particle (e⁻) flying left-to-right through the medium, emitting expanding spherical wavelets; when above threshold these wavelets build the characteristic blue Cherenkov cone trailing the particle, with the live angle arc θ marked; below threshold the wavelets quench and a sub-threshold banner appears. (2) Cone Angle vs Speed plot tracing cos θ = 1/(nβ) for the current medium with the threshold β_min = 1/n marked, ghost curves for other media (air/water/glass/diamond) for comparison, and the live operating point. (3) Emission Spectrum I(λ) based on the Frank-Tamm formula I ∝ (1 − 1/n²β²)/λ² over the visible band (380–700 nm), rendered with a wavelength-to-RGB color gradient showing why the glow is blue-dominated. Physics: Cherenkov angle cos θ = 1/(nβ), threshold β_min = 1/n, maximum angle θ_max = arccos(1/n) as v → c, Frank-Tamm factor (1 − 1/n²β²). Acoustic Mach-cone analogy: sin μ = 1/Ma is mathematically isomorphic to cos θ = 1/(nβ). Adjustable parameters: particle speed v/c (0–1.5), refractive index n (1.0–2.5), medium preset (Air n=1.0003, Water n=1.333, Glass n=1.52, Diamond n=2.417). Four scenario presets: Reactor Pool (water β=0.95, classic blue glow), Sub-threshold (water β=0.70, cone collapses), In Glass (glass β=0.90, wide cone), Mach Cone (supersonic source for the acoustic analog). Real-time statistics: n·v/c ratio, cone angle θ, threshold β, regime (sub-threshold / Cherenkov / Mach). Educational content covers Cherenkov radiation theory (Heaviside 1888, Cherenkov 1934, Tamm-Frank 1958 Nobel), the Mach cone mathematical isomorphism, and applications (RICH detectors at LHCb/ALICE for π/K/p identification, IceCube and Super-Kamiokande neutrino telescopes, reactor pool glow from Compton electrons). Multi-language support (zh, en, es, fr, de, ru, pt).

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