The blue glow in water around a nuclear reactor is light born when a charged particle outruns light in that medium. The effect was discovered by Pavel Cherenkov in 1934, with the theory provided by Igor Tamm and Ilya Frank. Since then, Cherenkov radiation has become a workhorse tool, from particle detectors to astrophysics. But until now, its coherent enhancement, where the contributions of many particles add up in sync, like voices in a choir rather than the noise of a crowd, has been limited to the terahertz range. The reason lies in beam sizes: millimeter-scale radii and picosecond durations prevented the phases of individual electrons from matching at high frequencies.
Next-generation plasma accelerators promise beams with previously unattainable parameters: energies up to 10 GeV, durations of a few femtoseconds, and transverse sizes of tens of micrometers. This opens the door to coherent Cherenkov radiation in the optical and ultraviolet. The authors of the new work built an analytical model for three electron bunch shapes: Gaussian, super-Gaussian, and cylindrical with constant density. The medium is helium at normal conditions, whose refractive index is very close to unity (difference on the order of 10⁻⁵).
For a beam with an energy of 1 GeV (gamma factor 2000), an electron number of 10⁵, a radius of 20 μm, and a length of 1 μm in helium, coherent enhancement extends to photon energies around 2 eV (red light) for the Gaussian shape. For a cylindrical beam with constant density, it reaches 10 eV (near ultraviolet). Super-Gaussian beams fall in between: with a power index of 4, up to 4 eV; with 10, up to 7 eV; with 40, almost like the cylinder. The difference is explained by sharp density edges: they produce high-frequency components in the Fourier transform. The spectra of cylindrical and super-Gaussian beams oscillate, with oscillation periods linked to the bunch length and radius. This allows the bunch geometry to be reconstructed from the spectrum.
The photon spectrum on a ring detector (radii 1–2 mm) shows that the coherent part exceeds the incoherent part by orders of magnitude. Bremsstrahlung from a 30 cm helium target contributes at the same level as the minimum coherent Cherenkov signal, but its angular distribution is concentrated in a cone of 1/γ ≈ 0.5 mrad, whereas the Cherenkov angle is about 8.7 mrad, so they can be separated.
Previously, coherent Cherenkov radiation was observed only in the terahertz and microwave ranges, because beams were too large. Now it is shown that ultracompact relativistic beams in a gas with a refractive index close to unity produce coherent Cherenkov radiation in the optical and near ultraviolet. This is a new tool for noninvasive diagnostics of the shape and size of electron bunches in plasma accelerators, and potentially for compact UV sources. The chorus of electrons singing in unison becomes audible at new frequencies.
Cherenkov radiation is often called 'blue glow,' but in this case it can extend into the ultraviolet, invisible to the eye. For a beam with energy 1 GeV, the Cherenkov angle in helium is only 0.5 degrees, so the radiation goes almost strictly forward.
In Arthur C. Clarke's novel 'The Light of Other Days,' Cherenkov radiation is used to detect particles in water; the idea of coherent enhancement from dense bunches echoes the description of radiation from relativistic streams in space.