Cherenkov radiation has been known since 1934, when Pavel Cherenkov noticed a blue glow in liquids exposed to gamma radiation. The theory was provided by Igor Tamm and Ilya Frank, and the three shared the Nobel Prize. Since then, the effect has become a working tool, from particle detectors to astrophysics. However, coherent enhancement of Cherenkov radiation, where the contributions of many particles add up not randomly but synchronously, was long 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. Alongside this work on the archive are studies on beam diagnostics via coherent diffraction radiation, generation of terahertz pulses in dielectric waveguides, and ultrafast detectors. All of them, like this paper, seek ways to extract information about the beam from its radiation, but they remain in the millimeter and terahertz ranges. New-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 path to coherent Cherenkov radiation in the optical and ultraviolet.
The authors built an analytical model of coherent Cherenkov radiation for three electron bunch shapes: Gaussian, super-Gaussian, and cylindrical with constant density. The medium is helium at normal conditions, and its dielectric permittivity is described by a Lorentz model with the six strongest transitions from the ground state (NIST data). The refractive index of helium is very close to unity (difference on the order of 10⁻⁵), which is critical for transverse coherence. They calculated energy spectra through the side surface and the end face of a cylinder surrounding the beam path. They accounted for competing processes: transition radiation (negligible for a long medium) and bremsstrahlung (estimated and shown to have a much narrower angular distribution than Cherenkov). Formulas for the coherence factor were obtained via the Fourier transform of the beam density distribution.
For a beam with energy 1 GeV (gamma factor 2000), electron number 10⁵, radius 20 μm, and length 1 μm in helium, coherent enhancement of Cherenkov radiation extends to photon energies around 2 eV (red light) for the Gaussian shape. For a cylindrical beam with constant density, it extends to 10 eV (near ultraviolet). Super-Gaussian beams fall in between: with power index 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 image. The spectra of cylindrical and super-Gaussian beams oscillate, with oscillation periods related to the beam length and radius. This allows recovering the bunch geometry 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 gives a contribution of the same order 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.
This work stands somewhat apart from its archive neighbors. Most of them use Cherenkov or diffraction radiation for beam diagnostics in the terahertz range, where beams have millimeter sizes. Here, for the first time, it is shown that plasma accelerators with their micron-scale and femtosecond-scale beams can produce coherent Cherenkov radiation in the optical and ultraviolet. The key trick is choosing a medium with a refractive index very close to unity: this increases the transverse coherence length and compensates for the large difference between the beam radius and length. Such an approach is not found among neighbors, which work with dielectrics or vacuum. The result provides a new tool for noninvasive diagnostics of the shape and size of ultracompact beams.
Experimental verification of the predictions is possible on existing plasma accelerators, for example, with a plasma photocathode. It would require a helium target a few tens of centimeters long and a ring detector for the optical range. If the spectrum matches the calculated one, this would become a new method for measuring the beam length and radius with femtosecond and micron resolution. Further, one could study more complex beam shapes, including those with periodic density modulation, which could make the radiation narrowband. Other gases with different refractive indices could be used to tune the range.
The results will affect beam diagnostics in plasma accelerators, the development of compact optical and ultraviolet radiation sources, and the physics of interaction of dense electron bunches with matter.
Conduct an experiment on a plasma accelerator with a helium target and a ring photodetector; compare the measured spectrum with the calculated one for different bunch shapes.
For beam and accelerator physics, a key unsolved problem is noninvasive diagnostics of ultrashort bunches. Existing methods (transverse deflection, transition radiation) either destroy the beam or are limited in resolution. Coherent Cherenkov radiation in the optical range could provide simultaneous measurement of length and radius without perturbing the beam.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
This study examines coherent Cherenkov radiation from ultracompact electron beams produced by plasma accelerators as they travel through a gaseous medium. An analytical model is developed for three beam shapes (Gaussian, super-Gaussian, and cylindrical), and the radiation spectra are calculated in the optical and near-UV ranges. It is shown that coherent enhancement depends on the beam shape and can reach photon energies up to 10 eV.
Where its strength is
The work demonstrates the feasibility of coherent Cherenkov radiation in the optical range, thanks to the extreme parameters of beams from plasma accelerators. The analytical model, which accounts for the beam shape and the realistic dielectric permittivity of helium, allows estimation of the spectra and reveals the role of transverse coherence.
Where it could go next
Worth trying
Why this may matter
Advancing diagnostic methods for ultrashort beams and creating compact sources of coherent radiation in the optical and UV ranges.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.52, against a usual 0.64. It looks like few have drilled nearby.
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.