www.nature.com/scientificreports OPEN Ultra‑monochromatic far‑infrared Cherenkov difraction radiation in a super‑radiant regime P. Karataev1*, K. Fedorov1,2, G. Naumenko2, K. Popov2, A. Potylitsyn2 & A. Vukolov2 Nowadays, intense electromagnetic (EM) radiation in the far‑infrared (FIR) spectral range is an advanced tool for scientifc research in biology, chemistry, and material science because many materials leave signatures in the radiation spectrum. Narrow‑band spectral lines enable researchers to investigate the matter response in greater detail. The generation of highly monochromatic variable frequency FIR radiation has therefore become a broad area of research. High energy electron beams consisting of a long train of dense bunches of particles provide a super‑radiant regime and can generate intense highly monochromatic radiation due to coherent emission in the spectral range from a few GHz to potentially a few THz. We employed novel coherent Cherenkov difraction radiation (ChDR) as a generation mechanism. This efect occurs when a fast charged particle moves in the vicinity of and parallel to a dielectric interface. Two key features of the ChDR phenomenon are its non‑invasive nature and its photon yield being proportional to the length of the radiator. The bunched structure of the very long electron beam produced spectral lines that were observed to have frequencies upto 21 GHz and with a relative bandwidth of 10–4 ~ 10–5. The line bandwidth and intensity are defned by the shape and length of the bunch train. A compact linear accelerator can be utilized to control the resonant wavelength by adjusting the bunch sequence frequency. A fast particle passing by an atom interacts with the electron shell forming a dipole that oscillates, inducing polarization currents that are changing in time 1. Tose currents give rise to an entire family of polarization radia- tion mechanisms that have been widely applied for both charged particle beam diagnostics and the generation of intense EM radiation beams, e.g. transition radiation2,3, difraction radiation4,5, Smith-Purcell radiation6–9, and parametric X-ray radiation 10. More recently it has been proposed to use plasmons generated by the feld of passing particle in a thin conducting material to reinforce polarization radiation photon yield at well-defned frequencies11,12. Classic Cherenkov Radiation (ChR) is a member of the polarization radiation family and appears whenever a fast charge particle moves in a medium with the speed higher than the speed of light inside that medium. In 1934 it has been discovered experimentally by Pavel Cherenkov13, who was awarded the Nobel Prize in 1958. Te radiation propagates radially away from the particle trajectory at a classical Cherenkov angle defned as: vphoton 1 cos(θch) = = , (1) velectron βn where vphoton = c/n is the speed of light inside the medium, β = v/c is the speed of the particle, v = velectron, in units of the speed of light in vacuum, c, and n is the refractive index. Tamm and Frank have developed a theoretical approach to describe the classical ChR characteristics14. Recently more advanced ChR mechanisms have been considered for intense radiation generation including excitation of structural materials such as metamaterials15, gratings8,9,16, or photonic crystals17,18. For a considerably long time it was assumed that a charged particle must physically interact with the medium to generate ChR photons. Modern accelerator facilities produce ultra-relativistic electrons. Any medium will be polarised if it is placed at an impact parameter (h – the shortest distance between the particle trajectory and the medium19,20) smaller than the efective ultra-relativistic electron feld radius defned as γ h ≤ , (2) 2π 1John Adams Institute at Royal Holloway, University of London, Egham TW20 0EX, Surrey, UK. 2National Research Tomsk Polytechnic University, Lenin Ave. 30, 634050 Tomsk, Russia. *email: [email protected] Scientifc Reports | (2020) 10:20961 | https://doi.org/10.1038/s41598-020-76996-1 1 Vol.:(0123456789) www.nature.com/scientificreports/ Figure 1. Schematic layout of the experimental installation. Te pre-bunched 6.1 MeV electron beam is generated in a microtron accelerator (5) (see “Methods”). A dipole magnet (4) directs the beam into the experimental area. Two quadrupole magnet doublets (3) shape the beam in the vicinity of the target (2). Te target itself is a Tefon triangular prism made such that its output interface is normal to the Cherenkov direction to minimize the refraction defection shown in the top insertion. Te radiation extracted from the target is fed into a multi-octave horn-antenna (1) (see “Methods”). Te radiation feld induced currents were fed into a high- speed spectrum analyser (see “Methods”) which monitors the radiation spectrum from every train shot-by-shot. where γ is the charged particle Lorentz-factor and λ is the radiation wavelength. Tis parameter can reach mac- roscopic values, e.g. for γ = 12 and λ = 28.5 mm, any object placed within 54 mm will interact with the charged particle feld. If a fast charged particle moves in the vicinity of and parallel to a dielectric interface, its feld will polarize every atom along the medium surface generating photons propagating into the medium (Fig. 1 top insertion). Since the particle speed is higher than the speed of light inside the medium, the radiation propagates at a classical Cherenkov angle defned by the ratio of the velocities resulting in Eq. (1). Te spectral-angular properties of the radiation are signifcantly diferent from classical ChR, e.g. the fnite boundaries of the radiator cause difraction, narrowing down the radiation cone and the non-zero impact parameter introduces additional frequency dependence19,20. Terefore, a new name was introduced – Cherenkov Difraction Radiation (ChDR)19. Incoherent ChDR, which is a linear function in relation to the number of electrons in a single bunch, has recently been directly observed at the University of Cornell 19. Tis experiment has demonstrated fundamental features of the ChDR phenomenon including high directionality in a narrow solid angle and an exponential decrease of intensity as a function of the impact parameter. Coherent radiation is generated at a wavelength comparable to or larger than a single bunch length 21, i.e. when all electrons emit radiation more or less in phase. Te emission of radiation in the presence of the feld from neighbouring particles results in coherent enhancement, which makes the intensity be proportional to the square of the bunch population. A super-radiant emission appears when a train of equally spaced bunches emits radiation coherently. Assum- ing a train moving in the vicinity of and parallel to an interface with known dielectric properties as is shown in Fig. 1, a general expression for radiation intensity is21,22 dWtrain 2 dWe = Ne Fb(ω, σ )Gtrain ω, fb , (3) dω dω where Ne is the number of particles in a single bunch, ω = 2πc/λ is the photon frequency, fb is the bunch sequence frequency, σ is the rms longitudinal beam size, dWe/dω is the spectrum generated by a single particle (for calcula- tions we used the model derived by Konkov and Shevelev 24, see “Methods”). Te longitudinal bunch form factor, Fb, is defned as a Fourier transform of the longitudinal particle distribu- tion, ρ, in a bunch21. For a Gaussian profle 2 2 2 ∞ ωz σ ω −i − 2 Fb(ω, σ ) = ∫ ρ(z, σ)e c dz = e c . (4) −∞ Te train form factor, Gtrain, is defned as a superposition of the radiation felds generated by a series of con- secutive bunches. Assuming that each bunch out of Nb bunches generates the same amplitude, the train form factor is22,23 2 −i ω −i 2ω Gtrain ω, fb = 1 + e fb + e fb + ... N ω 2 − b 2 Nbω i f sin (5) 1 − e b 2fb = = −i ω fb 2 ω 1 − e sin 2 fb As a target we considered a triangular Tefon prism. Te radiation generated inside the prism, propagates towards the outer interface, and refracts out towards the observation point (see Fig. 1). ChDR spectral-angular 0 distribution is illustrated in Fig. 2a. Te Cherenkov angle for n = 1.45 is θch = 46.5 which coincides with the Scientifc Reports | (2020) 10:20961 | https://doi.org/10.1038/s41598-020-76996-1 2 Vol:.(1234567890) www.nature.com/scientificreports/ Figure 2. Teoretical calculations. (a) Te spectral-angular distribution of Cherenkov difraction radiation calculated for a wavelength of 28.5 mm for a single 6.1 MeV electron passing at an impact parameter of 10 mm away from the Tefon target. Te vertical axis is the photon linear frequency f = ω/2π. Te horizontal axis is the polar observation angle. Te maximum of the angular distribution corresponds to the Cherenkov angle 0 (θch = 46.5 shown with a red arrow) defned by Eq. (1) and refracted due to Snell’s law (for Tefon n = 1.45 in the frequency range of interest); (b) Te red line is the normalized form factor of coherent super-radiant 4 Cherenkov difraction radiation generated by a train of Nb = 10 bunches (6.3 mm long) spaced by 114 mm. Te green dashed line is the envelope function defned by a single bunch longitudinal dimension Eq. (4). Te train generates a series of monochromatic lines starting from a fundamental frequency of f1 = 2.63 GHz representing the frequency of the accelerating cavity used to boost the energy into the electron beam. Te lines are spaced in 2.63 GHz intervals and the intensity goes down for higher harmonics due to the decrease in coherency of each individual bunch. Te insertion in Fig. 2b shows the zoomed in section of the 4th intra-train resonance order. Te width of the monochromatic line is defned as a distance from the principal maximum to the frst minimum and for each line is given as Δf/fk = 1/kNb, where k is the intra-train resonance order, or Δf/f1 = 1/Nb.