Universal description for different types of polarization radiation

Abstract

When a charged particle moves nearby a spatially inhomogeneous condensed medium or inside it, different types of radiation may arise: Diffraction radiation (DR), Smith-Purcell radiation (SPR), Transition radiation (TR), Cherenkov radiation (CR) etc. Along with transverse waves of radiation, the charged particle may also generate longitudinal oscillations. We show that all these phenomena may be described via quite simple and universal approach, where the source of the field is the polarization current density induced inside the medium by external field of the particle, that is direct proof of the physical equivalence of all these radiation processes. Exact solution for one of the basic radiation problems is found with this method: emission of a particle passing through a cylindrical channel in a screen of arbitrary width and permittivity ε(ω) = ε ′ + iε ′′ . Depending on geometry, the formula for radiated energy obtained describes different types of polarization radiation: DR, TR and CR. The particular case of radiation produced by the particle crossing axially the sharp boundary between vacuum and a plasma cylinder of finite radius is also considered. The problem of SPR generated when the particle moves nearby a set of thin rectangular strips (grating) is solved for the arbitrary value of the grating's permittivity. An exact solution of Maxwell's equations for the fields of polarization current density suitable at the arbitrary distances (including the so-called pre-wave zone) is presented. This solution is shown to describe transverse fields of polarization radiation and the longitudinal fields connected with the zeros of permittivity.

Comparison of coherent Smith-Purcell radiation generated by 6.1 MeV electron beam in metal and dielectric lamellar gratings

“…In our theoretical estimations we will follow the recent papers of Karlovets and Potylitsyn [18,19] where authors have shown a simple and elegant method of the Maxwell's equations solution that makes it possible to simulate the characteristics of any type of polarization radiation (including transition radiation, diffraction radiation, CR, SPR) appearing simultaneously. The term "polarization radiation" clearly shows a nature of the radiation that is a polarization of a target (grating) material by electromagnetic field of the traveling charged particle.…”

“…The term "polarization radiation" clearly shows a nature of the radiation that is a polarization of a target (grating) material by electromagnetic field of the traveling charged particle. In the cited articles [18,19] it was shown that the method developed gives well known results for transition radiation, diffraction one, CR and SPR that are just different "kinematic" cases of the polarization radiation.…”

“…Such unusual grating orientation was chosen because we need to satisfy a condition that the radiation wavelength is less than the size of a surface of the grating through which we refract the radiation in order to use simlpe Fresnel coefficients (see further). In cited paper [19] this condition was satisfied in another way, it was assumed that a ≪ λ.…”

“…According to the used method a magnetic field of the polarization radiation H pol (r, ω) in a general case may be written as [18,19]:…”

“…where in order to find the squared absolute value of the radiation electrical field |E R vac | 2 we will use a reciprocity theorem [20] that was applied to the polarization radiation in [18,19].…”