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Register a new userCherenkov radiation and emission of surface polaritons from charges moving paraxially outside a dielectric cylindrical waveguide
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We investigate the radiation from a charged particle moving outside a dielectric cylinder parallel to its axis. It is assumed that the cylinder is immersed into a homogeneous medium. The expressions are given for the vector potential and for the electric and magnetic fields. The spectral distributions are studied for three types of the radiations: (i) Cherenkov radiation (CR) in the exterior medium, (ii) radiation on the guided modes of the dielectric cylinder, and (iii) emission of surface polaritons. Unlike the first two types of radiations, there is no velocity threshold for the generation of surface polaritons. The corresponding radiation is present in the spectral range where the dielectric permittivities of the cylinder and surrounding medium have opposite signs. The spectral range of the emitted surface polaritons becomes narrower with decreasing energy of the particle. The general results are illustrated for a special case of the Drude model for dispersion of the dielectric permittivity of the cylinder. We show that the presence of the cylinder may lead to the appearance of strong narrow peaks in the spectral distribution of the CR in the exterior medium. The conditions are specified for the appearance of those peaks and the corresponding heights and widths are analytically estimated. The collective effects of particles in bunches are discussed.
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It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz transformations. The electrodynamics problem can then be treated within a single inertial frame description. To evaluate radiation fields from moving charged particles we need their velocities and positions as a function of the lab frame time t. The relativistic motion of a particle in the lab frame is described by Newtons second law corrected for the relativistic dependence of the particle momentum on the velocity. In all standard derivations the trajectories in the source part of the usual Maxwells equations are identified with the trajectories $vec{x}(t)$ calculated by using the corrected Newtons second law. This way of coupling fields and particles is considered correct. We argue that this procedure needs to be changed by demonstrating a counterintuitive: the results of conventional theory of radiation by relativistically moving charges are not consistent with the principle of relativity. The trajectory of a particle in the lab frame consistent with the usual Maxwells equations, is found by solving the dynamics equation in manifestly covariant form, with the proper time $tau$ used to parameterize the particle world-line in space-time. We find a difference between the true particle trajectory $vec{x}(t)$ calculated or measured in the conventional way, and the covariant particle trajectory $vec{x}_{cov}(t)$ calculated by projecting the world-line to the lab frame and using t to parameterize the trajectory curve. The difference is due to a choice of convention, but only $vec{x}_{cov}(t)$ is consistent with the usual Maxwells equations: therefore, a correction of the conventional synchrotron-cyclotron radiation theory is required.
It is shown that in some special cases the Cherenkov radiation from a charged particle moving along the axis of cylindrical waveguide filled with a semi-infinite material consisting of dielectric plates alternated with vacuum gaps is many times stronger than that in the waveguide filled with semi-infinite solid dielectric without vacuum gaps.
We propose a new type of axisymmetric dielectric target which effectively concentrates Cherenkov radiation (CR) generated in the bulk of the material into a small vicinity of focus point. It can be called the axicon-based concentrator for CR. A theoretical investigation of radiation field produced by a charge moving through the discussed radiator is performed for the general case where a charge trajectory is shifted with respect to the structure axis. The idea of dielectric target with specific profile of the outer surface was presented and developed in our preceeding papers. However, contrary to the previous configuration of such a target (which was investigated for both centered and shifted charge trajectory), the current version allows efficient concentration of CR energy from relativistic particles, making this device extremely prospective for various applications.
We study the angular distribution of the radiation from a relativistic charged particle uniformly rotating along an equatorial orbit around a dielectric ball. Earlier it was shown that for some values of the problem parameters and in the case of weak absorption in the ball material, the radiation intensity on a given harmonic can be essentially larger than that for the same charge rotating in the vacuum or in a homogeneous transparent medium having the same real part of dielectric permittivity as the ball material. The generation of such high power radiation is a consequence of the constructive superposition of electromagnetic oscillations of Cherenkov radiation induced near the trajectory of the particle and partially locked inside the ball. The angular distribution of the number of the emitted quanta is investigated for such high power radiation. It is shown that the radiation is mainly located in the angular range near the rotation plane determined by the Cherenkov condition for the velocity of the charge image on the ball surface. The numerical analysis is given for balls made of strontium titanate, melted quartz and teflon in the gigahertz and terahertz frequency ranges.
A problem of diffraction of a symmetrical transverse magnetic mode $ text{TM}_{0l} $ by an open-ended cylindrical waveguide corrugated inside is considered. A depth and a period of corrugations are supposed to be much less than the wavelength and the waveguide radius. Therefore a corrugated waveguide wall can be described in terms of equivalent boundary conditions, i.e. a corresponding impedance boundary condition can be applied. Both vacuum case and the case of uniform dielectric filling of the waveguide is considered. The diffraction problem is solved using the modified tayloring technique in Jones formulation. Solution of the Wiener-Hopf-Fock equation of the problem is used to obtain an infinite linear system for reflection coefficients, the latter can be solved numerically using the reduction technique.
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