Radiation of a charge in dielectric concentrator for Cherenkov radiation: Off-axis charge motion

Abstract

A theoretical investigation of radiation field produced by a charge moving through the dielectric concentrator for Cherenkov radiation is performed for the general case where a charge trajectory is shifted with respect to the target axis. The idea of dielectric target with specific profile of the outer surface was presented and investigated in our previous papers for the symmetric case. Here we show how non-symmetric field components generated in the bulk of target affect field distribution near the focus where strong concentration of the energy occurs. Possible applications of this target are discussed. arXiv:1904.05188v3 [physics.acc-ph]

Wakefields in Hollow Channel of Magnetized Plasma

“…This is probably a pole singularity which we are seeking for. Further we will perform EM field calculations for gaussian bunch (4). Therefore in order to observe the contribution of this pole in the EM field, the length of the bunch σ should be chosen small enough so that ω σ will be of order or less then the pole singularity frequency.…”

“…First, let us consider the area (1), 0 < ρ < b. As it is known (see, for example, [4]), self-field of a moving charge (this is an incident field for our boundary problem) can be written in the following form:…”

“…where A and B are unknown constants, I 0 is a modified Bessel function. Note that while deriving (9) we have utilized the following facts: E ω z and H ω z in vacuum satisfy the modified Bessel equation of the 0-th order and scattered field should be free of singularity for ρ → 0 [4]. Similar considerations lead to the following representation in the region outside the plasma layer, area (3), ρ > a:…”

Radiation of a charge moving along the boundary of dielectric prism

“…First of all, we remind the Straton-Chu formulas (known as well as "aperture integrals") in a form convenient for our researches [5][6][7][8][9]. According to them the Fourier transform of electric field can be written in the following general form (we use Gaussian system of units):…”

“…Both these methods are valid for objects which are much larger than the wavelengths under consideration. The basis of the methods and solutions of different problems with the use of them are described in series of our works (the last of them are the papers [5][6][7][8][9][10][11]). We do not repeat here the main steps of the methods.…”