Transition radiation generated by a particle passing through the apex of a conducting cone
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PROPERTIES OF SOLID
Transition Radiation Generated by a Particle Passing through the Apex of a Conducting Cone A. V. Kol’tsov* and A. V. Serov** Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia *email: [email protected] **email: [email protected] Received May 20, 2009
Abstract—The spatial field distribution is determined for the transition radiation generated by a particle pass ing through the apex of a cone along its axis. Expressions for the angular distribution of the radiation intensity are obtained for apex angles between 0 and π. Characteristics of transition radiation emitted into a “funnel” and a dihedral angle are compared. PACS numbers: 41.60.m, 52.70.Gw DOI: 10.1134/S1063776109120127
1. INTRODUCTION
compared with those of the radiation in a dihedral angle.
Transition radiation, generated by a charged parti cle crossing the interface between two media, has properties that make it useful for solving various prob lems. The physics of this phenomenon has been dis cussed in numerous papers and several monographs [1–3]. However, previous analyses focused on the radiation produced when one or several plane inter faces are crossed, whereas the cases of more compli cated interfaces are far from well studied. It should be noted that characteristics of spectralangular distribu tions of transition radiation generated at complicated interfaces can be used to deal with new problems and open additional opportunities in traditional applica tions of this kind of radiation. In particular, studies of the transition radiation generated by a particle cross ing a parabolic mirror [4] or a lens [5] showed that the radiation is refracted to the focus of the mirror or lens, respectively. Such interfaces can be used to increase the radiation intensity at the focus and focus the radi ation away from the particle’s trajectory. In [6–9], it was shown that the distribution of transition radiation in a dihedral angle is more sensitive to the direction of the emitting particle and to the position of the crossing point as compared to transition radiation generated at a plane interface. It was noted that the maximum in the angular intensity distribution of radiation in a dihedral angle is higher than at a plane interface.
2. TRANSITION RADIATION Figure 1 illustrates the radiation geometry. We introduce a spherical coordinate system (r, ϕ, θ) with origin at the apex of a conical “funnel,” denoting by α the apex angle (between the axis and the generatrix). A particle with charge q moves from the origin with velocity v at an angle of θ0 to the axis. The plane ϕ = 0 is spanned by the axis and the particle velocity vector. The angle between the axis and the direction to the observation point P is denoted by θ. In what follows, we use a system of units where the speed of light c = 1.
In this paper, we consider the transition radiation generated by a particle moving along the axis of a per fectly conducting cone. The expressions obtained here can be used to describe the radiation field b
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