Transition radiation in a dihedral angle formed by perfectly conducting planes
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Transition Radiation in a Dihedral Angle Formed by Perfectly Conducting Planes A. V. Kol’tsov* and A. V. Serov** Lebedev Institute of Physics, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991 Russia *email: [email protected] **email: [email protected] Received February 20, 2009
Abstract—The spatial distribution of the field of transition radiation generated by a relativistic particle flying into a dihedral angle formed by perfectly conducting plane surfaces is determined. The cases when particles are injected from the edge and from a plane of the dihedral angle are considered. The angular distributions of radiation intensity in dihedral angles of different values are calculated. PACS numbers: 41.60.m, 52.70.Gw DOI: 10.1134/S106377610907005X
One of such interfaces between two media is a surface in the form of a dihedral angle. The properties of transition radiation generated when a particle passes through a dihedral angle have been investigated both theoretically [3, 4] and experi mentally [5]. In [3], Ryazanov and Safonov consid ered transition radiation of a charged particle when the interface between two media is formed by two planes that form a dihedral angle of α = π/2. In [4], a more general case was considered when the planes intersect not only at a right angle but also at α = π/m, where m is an integer. In that paper, the authors used the method of images to describe transition radiation. In the present paper, we consider the specific fea tures of transition radiation in a dihedral angle of arbi trary value (0 < α < 2π). A particular case of radiation in a dihedral angle is radiation generated when a charged particle passes through a plane surface. To calculate the electromagnetic fields generated by an external source in a dihedral angle, we apply a stan dard electrodynamic method that is used when dealing with the fields generated in closed waveguides [6, 7]. In this method, a field in a waveguide is represented as a linear combination of modes of two types: transverse electric waves (H waves) and transverse magnetic waves (E waves).
1. INTRODUCTION Radiation produced when a charged particle passes through the interface between two media possesses certain properties that make this radiation useful for solving various problems [1]. One of the simplest and important particular cases in the theory of transition radiation is the radiation generated when a particle is incident on a perfectly conducting plane. This prob lem was considered in the first paper by Ginzburg and Frank on the theory of transition radiation [2]. They pointed out that the transition radiation on a perfectly conducting plane can be considered as radiation from two particles: a real particle with charge q and its image with charge –q. When a particle is incident on a per fectly conducting plane, the particle and its image meet at the point where the particle crosses the plane. The radiation emitted in this way can be considered as a sum of radiations produced when the charge and its image are
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