Deep modulation of a high-current relativistic electron beam in a system of coupled cavities
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Deep Modulation of a HighCurrent Relativistic Electron Beam in a System of Coupled Cavities V. A. Balakirev and V. O. Podobinsky National Science Center Kharkiv Institute of Physics and Technology, ul. Akademicheskaya 1, Kharkiv, 61108 Ukraine Received December 17, 2009
Abstract—The excitation of inphase (0type) and antiphase (πtype) electromagnetic oscillations by a rela tivistic electron beam in a system of identical coupled cavities is considered. It is shown that, in the case of excitation of antiphase oscillations, instability develops in a shorter system of cavities than it does when inphase oscillations are excited. In the nonlinear stage of the excitation of antiphase oscillations in a system of coupled cavities, a virtual cathode forms that breaks the initially uniform relativistic electron beam into a periodic sequence of spatially separated short bunches. DOI: 10.1134/S1063780X10090047
1. INTRODUCTION A relativistic microwave oscillator based on the interaction of a relativistic electron beam (REB) with a splitcavity oscillator (SCO) has been proposed and studied comparatively recently [1–5]. An SCO is a cavity divided into two equal halves by a conducting diaphragm so that there is a slit between the diaphragm and the side wall of the cavity. In other words, an SCO is a system of two cavities coupled through a slit. In such a system, an REB becomes deeply modulated. The modulated beam then passes into a cavity where its power is taken off to a useful load, e.g., a coaxial line. In a system of weakly coupled cavities, inphase (“0type”) and antiphase (“πtype”) oscillations are excited the frequencies of which differ by a small amount determined by the electromagnetic coupling between the cavities (i.e., by the slit width). The pat tern of the excitation of inphase electromagnetic oscil lations by an electron beam is the same as that in a tra ditional monotron [6–10]. As for antiphase oscilla tions, the scenario of their excitation is radically different. The main difference is that they are excited at an arbitrarily small transit angle (cavity length), thereby making it possible to create short microwave oscillators. This circumstance is fundamentally important because, in such oscillators, there is no need for an external magnetic field. Note that an SCO with a coaxial split cavity was investigated by Wenyuan and Wu [11]. Coaxial cavities can substantially increase the REB current in an SCO and, consequently, the SCO power. A microwave oscillator in which an REB is modulated by a system of three weakly coupled cav ities was considered in [12, 13]. Our paper presents theoretical results on the exci tation of microwaves and the modulation of an annu lar REB in an SCO. The cavities are coupled through a hole at the center of the oscillator [14], a coupling
that is preferable for an annular beam configuration. For a continuous electron beam, the cavities should be coupled through a gap at the periphery of the dia phragm [1–5]. In Section 2, we formulate the set of nonlinear equat
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