Fundamental Theory of the Electron Cyclotron Maser
This chapter builds up the theoretical foundation for the book. The fundamental theories of the uniform dielectric-lined waveguide and the periodic dielectric-loaded waveguide are reviewed first. Since high-power endurable lossy waveguide becomes an indis
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Fundamental Theory of the Electron Cyclotron Maser
Abstract This chapter builds up the theoretical foundation for the book. The fundamental theories of the uniform dielectric-lined waveguide and the periodic dielectric-loaded waveguide are reviewed first. Since high-power endurable lossy waveguide becomes an indispensable component of the gyrotron amplifier circuit, it is a precondition to understand the wave properties in the waveguide system for the beam-wave interaction study. Secondly, from the point of view of the partitioning transverse plane of the interaction space, it proposes a general ECM theoretical model, which fits well most of the waveguide interaction systems. Thirdly, using the waveguide theory and the general ECM model, the linear interaction theory and the nonlinear theory of the dielectric-lined gyro-TWT is developed. When the lossy dielectric layer becomes infinitely thin, the dielectric-lined interaction theory returns to classic form of the cylindrical waveguide theory. These theories build up the theoretical foundation for further investigating the instability competition in the interaction system. Keywords Electron cyclotron maser • Lossy dielectric-loaded waveguide • Modal transition • Absolute instability • Convective instability
2.1 Introduction The operation principle of a gyrotron traveling-wave tube (gyro-TWT) amplifier is based on the convective instability of the relativistic electron cyclotron maser (ECM) [1]. The ECM interaction employs a cycling electron beam with an inherent gyrating frequency se , which makes it feasible to interact with a fast electromagnetic wave (EM wave), in particular, a high-order waveguide mode. Figure 2.1a shows the transverse plane of an ECM system, for simpler illustration, using an angularly polarized waveguide mode. The electron projections on the transverse plane are gyrating with the Larmor radius rL , which is determined by the longitudinal static
C.-H. Du and P.-K. Liu, Millimeter-Wave Gyrotron Traveling-Wave Tube Amplifiers, DOI 10.1007/978-3-642-54728-7__2, © Springer-Verlag Berlin Heidelberg 2014
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2 Fundamental Theory of the Electron Cyclotron Maser
b a
B0 Eq
e
e
e
Eq
2rL
rg e
Eq
e
O e e
e
Eq Metal wall
Fig. 2.1 (a) A schematic plot of an electron cyclotron maser interaction system based on angular polarized waveguide mode, and (b) the cold electron beam-wave dispersion relation
magnetic field strength B0 eEz and electron transverse velocity. The centers of these Larmor circles locate on or around a guiding circle of radius rg . Normally, for a cycling electron beam with the guiding center radius larger than the Larmor radius rg > rL , it is called a small-orbit electron beam, which could be generated by a magnetron injection gun (MIG) [2]. On the contrary, for a cycling electron beam with relatively small guiding center radius rg rL , it is called large-orbit electron beam. Usually, a large-orbit electron beam could be generated by a magnetic cusp gun (MCG) [3]. Figure 2.1b shows the dispersion relation between
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