On the Effect of RF-Space Charge on the Beam-Field Interaction in Gyrotrons
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On the Effect of RF-Space Charge on the Beam-Field Interaction in Gyrotrons Edith Borie · Stefan Kern
Received: 19 March 2009 / Accepted: 15 May 2009 / Published online: 3 June 2009 © Springer Science + Business Media, LLC 2009
Abstract The effect of RF-space charge fields on the beam-field interaction in gyrotrons is reviewed. This effect, formerly considered unimportant, is found to cause recognisable differences in simulations of gyrotrons with high current density, such as today’s megawatt level gyrotrons. In this paper, a numerically efficient way of including RF-space charge in the common slow variables model is derived and numerical examples are presented. Keywords Gyrotrons · High power microwaves · RF-space charge
1 Introduction Gyrotrons are capable of providing high power at millimetric and sub–millimetric wavelengths. They are mainly used for plasma heating. Other applications include high power communications, industrial heating and material processing. For the past two decades, gyrotrons have been considered as the most promising sources for electron cyclotron resonance heating (ECRH) of plasmas for thermonuclear fusion experiments in tokamaks and stellarators because of the distinct advantage that they provide power levels of more than 1 MW at frequencies 30–170 GHz with long pulse to CW range of output, which is the basic requirement for plasma heating [1–3]. The so called slow variables model of the beam-field interaction in gyrotron oscillators is well known and has been used for decades [4–9]. It was first introduced by Bratman et al., as described in Ref. [4]. This model makes use of a number of approximations to permit fast and efficient numerical calculations. With ever increasing output powers some of these approximations need to be reassessed. One
E. Borie (B) · S. Kern Forschungszentrum Karlsruhe, Association Euratom-FZK, Institut für Hochleistungsimpuls und Mikrowellentechnik, Hermann von Helmholtzplatz 1, 76344 Eggenstein–Leopoldshafen, Germany e-mail: [email protected]
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J Infrared Milli Terahz Waves (2009) 30:915–923
of these is the effect of RF-space charge, which will be singled out for consideration in this paper. This effect describes the influence of electric fields caused by nonuniform charge distributions in the electron beam (bunching) on the interaction and is important for frequencies in the vicinity of the electron cyclotron frequency. This distinguishes it from other possible AC space charge fields. The electromagnetic radiation in a gyrotron is generated by the azimuthal bunching of electrons in their gyro-orbits. This bunching is also a source of electrostatic fields, which then could affect the electron motion. While it has been investigated by many authors before [9–13], it was widely considered unimportant for high power gyrotron oscillators. Kleva et al. [12] examined the nonlinear effects of the electrostatic field of a quasioptical gyrotron, and Latham [13] performed a similar analysis for a gyroklystron. Voltage depression is also important and has been discu
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