The Influence of Initial Electron Velocities Distribution on the Energy Spectra of the Spent Electron Beam in Gyrotron
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The Influence of Initial Electron Velocities Distribution on the Energy Spectra of the Spent Electron Beam in Gyrotron I. G. Gachev & M. Yu. Glyavin & V. N. Manuilov & M. V. Morozkin & N. A. Zavolsky
Received: 28 June 2010 / Accepted: 27 July 2010 / Published online: 17 August 2010 # Springer Science+Business Media, LLC 2010
Abstract The results of numerical analysis of the electron beam parameters influencing on the efficiency of energy recovery in gyrotrons are given. The weak dependence of minimal electron beam energy in collector region versus velocity distribution function is demonstrated. This fact may simplify the electron-optical system design of modern gyrotrons. Keywords Gyrotron . Energy recovery . Velocity spread . Distribution function
1 Introduction The energy distribution function of electrons F(W), where W is the electron energy at the cavity output, influences on the efficiency of the recuperation of the residual energy of the spent electron beam [1, 2] and, therefore, the total efficiency of the gyrotron significantly. Usually, F(W) is calculated by integrating the averaged gyrotron equations with a fixed structure of the high-frequency field [3] within the framework of the assumption that the function f (v⊥) of electron distribution over oscillatory velocities in the helical electron beam (HEB) at the entrance of the cavity is close to the Gaussian one [4]. A similar assumption about the function of electron distribution over oscillatory velocities is made in a more accurate model, which is based on solving a self-consistent system of equations that contains the equation of the electron motion and the equation for the complex amplitude of the excited mode [5]. As follows from the results of numerical simulation [6, 7] and
I. G. Gachev : M. Y. Glyavin : M. V. Morozkin : N. A. Zavolsky Institute of Applied Physics of the Russian Academy of Sciences and GYCOM Ltd., Nizhny Novgorod, Russia V. N. Manuilov (*) Nizhny Novgorod State University, Nizhny Novgorod, Russia e-mail: [email protected]
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J Infrared Milli Terahz Waves (2010) 31:1109–1114
experiments [7, 8], this assumption is justified, as a rule, only at relatively low beam currents and pitch factors, namely, g≈1–1.2. HEBs are formed by magnetron-injection guns (MIGs). Numerous theoretical and experimental studies of MIGs show that when the beam current increases to the level of approximately 0.1 of the Langmuir current IL of the gun, f (v⊥) is often transformed from the Gaussian function to the non-unimodal one, which has at least two maxima. There are some reasons for this phenomenon [7, 8]. One of the most important is the catching of electrons into the adiabatic trap between the cathode and the interaction space of the gyrotron, which happens when one tries to increase g to the maximum possible values, at which the beam retains its stability. In this case, the number of maxima can reach 3–4 [10]. As a rule, the breach of unimodality is accompanied by the development of various instabilities of the electron beam and reduces the devi
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