Moment-based, self-consistent linear analysis of gyrotron oscillators

Abstract

A new model for simulating gyrotron oscillators in the monomode time-dependent linear self-consistent regime is presented. Starting from a nonlinear time-dependent monomode model, the linearization and the following simplification of the model, based on a moment approach, are described. This simplified model represents a numerically efficient model and allows to have a deeper physical insight, in particular, for regimes dominated by self-consistent effects such as for the gyro-backward wave instability. One specific case of a gyrotron cavity is studied in detail and compared with experimental results, with special attention to self-consistent effects and to the differences with a model using a fixed field profile. Self-consistent linear simulations are, amongst other applications, important for the design of frequency-tunable gyrotrons or high-power gyrotrons with cavities having a relatively low quality factor, but also for studies of parasitic oscillations as they may occur in beam ducts and/or in the launcher section following the interaction cavity.

Novel linear analysis for a gyrotron oscillator based on a spectral approach

“…This is in good agreement with what is observed experimentally 22 . On the contrary, with the intermediate, B int , or real magnetic field profiles, B real , shown in figure 10, the mode TE 21,6,q has a larger starting current than the TE 22,6,q mode. Even though the relative difference in magnetic field amplitude is only around 2% at the end of the simulated cavity region and lower than 0.2% until the end of the initial uptaper region, the starting current for the TE 21,6,3 mode is almost two times larger for the real magnetic field profile.…”

“…Together with its linearization it is described in details in references 6,14,15 . An important point to be stressed is that the amplitude and phase of the rf-field profile were considered to vary on a time-scale much longer than the electron transit-time in previous models 6,14 (in the model presented in this paper and in a new reduced 1D ParticleIn-Cell (PIC) model 15 , this assumption is relaxed). The equations describing respectively the perpendicular and parallel electron motion for each electrons are…”

“…The starting current of the first longitudinal mode to be excited for the two transverse modes TE 21,6 and TE 22,6 are listed in table IV. For these parameters, all the modes correspond to backward-wave modes.…”

“…Most of the models that have been used in the past to calculate the self-excitation condition, expressed in terms of a starting current, are not self-consistent 2,5,[7][8][9] , in the sense that the emptycavity longitudinal eigenmode is used. However, the necessity of using a self-consistent model has been discussed in several publications 6,[10][11][12][13] , especially for backwardwave interactions where self-consistent effects are important. The majority of these models are time-dependent, describing the time evolution of the most unstable mode.…”

“…The full description of the interaction between the slightly relativistic electron beam and the resonant mode of the cavity requires self-consistent nonlinear models [1][2][3] . On the other hand, to describe the excitation limits, linear models are appropriate and have already been extensively studied [2][3][4][5][6] . Most of the models that have been used in the past to calculate the self-excitation condition, expressed in terms of a starting current, are not self-consistent 2,5,[7][8][9] , in the sense that the emptycavity longitudinal eigenmode is used.…”