Investigations on Improving Broadband Boundary Conditions in Gyrotron Interaction Modelling

Abstract

Gyrotrons are microwave tubes capable of providing mega-watt power at millimetric wavelengths. The microwave power is produced by the conversion of the kinetic energy of an electron beam to electromagnetic wave energy. Simulations of the beam-wave interaction in the gyrotron cavity are essential for gyrotron design, as well as theoretical and experimental studies. In the usual gyrotron operation the spectrum of the generated radiation is concentrated around the nominal frequency. For this reason, the usual simulations consider only a narrow-band output spectrum (e.g. several GHz bandwidth comparing with the working frequency in the range of 100-200 GHz). As a result, the typical existing codes use a single-frequency radiation boundary condition for the generated electromagnetic field in the cavity. This condition is matched only at one frequency. However, there are two important aspects, which motivate an advanced formulation and implementation of the cavity boundary condition. Firstly, the occurrence of broadband effects (which may be several tens of GHz) in some cases, like dynamic after-cavity-interaction or modulation side-bands, requires a broadband boundary condition. Secondly, there are reflections from inside and outside of the gyrotron, which can only be considered in the simulation through a boundary condition with user-defined, frequency-dependent reflections. This master thesis proposes an improved formulation of the broadband boundary condition in the self-consistent, beam-wave interaction code Euridice. In this new formulation, two physical variables — the wave impedance and the axial wavenumber are expanded in polynomial series in the frequency domain. Because the beam-wave interaction process is simulated transiently in the time domain, the boundary condition should be also expressed in the time domain. This involves a non-trivial inverse Fourier transform, for which two solutions are proposed, tested and validated. It has been shown that, through the newly developed formulation, the existing matched boundary condition (that should yield zero-reflection in ideal case) can be improved by 15 dB even with a first-order polynomial series. Moreover, a user-defined, frequency-dependent complex reflection coefficient can be introduced. This was not possible with the previously existing boundary condition in Euridice.