Self-consistent, time-dependent gyrotron linear analysis in nonhomogeneous RF-structures

We present an analysis of the linear behavior of the gyrotron interaction in both the forward-wave regime with positive parallel wavevector, k
_∥
and the backward-wave regime with k
_∥
<; 0. The considered electromagnetic (EM) structures are longitudinally non-homogeneous and the electron beam properties have, in general, also a longitudinal dependence. The set of time-dependent linearized self-consistent interaction equations allows to calculate the self-consistent starting-current for a given TE
_m,p
transverse mode. These effects have to be included in particular for the backward-wave regime for which the longitudinal EM field profile is fully determined by self-consistent effects. The analysis can be used for calculating the starting conditions for parasitic oscillations occurring in beam-ducts and/or the launcher section following the gyrotron cavity. This paper presents the general model and first results of the code.