Investigations and advanced concepts on gyrotron interaction modeling and simulations
In gyrotron theory, the interaction between the electron beam and the high frequency electromagnetic field is commonly modeled using the slow variables approach. The slow variables are quantities that vary slowly in time in comparison to the electron cyclotron frequency. They represent the electron momentum and the high frequency field of the resonant TE modes in the gyrotron cavity. For their definition, some reference frequencies need to be introduced. These include the so-called averaging frequency, used to define the slow variable corresponding to the electron momentum, and the carrier frequencies, used to define the slow variables corresponding to the field envelopes of the modes. From the mathematical point of view, the choice of the reference frequencies is, to some extent, arbitrary. However, from the numerical point of view, there are arguments that point toward specific choices, in the sense that these choices are advantageous in terms of simulation speed and accuracy. In this paper, the typical monochromatic gyrotron operation is considered, and the numerical integration of the interaction equations is performed by the trajectory approach, since it is the fastest, and therefore it is the one that is most commonly used. The influence of the choice of the reference frequencies on the interaction simulations is studied using theoretical arguments, as well as numerical simulations. From these investigations, appropriate choices for the values of the reference frequencies are identified. In addition, novel, advanced concepts for the definitions of these frequencies are addressed, and their benefits are demonstrated numerically.