Simulation of high-power klystrons with heterogeneous focusing magnetic field

Abstract

The work shows a significant effect of the focusing magnetic field on the output characteristics of the klystron. When the calculations are done using nonlinear one-dimensional models, optimization of the parameters makes it possible to obtain versions of devices with the efficiency of 0.8 – 0.9 and higher. However, when testing these options using nonlinear two-dimensional models that take into account the radial motion of electrons, there is a significant discrepancy in the output characteristics obtained from the one-dimensional and two-dimensional models. This is due to the fact that during the motion of the electron beam, the radii of the leading centers of the large particles change the coefficients of interaction of the particle fields with the electromagnetic fields of the resonators change, which leads to a change in the output characteristics of the klystrons: efficiency, output power, and gain. On the other hand, it seemed that setting a large focusing magnetic field to exclude the radial motion of particles could eliminate this drawback, however, another problem arises here - the magnetic system for focusing becomes unacceptably large and it is technically difficult to obtain magnetic induction values of more than 2 T (the weight of the magnetic system can be several hundred kilograms). Therefore, one should choose the magnetic field induction for focusing the electron beam no more than 1T. In this paper, a twodimensional nonlinear mathematical model (2.5D) is proposed that takes into account the azimuthal component in the equations of motion. In the model, the induction of the focusing magnetic field is set in the form of tables. This makes it possible to set the inhomogeneity of the magnetic field at any place in the interaction space of the klystron. The calculation of a powerful relativistic klystron with an accelerating voltage of 1000 kV and the beam current of 250 A was carried out. The use of an inhomogeneous magnetic field makes it possible to reduce the deposition of electrons in the region of the gaps. Therefore, a decrease in the electron deposition leads to an increase in the durability of klystrons.