Two-dimensional particle trajectory integration in axisymmetric static electric and magnetic field for electron gun and collector simulations
C. Wu, I. Pagonakis, S. Illy, J. Jelonnek
31st Joint Russian-German Workshop on ECRH and Gyrotrons, 2019, Jun
The electron guns and collectors in various vacuum tubes, such as gyrotrons and (gyro-) TWTs, are usually assumed to be axisymmetric. As the system has a symmetric axis, only two dimensions are needed for the description of the geometry, electric and magnetic static fields, and the trajectories of the particles. A two dimensional integration of the particle trajectories can be faster and more accurate than the general three-dimensional one. In addition, the conservation of physical quantities (in this case: the canonical angular momentum) in the symmetric dimension can be numerically guaranteed. Moreover, the trajectory integration can be further simplified, if no interaction between particles and RF waves is considered. Hence, one might expect several advan-tages in the design and simulation of guns and collectors, if such axisymmetric components are analyzed in 2D while taking into account only the static fields. However, the general particle trajectory integration algorithms (e.g. Boris algorithm and its variants) are usually implemented in three-dimensional Cartesian coordinates. In this presentation, the formulations of a two-dimensional particle trajectory integrator and its advantages will be shown.