2D Simulation of High-Efficiency Cross-Field RF Power Sources
  An efficient method for frequency domain analysis of 2D cross-field devices is presented. This work was done to analyze and design high efficiency magnetrons. Arbitrary device-geometries are described by a piecewise planar boundary. The method is based on an expansion of the electromagnetic fields into a set of cavity eigenmodes. In order to obtain the self-consistent solution, iterations are performed until the energy balance is reached. A boundary integration method is used to take into account space charge effects. The cavity eigenmodes are found by a method based on the scattering matrix technique. The geometry is divided into regions. The boundary contour mode-matching method is used to obtain the scattering matrices for each region. Electromagnetic fields in each region are expanded into a series of plane waves. Due to choice of plane wave expansion, all integration in the mode-matching process is carried out analytically. The scattering matrices of the regions are combined using a generalized scattering matrix technique to obtain the scattering matrix for the full geometry, and then the eigenmode resonance frequencies and the fields. Periodic boundary condition is used for the field calculation and the particle tracking. 
Valery A. Dolgashev, Sami G. Tantawi