2D Simulation of High-Efficiency Cross-Field RF Power Sources

In a cross field device[1] such as magnetron or cross field amplifier electrons move in crossed magnetic and electric fields. Due to synchronism between electron drift velocity and phase velocity of RF wave, the wave bunches the beam, electron spokes are formed and the bunched electrons are decelerated by the RF field. Such devices have high efficiency (up to 90%), high output power and relatively low cost. Electrical design of the cross-field devices is difficult. The problem is 2D (or 3D) and highly nonlinear. It has complex geometry and strong space charge effects. Recently, increased performance of computers and availability of Particle-In-Cell (PIC) codes[2, 3], have made possible the design of relatively low efficiency devices such as relativistic magnetrons or cross field amplifiers [4]. Simulation of high efficiency ( 90%) devices is difficult due to the long transient process of starting oscillations. Use of PIC codes for design of such devices is not practical. In this report we describe a frequency domain method that developed for simulating high efficiency cross-field devices. In the method, we consider steady-state interaction of particles with the modes of RF cavity at dominant frequency. Self-consistency of the solution is reached by iterations until power balance is achieved.