GUIDING CENTER FLUID MODEL OF THE CROSSED-FIELD AMPLIFIER

A closed, nonlinear set of fluid equations, based on the electron guiding center orbits, is developed to model the CFA behavior. In the synchronous with the RF signal frame, the streamlines follow the equipotential surfaces of the transformed fields. In steady state, the flow is incompressible. The effects of the electron hub surrounding the cathode are included. The secondary production at the cathode is computed self-consistently through the secondary emission coefficient and the average impact energy. The equations are implemented in a numerical algorithm that is much faster and more efficient than existing particle codes and shows good agreement with experimental results for V-I curves, over a wide parameter regime. Both analysis and simulation point out that the hub density controls the RF amplification and saturation mechanisms. Anode current is determined by the difference of the E x B drift at the top of the hub from the RF phase velocity. Secondary production depends on the energy of the impacting electrons, thus is sensitive to the electrostatic shielding of the cathode. The pass-to-pass fluctuations at the tube's output are connected to the oscillations in the hub density during each pass.