Guiding center theory and simulations of the crossed-field amplifier

Abstract

Electrons in crossed-field devices execute complicated orbits in crossed static electric and magnetic fields, driven at the same time by slow rf waves. The dynamics is considerably simplified by averaging the fast-time-scale, periodic gyromotion. The reduced equations derived here follow the slow guiding center drift in the synchronous frame of reference moving at the phase velocity of the wave. In that frame, the streamlines follow the equipotential surfaces of the transformed fields. In steady-state, the flow is incompressible. A closed, nonlinear set of equations, based on the guiding center flow, is developed to model the crossed-field amplifier behavior. 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 excellent agreement with experimental results for characteristic curves, tube gain, and efficiency, over a wide parameter regime.