MICROWAVE SIGNAL AMPLIFICATION AND PIERCE INSTABILITY ON RADIAL ELECTRON FLOWS IN CYLINDRICAL AND SPHERICAL DIODES

Linear space charge perturbations of focused electron beams flowing be tween cylindrical and spherical electrodes on convergent or divergent trajectories are studied, and the amplification of high-frequency sign als when the flow is modulated at one electrode is computed. It is sho wn that divergent beams give the largest amplification effect. The ins tability of electron beams drifting through grounded grids (Pierce ins tability in cylindrical or spherical diodes) is also considered. The i nstability threshold occurs at higher critical currents when the curva ture of the electrodes is large. Results for planar electrodes are rec overed in the limit of zero curvature devices. Spherical configuration s have better signal amplification and stability properties than simil ar planar or cylindrical systems.