Effects of Magnetic Focusing on Power and Stability of VE Amplifiers

Theory and modeling of new discovered effects of the oscillating e-beam boundary formed in a magnetic focusing channel on the stability, gain, and power of VE amplifiers are presented. The RF structure and e-beam circuit parameters are computed for different beam envelope radii and oscillation amplitudes and then the self-excitation thresholds are obtained from the Determinant equations. A new solution of the beam envelope equation not limited by the small-amplitude oscillations is derived and used to determine the magnetic focusing conditions providing various beam envelope radii and oscillation amplitudes. It is shown for the example Ka-band serpentine structure that the optimum radius as well as axial position of the oscillating beam envelope allow achieving significantly greater gain and power of RF amplifiers.