Noise analysis of a single-velocity electron gun of finite cross section in an infinite magnetic field

摘要

The Rack-Llewellyn-Pierce noise analysis,6,10,12,13 which has been applied to the problem of microwave noise in electron beams of large transit angle, utilizes the sinusoidal solutions for a space-charge-limited, infinite parallel plane diode, as derived by Llewellyn3 and Smullin,11 in the gun region and Ramo's solution for the lowest mode of a finite beam confined by an infinite longitudinal magnetic field in the drift space.8 In this calculation the input boundary condition which must be specified is the velocity modulation at the cathode. This was calculated by Rack7 as the mean square fluctuation of the instantaneous average velocity of all electrons crossing the plane of the potential minimum.