The effect of space charge on shot noise in crossed-field electron guns

The two-dimensional electronic behavior of the crossed-field potential minimum is analyzed by means of a feedback network which provides a vehicle for understanding the complex phenomena, while allowing quantitatively accurate numerical calculations. The solutions, limited to the low-frequency range where transit time may be neglected, Show shot-noise smoothing as a function of magnetic field and cathode length. For low magnetic fields and short cathodes, the smoothing approaches the results of the North theory for zero magnetic field. It is also shown that if the cathode length is greater than about 11 normalized (Kino) units or 0.55 of the cycloid length for the existing field conditions, an initial perturbation of the emission current will lead to growing fluctuations of the beam current. This instability is considered to be responsible for the observation, in some crossed-field tubes, that the output noise increases when the cathode is heated sufficiently to form a potential minimum in front of the cathode. This criterion for the existence of excess noise is applied to all the experiments for which sufficient data have been published and no disagreement is found.