STATISTICAL THEORY OF ELECTRON TRANSPORT IN CROSSED FIELDS: CHARACTERISTICS OF THE SMOOTH-BORE MAGNETRON.

Abstract : Electron transport across the magnetic field in crossed electric and magnetic fields is described on the basis of random fluctuations in the flields. The theory is formulated in terms of the slipping-stream instability, so that a definite mechanism behind the fluctuations in the fields is established. The transport equation appropriate to the analysis is shown to be the diffusion equation; a definite expression for the diffusion tensor is obtained. The components of the diffusion tensor transverse to the magnetic field are found to be proportional to the square of the electric field, and inversely proportional to the cube of the magnetic field; the exponential-growth rate of the slipping-stream instability determines the magnitude of the diffusion coefficients. Application of the theory is made to find the cut-off characteristics of the smooth-bore magnetron. Explicit expressions for the space-charge distribution, the electric-field distribution, the anode current, and the circulating current are obtained. The results are compared with available experimental results. The agreement between theoretical and experimental values is good, particularly for the anode current. The new theory thus appears to provide, for the first time, a correct theoretical explanation of the cut-off characteristics of the smooth-bore magnetron. (Author)