Experimental and Theoretical Investigations of Stochastic Oscillatory   Phenomena in a Nonrelativistic Electron Beam with a Virtual Cathode
  Results are presented from experimental investigations of oscillatory phenomena in an electron beam with a virtual cathode in a diode gap with a decelerating field. Experiments have revealed a stochastic broadband generation of the microwave oscillations of a virtual cathode in a decelerating field. Numerical simulations based on a simple one-dimensional model have shown that the onset of the stochastic generation and the broadening of the oscillation spectrum with increasing beam deceleration rate are governed by the processes of regrouping of the electrons in a beam with a virtual cathode. 
Yu.A. Kalinin, A. A. Koronovskii, A.E. Hramov, E.N. Egorov, and R.A.   Filatov