In a system of magnetized electron beams, multiplication of electrons can occur if the incident and return beams (the latter one is produced by secondary electrons emitted at the end of the incident beam) satisfy a resonance condition on the gyration phase. The beams propagate between two boundaries; one is an electron gun and the other is a Faraday cup detector. The resonance condition demands discrete energies (eigenvalues) of the Hamiltonian that generates a propagator of the beam. This model has been compared with Varma’s formulation of discrete energies [R. K. Varma and A. M. Punithavelu, Mod. Phys. Lett. A 8, 167 (1993)].

• Received 11 January 2000

DOI:https://doi.org/10.1103/PhysRevE.63.026502