The negative energy cyclotron wave will couple to a positive energy, slow waveguide mode with a growth rate which can be even larger than the space charge mode for intense, high voltage electron beams. 2-D fluid theory, 1-D Vlasov theory and 1 2/2-dimensional simulations are presented along with the design parameters for a proposed proof-of-principle experiment.
E. E. Lednum, E. E. Lednum,
"Negative energy cyclotron resonance maser", Proc. SPIE 1514, 15th International Conference on Infrared and Millimeter Waves, 15144K (1 December 1990); doi: 10.1117/12.2301574; https://doi.org/10.1117/12.2301574