Monte Carlo simulation of a finite thickness neutralized electron beam

Cyclotron resonance maser (CRM) instability^1-2 is characterized by the oscillation condition ω >;Ω̃ + k_zV_z, where the Doppler-shift term k_zV_z in the fast electron cyclotron mode ω =Ω̃ + k_zV_z is negligibly small. Here, ω, k_z, Ω̃ = eB₀/mγ₀ and V_z are, respectively, angular frequency and wavenumber of oscillation, relativistic cyclotron frequency and beam velocity in the axial direction; whereas -e, B₀, m, and γ₀ are respectively, the charge on the electron, axial magnetic field, mass of the electron, and the relativistic factor. The CRM instability, however, may not be the unique principle of cyclotron emission near Ω̃. Another principle of cyclotron emission different from the CRM instability was found to exist theoretically, if high-density electron beams were neutralized by ions^3-4. It was named Cherenkov instability in azimuthal direction (CIAD) that was expected to arise at an oscillation frequency ω <; Ω̃. It was shown that the instability is non-relativistic principle of cyclotron emission in fast wave device region, namely, ω/k_z >; c. Here, c is the velocity of light in vacuum.