Comparison between the Landau and cyclotron resonances in the electron beam-plasma interactions

It is well-known that a cool field-aligned electron beam streaming in a plasma can destabilize electrostatic waves, in the frequency ranges of 0 < ω < min(Ω_e, ω_p) and max(Ω_e, ω_p) < ω < ω_uh, where ω_p, Ω_e, and ω_uh are the plasma, the electron cyclotron, and the upper-hybrid frequencies, respectively. Although both the Landau and cyclotron resonances lead to the generation of the waves, not much attention has been paid to the wave generation via the cyclotron resonance. In this paper we compare the two types of interactions for both non-relativistic and relativistic electron beams by considering a simple plasma model which consists of main and beam electrons and background ions. The plasma is charge neutral and current carrying. The linear theory based on this model predicts that, when the electron beams are non-relativistic, the waves are generated predominantly via the Landau interaction for a wide range of plasma parameters, except for a limited parameter regime with cool main electrons, Ω_e/ω_p > 1, and at oblique propagation angles. On the other hand, when the beam electrons have relativisitic drift momentum, the cyclotron interaction becomes more important than the Landau interaction.