Recent observations at low altitudes made in the source region of the auroral kiloimetric radiation (AKR hereinafter) strongly support the maser synchrotron instability (MSI) as the relevant generation process for the AKR. This was first realized by Wu and Lee (1979). In the recent work (Le Qu¿au et al. (1984), hereinafter called reference 1) we have proposed an analytical treatment of the MSI. The present work is a continuation of this analytical study. First we investigate the physical process of the MSI, and simple analytical expressions, valid for any distribution functions of nonthermal electrons are given. It is shown that supraluminous X mode waves (&ohgr;/k∥c≫1) can resonate with relatively low energy electrons provided that the cold plasma parameter, ϵc=&ohgr;pc 2/&ohgr;c2, is much smaller than unity. The proper frame of reference for studying the resonant coupling between the X mode and nonthermal electrons moves at a parallel velocity k∥c2/&ohgr;. Resonance curves are then circles centered around this value and electrons diffuse with almost constant parallel velocities. The differences between the MSI and the standard cyclotron theory (where resonance curves are straight lines while diffusion curves are circles centered around &ohgr;/k∥) is stressed. A parametric study of the instability conditions for such a supraluminous wave is conducted. We investigate the role played by &thgr;, the propagation angle ϵb, the normalized density of energetic electrons Δ, the energy width of the part of the distribution function where an inversion of population (∂f/∂v⊥>0) occurs, and finally u, the parallel velocity which characterizes the maximum of ∂f/∂v⊥ integrated along a resonance circle. In the case of the shifted loss cone distribution used here, u is simply its parallel bulk velocity. Largest growth rate are obtained for k∥c2/&ohgr;=u.