  A case of two interpenetrating, cold and quasi-neutral ion-electron plasmas
is investigated with the multi-fluid approach. We consider that one plasma
flows quasi-parallel to the lines of a background magnetic field embedded in
another static plasma. If the flow turns super-Alfv\'enic, we show that
parallel R/L-modes and perpendicular X/O-modes become unstable and grow in
amplitude. Within the linear theory, we find that the growth rate curve of an
unstable mode has a maximum at some wavenumber specific to each mode. If we
consider a shock-like plasma configuration, we find that the fastest growing
mode is the resonant one (with $k \sim r_{gi}^{-1}$) which strongly interacts
with ions. In Particle-In-Cell (PIC) simulations, we observe that a resonant
wave with the same properties is excited during the early phases of shock
formation. Once the wave becomes non-linear, it efficiently scatters ions and
triggers the initial shock formation. This implies that the typical compression
ratio of $\sim 4$ could naturally arise as a consequence of a highly resonant
micro-physical process. We model the interaction of ions reflected from the
reforming shock barrier in a weak-beam case, and we show that the upstream wave
now matches the instability we expect from the equations. By using PIC
simulations, we explain how the strong-beam resonant instability triggers shock
formation in the non-linear stage, and how the weak-beam instability reforms
and transmits the shock afterwards. The micro-instabilities that we study here
could largely contribute to shock triggering as well as to the reformation and
transmission of the shock itself.
