  The non-thermal particles escaping from collisionless shocks into the
surrounding medium can trigger a non-resonant streaming instability that
converts parts of their drift kinetic energy into large amplitude magnetic
field perturbations, and promote the confinement and acceleration of high
energy cosmic rays. We present simulations of the instability using an
hybrid-Particle-in-Cell approach including Monte Carlo collisions, and
demonstrate that the development of the non-resonant mode is associated with
important ion pressure anisotropies in the background plasma. Depending on the
initial conditions, the anisotropies may act on the instability by lowering its
growth and trigger secondary micro-instabilities. Introducing collisions with
neutrals yield a strong reduction of the magnetic field amplification as
predicted by linear fluid theory. In contrast, Coulomb collisions in fully
ionized plasmas are found to mitigate the self-generated pressure anisotropies
and promote the growth of the magnetic field.
