Study of the non-resonant streaming instability including thermal effects and particle collisions

Streaming cosmic rays can power the exponential growth of a seed magnetic field by exciting a non-resonant instability that feeds on their bulk kinetic energy. In this work we investigate analytically and numerically the effects of the background plasma temperature and particle collisions on the instability. We find that increasing the temperature of the ambient plasma can substantially reduce the growth rate and the magnitude of the saturated magnetic field. In collisionless or poorly collisional plasmas, we demonstrate that the instability generates pressure anisotropies that act to reduce the magnetic field amplification. We show that when proton Coulomb collisions are sufficiently frequent, these pressure anisotropies are suppressed and the magnetic field energy density can be amplified to values 20% higher than in the collisionless case. In contrast, simulations of poorly ionized plasmas confirm the rapid damping of the instability with increasing proton-neutral collisions predicted by linear fluid theory calculations. In addition to astrophysical applications, these results pave the way for the design of laboratory experiments on the non-resonant streaming instability.