Synchrotron firehose instability: A numerical analysis

Synchrotron emission from electrons modifies their distribution function on the radiative cooling timescale. This process enhances the particle pressure along the magnetic field direction, resulting in pressure anisotropy where P∥>P⊥. Under these conditions, the plasma becomes unstable to the synchrotron firehose instability (SFI). We aim to develop a numerical model to investigate this instability by analyzing its evolutionary timescales and identifying the range of plasma beta (i.e., the ratio of plasma pressure to the magnetic pressure β=8πnkBT/B02) values conducive to its growth. Using linear theory and the linearized Vlasov–Maxwell equations, we numerically solve the dispersion relation for perturbations propagating parallel to the magnetic field, enabling an analysis of the SFI spectrum. We demonstrate that the SFI is triggered on timescales shorter than the radiative cooling time in ultra-relativistic pair plasmas. In ultra-relativistic electron–ion plasmas, the SFI also develops within the cooling time, but only for sufficiently high initial beta values (β0>40). The growth rate of the SFI is higher in pair plasmas than in electron–ion plasmas, and the instability persists for a longer duration in the pair plasma case.