On the linear and non linear evolution of the RMHD Kelvin Helmholtz instability in a magnetically polarized fluid

The origin of the magnetic field in some systems like AGNs or GRBs is still an open question in astrophysics. A possible mechanism to explain the magnetic field generation is the Kelvin-Helmholtz instability, since it is able to transform the kinetic energy, in a shear flow, into magnetic energy. Through the present work, we investigate the linear and non linear effects produced by the magnetic susceptibility in the development of the Kelvin-Helmholtz instability in a relativistic plasma. The magnetic field in the system is parallel to the flows and the susceptibility is assumed to be homogeneous, constant in time, and equal in both fluids. In particular, we analyze the instability in three different cases, when the fluids are diamagnetic, paramagnetic, and when the susceptibility is zero. We compute the dispersion relation in the linear regime and found that the interface between diamagnetic fluids is more stable than the original case without magnetic susceptibility. On the contrary, the paramagnetism makes the interface more unstable. This behavior is increasingly important the higher the magnetization parameter. Additionally, the interval of relativistic Mach numbers for which the interface is unstable grows with the magnetic susceptibility, i.e., it is larger for paramagnetic fluids. We check these analytical results with numerical simulations, and explore the effect of the magnetic polarization in the non linear regime. We found that the magnetic field is more amplified in paramagnetic fluids than in diamagnetic ones. Surprisingly, the effect of the susceptibility in the amplification is stronger when the magnetization parameter is smaller. These results make the KH instability a more efficient and effective amplification mechanism of seed magnetic fields when considering the susceptibility of matter.