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The origin of the magnetic field in some systems like AGNs or GRBs is stillan open question in astrophysics. A possible mechanism to explain the magneticfield generation is the Kelvin-Helmholtz instability, since it is able totransform the kinetic energy, in a shear flow, into magnetic energy. Throughthe present work, we investigate the linear and non linear effects produced bythe magnetic susceptibility in the development of the Kelvin-Helmholtzinstability in a relativistic plasma. The magnetic field in the system isparallel to the flows and the susceptibility is assumed to be homogeneous,constant in time, and equal in both fluids. In particular, we analyze theinstability in three different cases, when the fluids are diamagnetic,paramagnetic, and when the susceptibility is zero. We compute the dispersionrelation in the linear regime and found that the interface between diamagneticfluids is more stable than the original case without magnetic susceptibility.On the contrary, the paramagnetism makes the interface more unstable. Thisbehavior is increasingly important the higher the magnetization parameter.Additionally, the interval of relativistic Mach numbers for which the interfaceis unstable grows with the magnetic susceptibility, i.e., it is larger forparamagnetic fluids. We check these analytical results with numericalsimulations, and explore the effect of the magnetic polarization in the nonlinear regime. We found that the magnetic field is more amplified inparamagnetic fluids than in diamagnetic ones. Surprisingly, the effect of thesusceptibility in the amplification is stronger when the magnetizationparameter is smaller. These results make the KH instability a more efficientand effective amplification mechanism of seed magnetic fields when consideringthe susceptibility of matter.

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