Maximum magnetic field in cosmic outflows systems

Employing the cold fluid equations, together with Maxwell´s equations, as well as plasma shell concept and boost frame method, the exact solution of the filamentation instability growth rate has been obtained for any arbitrary currents systems. Then, the obtained maximum growth rate relation for the instability has been used to calculate the large-magnitude of induced magnetic field in astrophysical environments such as active galactic nuclei (AGNs), microquasars, supernova remnants (SNRs), and stellar wind. The calculations show that the maximum magnetic field up to around 10⁸ Gauss can be detected from classical cold counter-streaming system, after a saturation time.