Magnetic field amplification by the Weibel instability at planetary and astrophysical high-Mach-number shocks

Collisionless shocks are ubiquitous in the Universe and often associated with strong magnetic field. Here we use large-scale particle-in-cell simulations of non-relativistic perpendicular shocks in the high-Mach-number regime to study the amplification of magnetic field within shocks. The magnetic field is amplified at the shock transition due to the ion-ion two-stream Weibel instability. The normalized magnetic-field strength strongly correlates with the Alfv\'enic Mach number. Mock spacecraft measurements derived from PIC simulations are fully consistent with those taken in-situ at Saturn's bow shock by the Cassini spacecraft.