The magnetic turbulence prevalent in many astrophysical systems, such as the solar wind and supernova remnants, plays a crucial role in accelerating high-energy particles, particularly within collisionless shock waves. By trapping particles near the shock front, this turbulence facilitates their energy gain through repeated crossings between the upstream and downstream regions – a process known as Fermi acceleration, believed to be the origin of cosmic rays.
It happens that the turbulence surrounding supernova remnants is likely generated by the cosmic rays themselves via plasma instabilities as they stream ahead of the shock. In the specific case of a shock wave propagating parallel to the ambient magnetic field, the dominant instability is thought to be the non-resonant streaming instability, or Bell's instability, which acts to amplify the preexisting turbulence.
The objective of this PhD is to build a comprehensive analytical model of this instability within a turbulent plasma, and to validate its predictions against advanced numerical simulations.