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Cosmic ray (CR) currents through magnetised plasma drive strong instabilities producing amplification of the magnetic field. This amplification helps explain the CR energy spectrum as well as observations of supernova remnants and radio galaxy hot spots. Using magnetohydrodynamic (MHD) simulations, we study the behaviour of the non-resonant hybrid (NRH) instability (also known as the Bell instability) in the case of CR currents perpendicular and parallel to the initial magnetic field. We demonstrate that extending simulations of the perpendicular case to 3D reveals a different character to the turbulence from that observed in 2D. Despite these differences, in 3D the perpendicular NRH instability still grows exponentially far into the non-linear regime with a similar growth rate to both the 2D perpendicular and 3D parallel situations. We introduce some simple analytical models to elucidate the physical behaviour, using them to demonstrate that the transition to the non-linear regime is governed by the growth of thermal pressure inside dense filaments at the edges of the expanding loops. We discuss our results in the context of supernova remnants and jets in radio galaxies. Our work shows that the NRH instability can amplify magnetic fields to many times their initial value in parallel and perpendicular shocks.
We have performed magnetohydrodynamical simulations to study the amplification of magnetic fields in the precursors of shock waves. Strong magnetic fields are required in the precursors of the strong shocks that occur in supernova remnants. Observati
Galactic cosmic rays are believed to be accelerated at supernova remnants. However, whether supernova remnants can be Pevatrons is still very unclear. In this work we argue that PeV cosmic rays can be accelerated during the early phase of a supernova
Numerical simulations of the propagation of charged particles through magnetic fields solving the equation of motion often leads to the usage of an interpolation in case of discretely defined magnetic fields, typically given on a homogeneous grid str
Supernova remnants (SNRs) are believed to accelerate particles up to high energies through the mechanism of diffusive shock acceleration (DSA). Except for direct plasma simulations, all modeling efforts must rely on a given form of the diffusion coef
Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic-ray transport. The transition from a ballistic to a di