ULF wave transmission across collisionless shocks: 2.5D local hybrid simulations

We study the interaction of upstream ultra-low frequency (ULF) waves with collisionless shocks by analyzing the outputs of eleven 2.5D local hybrid simulation models. Our simulated shocks have Alfvénic Mach numbers between 4.29-7.42 and their θ_BN angles are 15º, 30º, 45º and 50º. Thus all are quasi-parallel or marginally quasi-perpendicular shocks. Upstream of all of the shocks the ULF wave foreshock develops. It is populated by transverse and compressive ULF magnetic field fluctuations that propagate upstream in the rest frame of upstream plasma. We show that the properties of the upstream waves reflect on the properties of the shock ripples. We also show that due to these ripples, as different portions of upstream waves reach the shocks, they encounter shock sections with different properties, such as the downstream magnetic field and the orientation of the local shock normals. This means that the waves are not simply transmitted into the downstream region but are heavily processed by the shocks. The identity of upstream fluctuations is largely lost, since the downstream fluctuations do not resemble the upstream waves in their shape, waveform extension, orientation nor in their wavelength. However some features are conserved. For example, the Fourier spectra of upstream waves present a bump or flattening at wavelengths corresponding to those of the upstream ULF waves. Most of the corresponding compressive downstream spectra also exhibit these features, while transverse downstream spectra are largely featureless.