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

TL;DR

This study uses 2.5D hybrid simulations to analyze how ultra-low frequency (ULF) waves interact with collisionless shocks, revealing complex dependencies of wave properties on shock parameters and their influence on shock rippling and wave transmission.

Contribution

It provides new insights into the dependence of ULF wave characteristics on shock parameters and their role in shock rippling through detailed 2.5D hybrid simulations.

Findings

ULF wave wavelength correlates with Mach number and shock angle.

Shock ripples are driven by upstream ULF waves and affect wave transmission.

Downstream wave features differ from upstream but retain some spectral signatures.

Abstract

We study the interaction of upstream ultra-low frequency (ULF) waves with collisionless shocks by analyzing the outputs of eleven 2D local hybrid simulation runs. Our simulated shocks have Alfv\'enic Mach numbers between 4.29-7.42 and their $\theta_{BN}$ angles are 15$^\circ$, 30$^\circ$, 45$^\circ$ and 50$^\circ$. The ULF wave foreshocks develop upstream of all of them. The wavelength and the amplitude of the upstream waves exhibit a complex dependence on the shock's M$_A$ and $\theta_{BN}$. The wavelength positively correlates with both parameters, with the dependence on $\theta_{BN}$ being much stronger. The amplitude of the ULF waves is proportional to the product of the reflected beam velocity and density, which also depend on M$_A$ and $\theta_{BN}$. The interaction of the ULF waves with the shock causes large-scale (several tens of upstream ion inertial lengths) shock rippling. The properties of the shock ripples are related to the ULF wave properties, namely thier wavelength and amplitude. In turn, the ripples have a large impact on the ULF wave transmission across the shock because they change local shock properties ($\theta_{BN}$, strength), so that different sections of the same ULF wave front encounter shock with different characteristics. Downstream fluctuations do not resemble the upstream waves in terms the wavefront extension, orientation or their wavelength. However some features are conserved in the Fourier spectra of downstream compressive waves that present a bump or flattening at wavelengths approximately corresponding to those of the upstream ULF waves. In the transverse downstream spectra these features are weaker.