ULF Wave Transmission Across Collisionless Shocks: 2.5D Local Hybrid Simulations

摘要

We study the interaction of upstream ultralow frequency (ULF) waves with collisionless shocks by analyzing the outputs of 11 2D local hybrid simulation runs. Our simulated shocks have Alfvénic Mach numbers between 4.29 and 7.42 and their θ_(BN) angles are 15°, 30°, 45°, and 50°. 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 θ_(BN). The wavelength positively correlates with both parameters, with the dependence on θ_(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 θ_(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 their 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 (θ_(BN), strength), so that different sections of the same ULF wavefront 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.