Characteristics and Generation of Upstream Ultra-low-frequency Waves at Quasi-parallel Shocks: Hybrid Simulations

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Abstract
This study investigates upstream wave generation at quasi-parallel shocks using large-scale one-dimensional hybrid simulations. The results reveal a spatial evolution of ultra-low-frequency waves from the far upstream region to the shock front. In the far upstream region, the waves are quasi-monochromatic, incompressible, and exhibit left-hand polarization in the downstream frame. Closer to the shock front, these waves transition into shorter-wavelength compressional fluctuations characterized by both left- and right-hand polarizations. Linear kinetic instability analysis based on simulated upstream proton velocity distributions confirms that the observed waves are primarily excited by local instabilities driven by backstreaming proton populations throughout the foreshock region. Near the shock front, the wave activity arises from a combination of locally excited waves from hot diffuse ions and upstream-generated waves convected downstream, jointly producing the chaotic polarization and compressional signatures observed. The parallel shock simulation also captures an early splitting of backstreaming protons into two beams. Trajectory analysis identifies the low-energy beam as an artifact resulting from proton reflection prior to full shock formation, underscoring the need for adequate simulation time to achieve a more realistic foreshock. A comparison of simulations of shock normal angles ranging from 0° to 40° indicates that while the overall pattern of wave evolution remains consistent across the quasi-parallel regime, increasing shock normal angle enhances wave compressibility and induces a polarization transition from circular to elliptical in the far upstream region.
Funding Information
  • MOST ∣ National Natural Science Foundation of China (42530202)

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