On the evolution of turbulent fluctuations at collisionless shock waves

Abstract

Earth`s bow shock is a collisionless shock wave that stands slightly upstream of the terrestrial magnetic field. The angle between the shock normal vector and the upstream magnetic field defines \tbn, which can be quasi-perpendicular \qper or quasi-parallel \qpar, separating two fundamentally different kinds of shock. \qper shocks are very abrupt transitions, whereas \qpar shocks are significantly more disordered and turbulent. Turbulence is an ubiquitous phenomenon in space plasmas, and recent space missions such as NASA`s Magnetospheric Multiscale (MMS) have been launched with the goal of specifically understanding its dynamics. Turbulence can be characterised by; 1) energy injection at scales larger than the largest eddies. 2) a cascade of energy to smaller scales at a constant rate, corresponding to a power law index of $-5/3$ in the `inertial' range. The ion scale is the lower bound of the inertial range below which energy is dissipated, e.g. through reconnection. 3) Fluctuations which are `intermittent', where the amount of intermittency grows larger at smaller scales. Each of these key properties can be assessed with the magnetic spectral index, correlation length, and scale-dependent kurtosis, respectively. Turbulence behaves differently in the solar wind (SW) compared to the magnetosheath (MS), and the role of the bow shock in this transition is currently not well understood. In this thesis, we used observations from MMS and hybrid particle in cell (PIC) simulations to assess how the key features of turbulence evolve through the shock transition region (STR), the area where shock-driven processes operate. First, it was experimentally verified that Taylor`s hypothesis (TH) can be applied accurately in the STR. It was found through multi-spacecraft methods that TH is often applicable, limited only at electron scales by the influence of whistler waves. Then, we used intervals identified to be valid for TH to observe 1) magnetic power spectral index with a novel power-law fitting technique, 2) scale-dependent kurtosis, and 3) correlation length, high-pass filtered to remove the discontinuous influence of the shock. We also used hybrid-PIC simulations of collisionless shocks of different \tbn, and upstream flow velocity, and investigated the shock transition region using the same parameters as above. It was found in observations that the shock displays turbulence properties at sub-ion scales that are not seen in the SW or MS. In simulations, the shock front shows strong intermittency, which decays rapidly downstream, as well as steep power laws with spectral index $|\alpha|>5/3$ in the inertial range. Other properties of the evolution of turbulent fluctuations are also observed. These results are important for the study of solar wind-magnetosphere coupling, the implications of which are discussed.

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ORCID for Imogen Gingell: orcid.org/0000-0003-2218-1909

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