Observational investigations of Earth's bow shock have highlighted distinct variations in turbulence characteristics when comparing fluctuations in the shock transition with those in the upstream and downstream plasma regions. To gain a more focused understanding in each of these areas, we have examined a range of local 2D and 3D hybrid simulations, using kinetic ions and fluid electrons. Each simulation has been chosen to cover a range of shock geometries, from quasi-parallel to quasi-perpendicular and high to low Mach number. In-situ observations, such as those from the Magnetospheric Multiscale (MMS) mission, are often unable to fully disentangle spatial and temporal effects. This is particularly evident in the shock transition and the magnetosheath, where, for example, whistler waves may have speeds comparable to the bulk flow and thus locally violate Taylor’s hypothesis for kinetic-scale fluctuations. Simulations overcome these limitations, enabling us to model the evolution of turbulence in the shock transition and further downstream. We characterize the turbulent fluctuations using the following three methods: Firstly, we examine the magnetic spectral indices spanning the inertial range and extending into the ion range as they change across the shock. Secondly, we investigate intermittency by means of the scale-dependent kurtosis. Lastly, we quantify the correlation lengths as measured across the shock, offering insights into the physical dimensions of fluctuations at scales smaller than the shock width. We will discuss the application of these measures to simulations in understanding the kinetic-scale behaviour of turbulence at Earth's bow shock.

Collisionless shock waves are efficient ion accelerators. Previous numerical and observational studies have shown that quasi-parallel (Q∥) shocks are more effective than quasi-perpendicular (Q⊥) shocks at generating energetic ions under steady upstream conditions. Here, we use a local, 2D, hybrid particle-in-cell model to investigate how ion acceleration at super-critical Q⊥ shocks is modulated when tangential discontinuities (TDs) with large magnetic shear are present in the upstream plasma. We show that such TDs can significantly increase the ion acceleration efficiency of Q⊥ shocks, up to a level comparable to Q∥ shocks. Using data from the hybrid model and test particle simulations, we show that the enhanced energization is related to the magnetic field change associated with the discontinuity. When shock-reflected ions cross the TD during their upstream gyromotion, the sharp field change causes the ions to propagate further upstream, and gain additional energy from the convection electric field associated with the upstream plasma flow. Our findings illustrate that the presence of upstream discontinuities can lead to bursts of energetic ions, even when they do not trigger the formation of foreshock transients. These results emphasize the importance of time-variable upstream conditions when considering ion energization at shocks.

A document by Konrad Steinvall. Click on the document to view its contents.

Turbulent plasmas such as the solar wind and magnetosheath exhibit an energy cascade which is present across a broad range of scales, from the stirring scale at which energy is injected, down to the smallest scales where energy is dissipated through processes such as reconnection and wave-particle interactions. Recent observations of Earth's bow shock reveal a disordered or turbulent transition region which exhibits features of turbulent dissipation, such as reconnecting current sheets. We have used observations from Magnetospheric Multiscale (MMS) over four separate bow shock crossings of varying θBn to characterise turbulence in the shock transition region and how it evolves towards the magnetosheath. We observe the magnetic spectrum evolving by fitting power laws over many short intervals and find that the power-law index in the shock transition region is separable from that of the upstream and downstream plasma, for both quasi-perpendicular and quasi-parallel shocks. Across the shock, we see a change in the breakpoint location between inertial and ion power-law slopes. We also observe the evolution of scale-independent kurtosis of magnetic fluctuations across the shock, finding a reduction of high kurtosis intervals downstream of the shock, which is more apparent in the quasi-perpendicular case. Finally, we adapt a method for calculating correlation length to include a high-pass filter, allowing estimates for changes in correlation length across Earth's bow shock. In a quasi-perpendicular shock, we find the correlation length to be significantly smaller in the magnetosheath than in the solar wind, however the opposite can occur for quasi-parallel shocks.

Collisionless shocks in astrophysical plasmas are important thermalizers, converting some of the incident flow energy into thermal energy, and non-thermalizers, partitioning that energy in unequal ways to different particle species, sub-populations thereof, and field components. This partition problem, or equivalently the shock equation of state, lies at the heart of shock physics. Here we employ systematically a framework to capture all the incident and downstream energy fluxes at two example traversals of the Earth's bow shock by the Magnetospheric Multiscale Mission. Here and traditionally such data has to be augmented by information from other spacecraft, e.g., to provide more accurate measurements of the cold solar wind beam. With some care and fortuitous choices, the energy fluxes are constant, including instantaneous measurements through the shock layer. The dominant incident proton ram energy is converted primarily into downstream proton enthalpy flux, the majority of which is actually carried by a small fraction of suprathermal protons. Fluctuations include both real and instrumental effects. Separating these, resolving the solar wind beam, and other considerations point the way to a dedicated mission to solve this energy partition problem across a full range of plasma and shock conditions.

Shock waves are common in the heliosphere and beyond. The collisionless nature of most astrophysical plasmas allows for the energy processed by shocks to be partitioned amongst particle sub-populations and electromagnetic fields via physical mechanisms that are not well understood. The electrostatic potential across such shocks is frame dependent. In a frame where the incident bulk velocity is parallel to the magnetic field, the deHoffmann-Teller frame, the potential is linked directly to the ambipolar electric field established by the electron pressure gradient. Thus measuring and understanding this potential solves the electron partition problem, and gives insight into other competing shock processes. Integrating measured electric fields is space is problematic since the measurements can have offsets that change with plasma conditions. The offsets, once integrated, can be as large or larger than the shock potential. Here we exploit the high-quality field and plasma measurements from NASA's Magnetospheric Multiscale mission to attempt this calculation. We investigate recent adaptations of the deHoffmann-Teller frame transformation to include time variability, and conclude that in practise these face difficulties inherent in the 3D time-dependent nature of real shocks by comparison to 1D simulations. Potential estimates based on electron fluid and kinetic analyses provide the most robust measures of the deHoffmann-Teller potential, but with some care direct integration of the electric fields can be made to agree. These results suggest that it will be difficult to independently assess the role of other processes, such as scattering by shock turbulence, in accounting for the electron heating.

Decomposing the electric field (E) into the contributions from generalized Ohm’s law provides key insight into both nonlinear and dissipative dynamics across the full range of scales within a plasma. Using high-resolution, multi-spacecraft measurements of three intervals in Earth’s magnetosheath from the Magnetospheric Multiscale mission, the influence of the magnetohydrodynamic, Hall, electron pressure, and electron inertia terms from Ohm’s law, as well as the impact of a finite electron mass, on the turbulent spectrum are examined observationally for the first time. The magnetohydrodynamic, Hall, and electron pressure terms are the dominant contributions to over the accessible length scales, which extend to scales smaller than the electron inertial length at the greatest extent, with the Hall and electron pressure terms dominating at sub-ion scales. The strength of the non-ideal electron pressure contribution is stronger than expected from linear kinetic Alfvén waves and a partial anti-alignment with the Hall electric field is present, linked to the relative importance of electron diamagnetic currents in the turbulence. The relative contribution of linear and nonlinear electric fields scale with the turbulent fluctuation amplitude, with nonlinear contributions playing the dominant role in shaping for the intervals examined in this study. Overall, the sum of the Ohm’s law terms and measured agree to within ~20% across the observable scales. These results both confirm general expectations about the behavior of in turbulent plasmas and highlight features that should be explored further theoretically.

We exploit novel “string-of-pearls” configuration of NASA’s Magnetospheric Multiscale mission to investigate properties of structures within the Earth’s magnetosheath that are short in duration but carry intense currents. Previous work has shown that the j.E energy conversion within current structures processes of order 10% of the total energy flux incident at the bow shock. This makes these events important contributors to the overall shock energy budget and ongoing thermalization within the magnetosheath. The present study, under very similar solar wind conditions and bow shock geometries, reveals significant qualitative differences from the previous study. Moreover, we find only modest, if any coherence, on scales <1000 km. We explore the implication of these observations in terms of both bow shock and turbulence energy transfer and dissipation.

The high latitude, lobe regions of the magnetosphere are often assumed to contain cool, low energy plasma populations. However, during periods of northward IMF, energetic plasma populations have occasionally been observed. We present three cases when Cluster observed uncharacteristically \say{hot} plasma populations in the lobe. For two of the three events, we present simultaneous observations of the plasma sheet observed by Double Star. The similarity between the plasma in the lobe and the plasma sheet suggests that the mechanism that produces plasma at high latitudes is likely to be tail reconnection, resulting in a trapped \say{wedge} of closed flux about the noon-midnight meridian. Complementary images from IMAGE and DMSP/SSUSI show that transpolar arcs, which form in each event in at least one hemisphere, directly intersect the footprint of the Cluster spacecraft in all three events. The intersection of the Cluster footprint with the transpolar arcs is synchronous with the observation of the energetic plasma populations in the lobe. This further supports the conclusion that it is likely this energetic plasma observed in the high latitude lobe regions of magnetosphere is on closed field lines.

Shock waves in collisionless plasmas rely on kinetic processes to convert the primary incident bulk flow energy into thermal energy. That conversion is initiated within a thin transition layer but may continue well into the downstream region. At the Earth’s bow shock, the region downstream of shock locations where the interplanetary magnetic field is nearly parallel to the shock normal is highly turbulent. We study the distribution of thin current events in this magnetosheath. Quantification of the energy dissipation rate made by the MMS spacecraft shows that these isolated intense currents are distributed uniformly throughout the magnetosheath and convert a significant fraction (5%-11%) of the energy flux incident at the bow shock.