Upstream of quasi-parallel bow shocks, reflected ions generate ion-ion instabilities. The resulting magnetic fluctuations can advect through the shock and interact with planetary magnetospheres. The amplitude of magnetic fluctuations depends on the strength of the shock, quantified by the Alfvén Mach number (MA), which is the ratio of solar wind velocity to the local Alfvén velocity. With increasing heliocentric distance, the solar wind MA generally increases, such that Mercury typically experiences a lower MA ∼ 5 compared to Earth (MA ∼ 8), and Mars a slightly higher MA ∼ 9. Farther out in the solar system, Saturn has even higher MA (∼10). However, the solar wind flow is highly irregular, and on top of solar cycle variations these values for average MA at each planet do not capture extreme events. Statistical analysis of OMNIWeb observations from 2015 to 2023 shows that sustained (30 minutes or more) high MA (30-100) occurs at Earth about once a month. Using a selection of events in the ion foreshock regions of Mercury, Earth, Mars, and Saturn, a linear scaling is calculated for the maximum magnetic fluctuation amplitude as a function of MA. The resulting slope is ∼0.2. Based on the dominant fluctuation frequency for the largest-amplitude events at each planet, it is found that Mars exists in a special regime where the wave period of the magnetic fluctuations can be similar to or longer than the magnetospheric convection timescale, making Mars more susceptible to space weather effects associated with foreshock fluctuations.

Collisionless shock waves, found in supernova remnants, interstellar, stellar, and planetary environments, and laboratories, are one of nature's most powerful particle accelerators. This study combines in situ satellite measurements with recent theoretical developments to establish a reinforced shock acceleration model for relativistic electrons. Our model incorporates transient structures, wave-particle interactions, and variable stellar wind conditions, operating collectively in a multiscale set of processes. We show that the electron injection threshold is on the order of suprathermal range, obtainable through multiple different phenomena abundant in various plasma environments. Our analysis demonstrates that a typical shock can consistently accelerate electrons into very high (relativistic) energy ranges, refining our comprehension of shock acceleration while providing insight on the origin of electron cosmic rays.

We use the Magnetospheric Multiscale mission to study electron kinetic entropy across Earth's quasi-perpendicular bow shock. We perform a statistical study of how the change in electron entropy depends on the different plasma parameters associated with a collisionless shock crossing. The change in electron entropy exhibits strong correlations with upstream electron plasma beta, Alfv & eacute;n Mach number, and electron thermal Mach number. We investigate the source of entropy generation by correlating the change in electron entropy across the shock to the measured electric and magnetic field wave power strengths for different frequency intervals within different regions in the shock transition layer. The electron entropy change is observed to be greater for higher electric field wave power within the shock ramp and shock foot for frequencies between the lower hybrid frequency and electron cyclotron frequency, suggesting electrostatic waves are important for electron kinetic entropy generation at Earth's quasi-perpendicular bow shock. Any eventual cross-shock potential contribution to the electron entropy generation has not been considered in this study.

We use the Magnetospheric Multiscale mission (MMS) to study electron acceleration at Earth's quasi-perpendicular bow shock to address the long-standing electron injection problem. The observations are compared to the predictions of the stochastic shock drift acceleration (SSDA) theory. Recent studies based on SSDA predict electron distribution being a power law with a cutoff energy that scales with upstream parameters. This scaling law has been successfully tested for a single Earth's bow shock crossing by MMS. Here we extend this study and test the prediction of the scaling law for seven MMS Earth's bow shock crossings with different upstream parameters. A goodness-of-fit test shows good agreement between observations and SSDA theoretical predictions, thus supporting SSDA as one of the most promising candidates for solving the electron injection problem.

Cosmic rays are ultra-relativistic particles traveling near the speed of light permeating the galaxy. Collisionless shock waves with their ubiquity throughout the universe and excellent capability of accelerating charged particles offer an explanation to the origin of cosmic rays. It is well established that the particles are predominately accelerated at young supernova remnant shocks through a mechanism called Diffusive Shock Acceleration (DSA). However, this theory only applies if the particles already have a relativistic starting energy. Therefore, the charged particles must be pre-accelerated up to relativistic energies by some unknown mechanism(s) before being injected into the cosmic ray acceleration process. This is known as the injection problem and a lot of effort has been put into resolving it over the past decades. This thesis will use spacecraft data from NASA's Magnetospheric Multiscale (MMS) mission to study electron acceleration at Earth's collisionless bow shock. In particular, we will study what mechanisms are able to accelerate electrons from solar wind thermal energies (~20 eV) up to mildly relativistic energies 10-100 keV. Paper III and Paper IV set out to study energetic electron events observed at Earth's bow shock by MMS. In Paper III, we investigate the most promising candidate for a solution to the long-standing electron injection problem, the Stochastic Shock Drift Acceleration (SSDA) mechanism. SSDA successfully describes a mechanism for electrons to be accelerated up to mildly relativistic energies. However, only one previous observation of the theory exists. Building on that study, we provide further evidence in favor of the theory by showing good agreement between predictions and observations. Observational evidence of an alternative electron acceleration mechanism is presented in Paper IV. The observation displays an increase in electron flux up to ~60 keV, and inconsistent features with the SSDA mechanism. The event exhibits bi-directional electron pitch angle distributions which are generally associated with magnetic bottles and are rarely observed around Earth's bow shock. The evidence led us to propose a two-step acceleration process where field-aligned electron beams are injected into a shrinking magnetic bottle configuration caused by either a shock surface deformation or a bent upstream magnetic field line intersecting the shock surface at two different locations. Papers I and II are directed more toward the heating of electrons at collisionless shocks. The studies investigate electron entropy generation at collisionless shocks and its dependence on shock parameters. Paper I states and deals mostly with the (instrumental) challenges of calculating entropy using the MMS spacecraft data. The close relation between entropy and irreversible heating is then discussed and used to classify different heating mechanisms at the shock. We show that the electron entropy generation at Earth's bow shock depends strongly on the upstream electron plasma beta and Alfvén Mach number. In the absence of collisions, the exact generation of entropy across collisionless shocks is an open question. Early theoretical studies suggest that particle-particle collisions are replaced by plasma wave-particle interaction. In Paper II, we build on the result from Paper I, by performing a statistical study of electron entropy change across Earth's bow shock and try to answer what plasma wave modes are important for entropy generation.

We use the Magnetospheric Multiscale mission to observe a bi-directional electron acceleration event in the electron foreshock upstream of Earth's quasi-perpendicular collisionless bow shock. The acceleration region is associated with a decrease in wave activity, inconsistent with common electron acceleration mechanisms such as Diffusive Shock Acceleration and Stochastic Shock Drift Acceleration. We propose a two-step acceleration process where an electron field-aligned beam acts as a seed population further accelerated by a shrinking magnetic bottle process, with the shock acting as the magnetic mirror(s).

Energetic electrons have been frequently observed during magnetic reconnection in the magnetotail. The acceleration process of the energetic electrons is not fully understood. In this paper, we select for a detailed study a case of energetic electron acceleration from the earlier reported interval of turbulent magnetic reconnection in Earth's magnetotail observed by the Magnetospheric Multiscale mission. We use the first-order Taylor expansion method to reconstruct the magnetic topology of electron acceleration sites from the data. We find that the energetic electron fluxes increase inside the flux rope forming in front of the magnetic pileup region. We show that the energetic electrons are produced by a two-step process where two different acceleration mechanisms are successively operating outside and inside the flux rope. First, the thermal electrons are energized in the field-aligned direction inside the magnetic pileup region owing to the Fermi mechanism forming a cigar-like distribution. Second, those energized electrons are further accelerated predominately antiparallel to the magnetic field direction by a parallel electric field inside the flux rope. Our findings provide information for a better understanding of the generation of energetic electrons during turbulent reconnection process.

We use Magnetospheric Multiscale (MMS) data to study electron kinetic entropy per particle Se across Earth's quasi-perpendicular bow shock. We have selected 22 shock crossings covering a wide range of shock conditions. Measured distribution functions are calibrated and corrected for spacecraft potential, secondary electron contamination, lack of measurements at the lowest energies and electron density measurements based on plasma frequency measurements. All crossings display an increase in electron kinetic entropy across the shock Delta S-e being positive or zero within their error margin. There is a strong dependence of Delta S-e on the change in electron temperature, Delta T-e, and the upstream electron plasma beta, beta(e). Shocks with large Delta T-e have large Delta S-e. Shocks with smaller beta(e) are associated with larger Delta S-e. We use the values of Delta S-e, Delta Te and density change Delta n(e) to determine the effective adiabatic index of electrons for each shock crossing. The average effective adiabatic index is <gamma(e)> = 1.64 +/- 0.07.

High-speed plasma jets downstream of Earth's bow shock are high velocity streams associated with a variety of shock and magnetospheric phenomena. In this work, using the Magnetosphere Multiscale mission, we study the properties of a jet found downstream of the Quasi-parallel bow shock using high-resolution (burst) data. By doing so, we demonstrate how the jet is an inherently kinetic structure described by highly variable velocity distributions. The observed distributions show the presence of two plasma population, a cold/fast jet and a hotter/slower background population. We derive partial moments for the jet population to isolate its properties. The resulting partial moments appear different from the full ones which are typically used in similar studies. These discrepancies show how jets are more similar to upstream solar wind beams compared to what was previously believed. Finally, we explore the consequences of our results and methodology regarding the characterization, origin, and evolution of jets. 

Magnetosheath jets are transient, localized dynamic pressure enhancements found downstream of the Earth's bow shock in the magnetosheath region. Using a pre-existing database of magnetosheath jets we train a neural network to distinguish between jets found downstream of a quasi-parallel bow shock (theta(Bn) < 45 degrees) and jets downstream of a quasi-perpendicular bow shock (theta(Bn)>45 degrees). The initial database was compiled using MMS measurements in the magnetosheath (downstream) to identify and classify them as "quasi-parallel" or "quasi-perpendicular," while the neural network uses only solar wind (upstream) measurements from the OMNIweb database. To evaluate the results, a comparison with three physics-based modeling approaches is done. It is shown that neural networks are systematically outperforming the other methods by achieving a similar to 93% agreement with the initial dataset, while the rest of the methods achieve around 80%. The better performance of the neural networks likely is due to the fact that they use information from more solar wind quantities than the physics-based models. As a result, even in the absence of certain upstream properties, such as the IMF direction, they are capable of accurately determining the jet class.