Session UO05: Collisionless Shocks and Reconnection

Collisionless ion-electron energy exchange in magnetized astrophysical shocks

Magnetized collisionless shocks are ubiquitous in the universe, and energy partition in these shocks has long been an open question. Independent thermalization would predict a largely uneven energy partition because of the large ion-electron mass ratio, contradicting astronomical observations. Our kinetic simulations of low Mach number magnetized collisionless shocks show a significant energy exchange between ions and electrons in the downstream of the shocks, which implies a collisionless electron heating mechanism. A multi-fluid model indicates a resonance between electron whistler and ion magnetohydrodynamic waves may provide new mechanisms that account for the energy transfer from ions to electrons.   

Magnitude of Short-Wavelength Electric Field Fluctuations in Simulations of Collisionless Plasma Shocks

Large-amplitude electrostatic fluctuations are routinely observed by spacecraft upon traversal of collisionless shocks in the heliosphere. Kinetic simulations of shocks have struggled to reproduce the amplitude of such fluctuations, complicating efforts to understand their influence on energy dissipation and shock structure. In this contribution, 1D particle-in-cell simulations with realistic proton-to-electron mass ratio are used to show that in cases with upstream electron temperature exceeding the ion temperature , the magnitude of the fluctuations increases with the ratio ω_pe/Ω_ce of electron plasma-to-cyclotron frequency ratio, reaching realistic values at ω_pe/Ω_ce=32 for the cases considered. The large-amplitude fluctuations are shown to be associated with ion phase-space holes. In the cases where upstream temperature ratio is reversed, the magnitude of the fluctuations remains small.   

Energy partition in high-Mach number collisionless shocks

Collisionless shock waves produced by violent interactions of supersonic plasma flows with the interstellar medium or planetary magnetospheres are observed to heat the plasma, amplify magnetic fields, and accelerate electrons and protons to relativistic speeds. However, the exact mechanisms that control energy partition in these shocks remain a mystery. This is particularly challenging for high Mach number shocks, such as those associated with supernova remnants, where spacecraft data in the relevant regime is scarce and the shock structure cannot be directly resolved from observations. We will discuss recent progress in using the combination of fully kinetic simulations and laser-driven laboratory experiments at the National Ignition Facility to study energy partition in high-Mach number collisionless shocks. In particular, we will focus on the shock microphysics and how the interplay between collisionless and collisional processes impacts electron and ion heating.   

Simulation study of energy partition in non-relativistic magnetized collisionless shocks

Collisionless shocks are common in astrophysical plasmas and are known to be important for the magnetic field amplification and acceleration of both high energy electrons and protons. While the diffusive shock acceleration mechanism is well established, particle injection remains an important puzzle. In this work we present the results of large-scale one-dimensional particle-in-cell simulations of magnetized, non-relativistic, collisionless shocks to investigate how electron heating and the properties of the injected particles depend on the Alfvénic Mach numbers and the orientation of the ambient magnetic field. Quasi-parallel and quasi-perpendicular shocks are analyzed. Reflected particles exchange energy through wave-particle interactions, triggering instabilities in the upstream that promote electron heating. We discuss the nature of these instabilities, and the development of a non-thermal power-law-like tail in the energy spectra, finding that quasi-parallel shocks with high Mach number are the most efficient in terms of injecting and accelerating particles to the highest energies.   

Study of early-stage, quasi-parallel, collisionless shock formation in the high Alfvénic Mach number regime

Collisionless shocks that form in the presence of an ambient magnetic field are the likely source of the highest energy cosmic rays in our universe. Both the magnetic field amplitude, through the Alfvénic Mach number (M_A), and the field orientation relative to the plasma flow will dictate the formation mechanism of the collisionless shocks. The quasi-parallel configuration has shown to produce efficient particle acceleration in satellite measurements [Johlander ApJ 914 (2021)] and in numerical studies [Caprioli ApJ 783 (2014)]. Laser-based experiments provide a unique means to create relevant plasma conditions to study the microphysics associated with electromagnetic field generation relevant to quasi-parallel collisonless-shock formation. To this end, we have developed a new experimental platform at the Omega Laser Facility to study the early stages of quasi-parallel collisionless shock formation by studying the streaming instabilities generated during the interpenetration of magnetized, asymmetric plasma flows at high M_A (>100). The interaction region is characterized using time-resolved Thomson scattering to fully characterize the plasma flows and short-pulse proton radiography to visualize the B-field structures driven by ion streaming instabilities. Recent experimental results will be shown and discussed.   

Study of the interpenetration of asymmetric plasma flows with experiments and simulations relevant to quasi-parallel magnetized collisionless shock formation

Collisionless shocks, where formation scales are much smaller than the collisional mean free path, are found throughout astrophysics and are potential candidates for high-energy particle acceleration and cosmic ray generation. When these shocks form in the presence of a pre-existing magnetic field, the orientation of the shock normal relative to the magnetic field determines characteristics of the shock formation. Quasi-parallel shocks, where this angle is less than 45°, are predicted to be very efficient particle accelerators. However, the underlying physics is not as well understood and challenging to study in the laboratory. We present experimental results from the OMEGA Laser Facility and supporting simulations to study the interpenetration of asymmetric plasma flows in a parallel magnetic field to study early formation processes relevant to quasi-parallel collisionless shock formation. We highlight analysis of Thomson scattering data collected from experiment and compare results with simulations.   

Electron motion and acceleration in magnetic flux ropes produced by magnetic reconnection in quasi-parallel shocks

In the Earth's bow shock, magnetic reconnection can occur in the shock transition and downstream regions, and many magnetic flux ropes are produced. We discuss electron motion and acceleration in these flux ropes, based on results obtained by theory and 2D particle-in-cell (PIC) simulations. In 2D PIC simulations where the parameters are consistent with a quasi-parallel Earth's bow shock, electron temperature becomes significantly large inside the flux ropes, and the electron energy distribution shows a power-law with an index of 6. 

We analyze the motion of an electron trapped in a flux rope that is moving in a certain direction. We derive a drift motion due to the magnetic field gradient in the flux rope, showing that the drift speed is much larger than the grad-B drift. However, we show that the combination of this drift motion and the gyromotion does not contribute to energize the electron at all. We also show that the work done by the ExB drift and the motional electric field can be canceled out with the work done by the non-ideal electric field. As a result, the work done by the Hall electric field and the in-plan velocity can become the most dominant source of the energization, when the island is moving. 

The simulation shows that almost half of the most energetic group of electrons can be explained by the Hall field acceleration. We also discuss the production of power law spectrum with this mechanism.    

Theory and observations of the interaction between magnetohydrodynamic waves and shocks

The problem of wave-shock interaction is of fundamental importance to plasma physics. Linear waves and shocks that are supported by the magnetohydrodynamics model are ubiquitous in many plasma environments. We revisit the theoretical problem of shock-wave interaction based on linearized boundary conditions of magnetohydrodynamics. The shock is regarded as an ideal discontinuity and an individual wave mode is considered to impact the shock from upstream. Depending on the type of the shock, there may be waves transmitted downstream or reflected upstream. The wavevector and fluctuation amplitude of the transmitted or reflected waves are calculated. We show how compressible and incompressible waves can be generated or amplified at the shock, and how the shock front is perturbed. We also demonstrate through examples how the theory can be directly applied to in-situ heliospheric observations.   

Turbulence properties and associated particle transport in 3D low-beta magnetic reconnection

Reconnection-generated turbulence plays a crucial role in particle acceleration and transport in the reconnection region. Using 3D kinetic simulations of magnetic reconnection, we investigate the characteristics of this turbulence and the associated particle transport. Our study focuses on the weak guide-field regime relevant to the Earth's magnetotail and solar flares, where particle acceleration is highly efficient. By analyzing cross-scale energy transfer with scale-filtering techniques, we observe that a substantial portion of the released magnetic energy cascades from large to small scales, resembling a turbulence cascade. The turbulence properties, including the turbulence spectrum and anisotropy scaling in the reconnection region, are broadly consistent with current turbulence theory. Tracing the magnetic field lines reveals that neighboring lines can separate exponentially, indicating a superdiffusion process. Particles moving along these lines also exhibit superdiffusion while simultaneously experiencing scattering by turbulence fluctuations, resulting in a mixing of superdiffusion and normal diffusion. Using test-particle simulations, we evaluate the spatial transport coefficients in such turbulence reconnection regions. These findings are essential for understanding high-energy particle acceleration in magnetic reconnection and have significant implications for fundamental reconnection and turbulence physics in space and astrophysical plasmas.   

Simulating Magnetic Reconnection using the PETSc Particle-In-Cell Framework

Numerical solutions to the Vlasov-Maxwell equations have important applications in solar and magnetospheric physics. At the microscale, electrons and ions capture energy released from powerful magnetic events, such as reconnection, and in-turn play a role in driving the macroscopic systems. Advancements in plasma modelling provide important insights used to design the next generation of solar imagers and other instruments. The goal of this research is to extend the existing electrostatic, Vlasov-Poisson, PETSc Particle-in-Cell (PETSc-PIC) framework to self-consistent electromagnetic systems. In the Vlasov-Maxwell PETSc-PIC framework, Maxwell's equations are solved using the finite element method while the Vlasov equation is solved with conservative, explicit basic symplectic time integrators. Collisions may be added to the formulation by means of a particle-basis Landau collision operator. With an electromagnetic, Vlasov-Maxwell, PETSc-PIC model, we may study the kinetic-scale transfer of magnetic energy to particles in reconnection systems, such as Harris current sheets.   

Data-driven discovery of fluid closures for magnetic reconnection from fully kinetic particle-in-cell simulations

Accurate fluid descriptions of collisionless plasmas are important to describe and understand the dynamics of magnetic reconnection in large-scale systems. However, one of the main challenges of such fluid descriptions is the development of accurate closure models that capture the important effects of unresolved higher-order moments of the distribution function on the lower-order moments. In this work, we explore the use of machine learning techniques to learn accurate closure models for the plasma pressure and heat flux tensors from the data of fully kinetic simulations of magnetic reconnection. We show the importance of embedding fundamental physical symmetries such as frame-invariance into the machine learned models to eliminate spurious correlations/dependencies in the data and to improve generalizability to different system sizes and plasma conditions. We also investigate the role of non-locality on the accuracy of the closure models using convolutional neural networks, and determine an optimal kernel sizes that balances between closure accuracy and complexity. Finally, we discuss the possibility of integrating these machine-learned closures into the loop of fluid plasma simulations.   

Plasmoid-mediated inverse energy transfer driven by coalescing magnetic islands

The dynamics of a large ensemble of magnetic islands in a turbulent environment are relevant to a wide range of heliospheric and astrophysical phenomena. We investigate such dynamics using high-resolution, two-dimensional magnetohydrodynamic (MHD) simulations. The coalescence of magnetic islands, enabled by magnetic reconnection, leads to both an inverse energy transfer to large spatial scales and a direct turbulent cascade to smaller scales. The successive island mergers dictate the decay of magnetic energy and formation of progressive larger-scale structures of magnetic fields, the time evolution of which can be explained by the conservation of the (ideal) invariants such as the magnetic potential. With a sufficiently high magnetic Reynolds number, the elongated reconnecting current sheets between the merging islands break into chains of small plasmoids. The mediation of plasmoids causes the magnetic energy spectrum to steepen to a spectral index of -2.2, as predicted by previous studies when the rate of energy cascade is controlled by that of the growth of plasmoids. This transition scale of spectra is time-dependent, collectively determined by the merging dynamics of energy-containing islands and that of small-scale plasmoids. The complex dynamics introduced by the dynamics of omnipresent plasmoids result in a new regime for the inverse and direct energy cascade of turbulence and thus have important implications for various long-standing problems such as corona heating and magnetogenesis.   

Understanding the Magnetic Power Spectra in Plasmoid-mediated Magnetic Reconnection

Reconnection driven turbulence is a frontier of research in plasma physics. Some theoretical studies and MMS observations in the plasmoid reconnection regime found some power spectral indices around 5/3 to indicate Goldreich–Sridhar turbulence vortex cascade. But the Goldreich–Sridhar theory is not strictly applicable to plasmoid reconnection with order-unity magnetic field change in the inertial range. Using 2D and 3D kinetic and MHD simulations, we find that while the power spectra in the x direction or the x-y plane (with x the reconnecting field and y the guide field direction) have indices close to 5/3, the spectra in the x-z plane (the k_⟂ spectra perpendicular to the guide field) have indices around 2.7, differing by 1 from 5/3. Surprisingly, 2D and 3D simulations have similar spectral indices even though 2D simulations only have magnetic islands without the 3D turbulence.  These results suggest that the power spectra may not indicate turbulence vortex cascade but may instead reflect the size distribution of magnetic islands/flux ropes. We use a theoretical model to predict the island-size (w) distribution (∝w^-1) and the corresponding various power spectra, which roughly agree with the simulation and observation results particularly the large 2D MHD simulation with clear island distributions. These findings are essential to understanding the nature of magnetic fluctuations driven by reconnection.   

Simulations underestimate wave amplitudes during magnetic reconnection

Collisionless plasma systems are often studied using fully kinetic simulations, where protons and electrons are treated as particles. Due to their computational expense, it is necessary to reduce the ion-to-electron mass ratio mi/me or the ratio between plasma and cyclotron frequencies in simulations of large systems. In this work we show that when electron-scale waves are present in larger-scale systems, numerical parameters affect their amplitudes. Using lower-hybrid drift waves during magnetic reconnection as an example, we find that the ratio between the wave electric field and the reconnection electric field scales like $sqrt(mi/me)$, meaning that typical simulations underestimate its contribution. Furthermore, the anomalous drag that contributes to momentum balance is found to be underestimated by an order of magnitude. The results suggest caution when interpreting the results of kinetic simulations, and may be relevant to other systems such as collisionless shocks