arXiv subjects

Paul A. Cassak

Publications and source records attributed to Paul A. Cassak.

At least 19 recordsLinked to original sources

arXiv2026

Velocity space origins of pressure-strain interaction in multi-population distributions and its application to magnetic reconnection

A forefront research question is how energy evolves in weakly collisional plasmas for which departures from local thermodynamic equilibrium (LTE) are significant. The standard approach is studying the terms in the non-LTE energy evolution equation derived by taking the second moment of the Boltzmann equation, but the resultant fluid metrics do not retain information about which particles at which velocities drive energy evolution. A widely studied channel for internal energy density evolution is the pressure-strain interaction. Here we employ the kinetic pressure-strain [S. A. Conley et al., ${\it Phys. Plasmas,} {\bf 31}$, 122117 (2024)], a phase space diagnostic whose velocity-space integral recovers the pressure-strain interaction to disambiguate the contributions to pressure-strain interaction from disparate particle populations in composite phase-space densities. We develop phase-space analogs of the pressure-strain interaction decompositions to provide the phase-space origins of normal vs. sheared flow. We introduce the "kinetic strain-rate" tensor, the phase-space analog of strain-rate tensor, which we argue is needed to interpret phase-space origins of pressure-strain interaction. To demonstrate the utility of these quantities, we investigate them for composite electron distributions near the electron diffusion region in two-dimensional particle-in-cell simulations of antiparallel symmetric magnetic reconnection. We find that the phase space-based diagnostics isolate the roles of distinct populations. These results contribute to a growing body of work providing new methods for quantifying phase space energy evolution for a broad array of processes, from magnetic reconnection to collisionless shocks and turbulence, opening new pathways for answering longstanding problems of particle energization in weakly collisional plasmas.

physics.plasm-ph↗

arXiv2025

The Importance of Heat Flux in Quasi-Parallel Collisionless Shocks

Collisionless plasma shocks are a common feature of many space and astrophysical systems and are sources of high-energy particles and non-thermal emission, channeling as much as 20\% of the shock's energy into non-thermal particles. The generation and acceleration of these non-thermal particles have been extensively studied, however, how these particles feed back on the shock hydrodynamics has not been fully treated. This work presents the results of self-consistent hybrid particle-in-cell simulations that show the effect of self-generated non-thermal particle populations on the nature of collisionless, quasi-parallel shocks. They contribute to a significant heat flux density upstream of the shock. Non-thermal particles downstream of the shock leak into the upstream region, taking energy away from the shock. This increases the compression ratio, slows the shock down, and flattens the non-thermal population's spectral index for lower Mach number shocks. We incorporate this into a revised theory for the Rankine-Hugoniot jump conditions that include this effect and it shows excellent agreement with simulations. The results have the potential to explain discrepancies between predictions and observations in a wide range of systems, such as inaccuracies of predictions of arrival times of coronal mass ejections and the conflicting radio and x-ray observations of intracluster shocks. These effects will likely need to be included in fluid modeling to accurately predict shock evolution.

physics.plasm-ph↗

arXiv2025

Flow Crossover and Parallel Outflow during Collisionless Magnetic Reconnection

Using particle-in-cell simulations that label ions and electrons according to their initial inflow region, we find that during 2D collisionless magnetic reconnection, the bulk flow of the plasma from each inflow side crosses paths with plasma from the other inflow side and crosses the midplane before being redirected into an outflow jet. This feature, which we term ``flow crossover,'' implies mechanisms to generate bulk motion in a direction parallel to the magnetic field. We find that ions and electrons undergo different parallel driving mechanisms, leading to different flow crossover patterns. The parallel bulk flow for ions is generated more locally within the ion diffusion region, whereas the parallel bulk flow for electrons is mostly generated outside the electron diffusion region. Consequently, the reconnection outflows are more of a parallel flow than a perpendicular flow, especially for the electron outflow. The flow crossover and the parallel outflow patterns occur not only in symmetric reconnection but also in the more complex scenario of a guide-field asymmetric reconnection, suggesting that it is a general feature of collisionless magnetic reconnection. Because the plasma on one side of the outflow mostly originates from the inflow plasma on the other side, we predict that near an asymmetric reconnection site in a collisionless space plasma, in situ observations across the outflow region could reveal locally reversed gradients in plasma properties.

physics.plasm-ph↗

arXiv2025

The Enhancement of Ion Heating in Kinetic, Anti-Parallel Reconnection in the Presence of a Flow Shear

We investigate the kinetic effects of upstream, magnetic field-aligned, flow shear on anti-parallel magnetic reconnection using 2.5D Particle-In-Cell simulations. Our results demonstrate that flow shear significantly alters the reconnection process, leading to enhanced ion heating, reduced outflow speeds, and a modified reconnection geometry. In contrast to previous Hall Magnetohydrodynaic (MHD) studies, we find that reconnection becomes a more efficient plasma heating mechanism in the presence of sub-Alfvénic flow shear, with ion heating increasing by as much as 300\%. This enhanced heating is achieved by efficiently converting the incoming flow shear energy into thermal energy through istropization in the exhaust. The enhanced heating leads to a pressure gradient away form the x-line exerting a force that reduces the outflow jet speed and slows down the reconnection process. This conversion is due to beam selection effects, mixing and scattering in the exhaust. A theoretical model is developed which predicts well the exhaust heating and outflow speed reduction. These results offer a potential explanation for recent Parker Solar Probe observations of suppressed reconnection in the presence of flow shear and carry significant implications for energy dissipation in turbulent plasmas.

physics.plasm-ph↗

arXiv2024

Identifying the Growth Phase of Magnetic Reconnection using Pressure-Strain Interaction

Magnetic reconnection often initiates abruptly and then rapidly progresses to a nonlinear quasi-steady state. While satellites frequently detect reconnection events, ascertaining whether the system has achieved steady-state or is still evolving in time remains challenging. Here, we propose that the relatively rapid opening of reconnection separatrices within the electron diffusion region (EDR) serves as an indicator of the growth phase of reconnection. The opening of the separatrices is produced by electron flows diverging away from the neutral line downstream of the X-line and flowing around a dipolarization front. This flow pattern leads to characteristic spatial structures in pressure-strain interaction that could be a useful indicator for the growth phase of a reconnection event. We employ two-dimensional particle-in-cell numerical simulations of anti-parallel magnetic reconnection to validate this prediction. We find that the signature discussed here, alongside traditional reconnection indicators, can serve as a marker of the growth phase. This signature is potentially accessible using multi-spacecraft single-point measurements, such as with NASA's Magnetospheric Multiscale (MMS) satellites in Earth's magnetotail. Applications to other settings where reconnection occurs are also discussed.

physics.plasm-ph↗

arXiv2024

Suppression of Collisionless Magnetic Reconnection in the High Ion $β$, Strong Guide Field Limit

In magnetic reconnection, the ion bulk outflow speed and ion heating have been shown to be set by the available reconnecting magnetic energy, i.e., the energy stored in the reconnecting magnetic field ($B_r$). However, recent simulations, observations, and theoretical works have shown that the released magnetic energy is inhibited by upstream ion plasma beta $β_{i}$ -- the relative ion thermal pressure normalized to magnetic pressure based on the reconnecting field -- for antiparallel magnetic field configurations. Using kinetic theory and hybrid particle-in-cell simulations, we investigate the effects of $β_{i}$ on guide field reconnection. While previous works have suggested that guide field reconnection is uninfluenced by $β_{i}$, we demonstrate that the reconnection process is modified and the outflow is reduced for sufficiently large $β_{i} > B_g^2/(B_r^2 + B_g^2)$. We develop a theoretical framework that shows that this reduction is consistent with an enhanced exhaust pressure gradient, which reduces the outflow speed as $v_0 \propto 1/\sqrt{β_{i}}$. These results apply to systems in which guide field reconnection is embedded in hot plasmas, such as reconnection at the boundary of eddies in fully developed turbulence like the solar wind or the magnetosheath as well as downstream of shocks such as the heliosheath or the mergers of galaxy clusters.

physics.plasm-ph↗

arXiv2024

The Kinetic Analogue of the Pressure-Strain Interaction

Energy transport in weakly collisional plasma systems is often studied with fluid models and diagnostics. However, the applicability of fluid models is necessarily limited when collisions are weak or absent, and using a fluid approach can obscure kinetic processes that provide key insights into the physics of energy transport. A kinetic technique that retains all of the information in 3D-3V phase-space for the study of energy transfer between electromagnetic fields and particle kinetic energy, which is quantified by the rate of electromagnetic work per unit volume $\mathbf{j} \cdot \mathbf{E}$ in fluid models, is the Field- Particle Correlation (FPC) technique. This technique has demonstrated that leveraging the full information contained in phase-space can elucidate the physical mechanisms of energy transfer. This provides a significant advantage over fluid diagnostics that quantify the rate at which energy is exchanged but do not distinguish between different physical processes. A different channel of energy transport, between fluid flow energy and particle internal energy, is quantified in fluid models via the pressure-strain interaction $-(\mathbf{P} \cdot \nabla ) \cdot \mathbf{u}$. Using a similar approach to that of the field-particle correlation technique, in this work we derive a kinetic analog of the pressure-strain interaction and use it alongside the field-particle correlation to analyze the flow of energy from electromagnetic fields into particle internal energy in two case studies of electron Landau damping.

physics.plasm-ph↗

arXiv2024

Higher-order nonequilibrium term: Effective power density quantifying evolution towards or away from local thermodynamic equilibrium

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A forefront research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here, we introduce the ``higher-order non-equilibrium term'' (HORNET) effective power density that quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, namely magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, $\rm{Pi-D}$, and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8\% and 35\% for electrons and ions, respectively, for reconnection; up to 67\% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed.

physics.plasm-ph↗

arXiv2023

Scale Filtering Analysis of Kinetic Reconnection and its Associated Turbulence

Previously, using an incompressible von Kármán-Howarth formalism, the behavior of cross-scale energy transfer in magnetic reconnection and turbulence was found to be essentially identical to each other, independent of an external magnetic (guide) field, in the inertial and energy-containing ranges (Adhikari et al., Phys. Plasmas 30, 082904, 2023). However, this description did not account for the energy transfer in the dissipation range for kinetic plasmas. In this letter, we adopt a scale-filtering approach to investigate this previously unaccounted-for energy transfer channel in reconnection. Using kinetic particle-in-cell (PIC) simulations of antiparallel and component reconnection, we show that the pressure-strain (PS) interaction becomes important at scales smaller than the ion inertial length, where the nonlinear energy transfer term drops off. Also, the presence of a guide field makes a significant difference in the morphology of the scale-filtered energy transfer. These results are consistent with kinetic turbulence simulations, suggesting that the pressure strain interaction is the dominant energy transfer channel between electron scales and ion scales.

physics.plasm-ph↗

arXiv2023

Quantifying Energy Conversion in Higher Order Phase Space Density Moments in Plasmas

Weakly collisional and collisionless plasmas are typically far from local thermodynamic equilibrium (LTE), and understanding energy conversion in such systems is a forefront research problem. The standard approach is to investigate changes in internal (thermal) energy and density, but this omits energy conversion that changes any higher order moments of the phase space density. In this study, we calculate from first principles the energy conversion associated with all higher moments of the phase space density for systems not in LTE. Particle-in-cell simulations of collisionless magnetic reconnection reveal that energy conversion associated with higher order moments can be locally significant. The results may be useful in numerous plasma settings, such as reconnection, turbulence, shocks, and wave-particle interactions in heliospheric, planetary, and astrophysical plasmas.

physics.plasm-ph↗

arXiv2023

Statistics of Pressure Fluctuations in Turbulent Kinetic Plasmas

In this study we explore the statistics of pressure fluctuations in kinetic collisionless turbulence. A 2.5D kinetic particle-in-cell (PIC) simulation of decaying turbulence is used to investigate pressure balance via the evolution of thermal and magnetic pressure in a plasma with beta of order unity. We also discuss the behavior of thermal, magnetic and total pressure structure functions and their corresponding wavenumber spectra. The total pressure spectrum exhibits a slope of -7/3 extending for about a decade in the ion-inertial range. In contrast, shallower -5/3 spectra are characteristic of the magnetic pressure and thermal pressure. The steeper total pressure spectrum is a consequence of cancellation caused by density-magnetic field magnitude anticorrelation. Further, we evaluate higher order total pressure structure functions in an effort to discuss intermittency and compare the power exponents with higher order structure functions of velocity and magnetic fluctuations. Finally, applications to astrophysical systems are also discussed.

physics.plasm-ph↗

arXiv2022

Pressure-Strain Interaction: I. On Compression, Deformation, and Implications For Pi-D

The pressure-strain interaction describes the rate per unit volume that energy is converted between bulk flow and thermal energy in neutral fluids or plasmas. The term has been written as a sum of the pressure dilatation and the collisionless analogue of viscous heating referred to as ${\rm Pi-D}$, which isolates the power density due to compressible and incompressible effects, respectively. It has been shown that ${\rm Pi-D}$ can be negative, which makes its identification as collisionless viscous heating troubling. We argue that an alternate decomposition of pressure-strain interaction can be useful for interpreting the underlying physics. Since ${\rm Pi-D}$ contains both normal deformation and shear deformation, we propose grouping the normal deformation with the pressure dilatation to describe the power density due to converging/diverging flows, with the balance describing the power density purely due to shear deformation. We then develop a kinetic theory interpretation of compression, normal deformation, and shear deformation. We use the results to determine the physical mechanisms that can make ${\rm Pi-D}$ negative. We argue that both decompositions can be useful for the study of energy conversion in weakly collisional or collisionless fluids and plasmas, and implications are discussed.

physics.plasm-ph↗

arXiv2022

Pressure-Strain Interaction: II. Decomposition in Magnetic Field-Aligned Coordinates

In weakly collisional and collisionless magnetized plasmas, the pressure-strain interaction describes the rate of conversion between bulk flow and thermal energy density. In this study, we derive an analytical expression for the pressure-strain interaction in a coordinate system with an axis aligned with the local magnetic field. The result is eight groups of terms corresponding to different physical mechanisms that can contribute to the pressure-strain interaction. We provide a physical description of each term. The results are immediately of interest to weakly collisional and collisionless magnetized plasmas and the fundamental processes that happen therein, including magnetic reconnection, magnetized plasma turbulence, and collisionless shocks. The terms in the field-aligned coordinate decomposition are likely accessible to measurement with satellite observations.

physics.plasm-ph↗

arXiv2022

Pressure-Strain Interaction: III. Particle-in-Cell Simulations of Magnetic Reconnection

How energy is converted into thermal energy in weakly collisional and collisionless plasma processes such as magnetic reconnection and plasma turbulence has recently been the subject of intense scrutiny. The pressure-strain interaction has emerged as an important piece, as it describes the rate of conversion between bulk flow and thermal energy density. In two companion studies, we presented an alternate decomposition of the pressure-strain interaction to isolate the effects of converging/diverging flow and flow shear instead of compressible and incompressible flow, and we derived the pressure-strain interaction in magnetic field-aligned coordinates. Here, we use these results to study pressure-strain interaction during two-dimensional anti-parallel magnetic reconnection. We perform particle-in-cell simulations and plot the decompositions in both Cartesian and magnetic field-aligned coordinates. We identify the mechanisms contributing to positive and negative pressure-strain interaction during reconnection. This study provides a roadmap for interpreting numerical and observational data of the pressure-strain interaction, which should be important for studies of reconnection, turbulence, and collisionless shocks.

physics.plasm-ph↗

arXiv2021

Scaling Theory of 3D Magnetic Reconnection Spreading

We develop a first-principles scaling theory of the spreading of three-dimensional (3D) magnetic reconnection of finite extent in the out of plane direction. This theory addresses systems with or without an out of plane (guide) magnetic field, and with or without Hall physics. The theory reproduces known spreading speeds and directions with and without guide fields, unifying previous knowledge in a single theory. New results include: (1) Reconnection spreads in a particular direction if an x-line is induced at the interface between reconnecting and non-reconnecting regions, which is controlled by the out of plane gradient of the electric field in the outflow direction. (2) The spreading mechanism for anti-parallel collisionless reconnection is convection, as is known, but for guide field reconnection it is magnetic field bending. We confirm the theory using 3D two-fluid and resistive-magnetohydrodynamics simulations. (3) The theory explains why anti-parallel reconnection in resistive-magnetohydrodynamics does not spread. (4) The simulation domain aspect ratio, associated with the free magnetic energy, influences whether reconnection spreads or convects with a fixed x-line length. (5) We perform a simulation initiating anti-parallel collisionless reconnection with a pressure pulse instead of a magnetic perturbation, finding spreading is unchanged rather than spreading at the magnetosonic speed as previously suggested. The results provide a theoretical framework for understanding spreading beyond systems studied here, and are important for applications including two-ribbon solar flares and reconnection in Earth's magnetosphere.

physics.plasm-ph↗

arXiv2019

Decomposition of Plasma Kinetic Entropy into Position and Velocity Space and the Use of Kinetic Entropy in Particle-in-Cell Simulations

We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particle-in-cell (PIC) simulations and use it to interpret plasma physics processes in heliospheric, planetary, and astrophysical systems. First, we calculate kinetic entropy in two forms -- the ``combinatorial'' form related to the logarithm of the number of microstates per macrostate and the ``continuous'' form related to $f \ln f$, where $f$ is the particle distribution function. We discuss the advantages and disadvantages of each and discuss subtleties about implementing them in PIC codes. Using collisionless PIC simulations that are two-dimensional in position space and three-dimensional in velocity space, we verify the implementation of the kinetic entropy diagnostics and discuss how to optimize numerical parameters to ensure accurate results. We show the total kinetic entropy is conserved to three percent in an optimized simulation of anti-parallel magnetic reconnection. Kinetic entropy can be decomposed into a sum of a position space entropy and a velocity space entropy, and we use this to investigate the nature of kinetic entropy transport during collisionless reconnection. We find the velocity space entropy of both electrons and ions increases in time due to plasma heating during magnetic reconnection, while the position space entropy decreases due to plasma compression. This project uses collisionless simulations, so it cannot address physical dissipation mechanisms; nonetheless, the infrastructure developed here should be useful for studies of collisional or weakly collisional heliospheric, planetary, and astrophysical systems. Beyond reconnection, the diagnostic is expected to be applicable to plasma turbulence and collisionless shocks.

physics.plasm-ph↗

arXiv2018

The Reduction of Magnetic Reconnection Outflow Jets to Sub-Alfvénic Speeds

The outflow velocity of jets produced by collisionless magnetic reconnection is shown to be reduced by the ion exhaust temperature in simulations and observations. We derive a scaling relationship for the outflow velocity based on the upstream Alfvén speed and the parallel ion exhaust temperature, which is verified in kinetic simulations and observations. The outflow speed reduction is shown to be due to the firehose instability criterion, and so for large enough guide fields this effect is suppressed and the outflow speed reaches the upstream Alfvén speed based on the reconnecting component of the magnetic field.

physics.plasm-ph↗

arXiv2018

Assessing the time dependence of reconnection with Poynting's theorem: MMS observations

We investigate the time dependence of electromagnetic-field-to-plasma energy conversion in the electron diffusion region of asymmetric magnetic reconnection. To do so, we consider the terms in Poynting's theorem. In a steady state there is a perfect balance between the divergence of the electromagnetic energy flux $\nabla \cdot \vec{S}$ and the conversion between electromagnetic field and particle energy $\vec{J} \cdot \vec{E}$. This energy balance is demonstrated with a particle-in-cell simulation of reconnection. We also evaluate each of the terms in Poynting's theorem during an observation of a magnetopause reconnection region by Magnetospheric Multiscale (MMS). We take the equivalence of both sides of Poynting's theorem as an indication that the errors associated with the approximation of each term with MMS data are small. We find that, for this event, balance between $\vec{J}\cdot\vec{E}=-\nabla\cdot\vec{S}$ is only achieved for a small fraction of the energy conversion region at/near the X-point. Magnetic energy was rapidly accumulating on either side of the current sheet at roughly three times the predicted energy conversion rate. Furthermore, we find that while $\vec{J}\cdot\vec{E}>0$ and $\nabla\cdot\vec{S}<0$ are observed, as is expected for reconnection, the energy accumulation is driven by the overcompensation for $\vec{J}\cdot\vec{E}$ by $-\nabla\cdot\vec{S}>\vec{J}\cdot\vec{E}$. We note that due to the assumptions necessary to do this calculation, the accurate evaluation of $\nabla\cdot\vec{S}$ may not be possible for every MMS-observed reconnection event; but if possible, this is a simple approach to determine if reconnection is or is not in a steady-state.

physics.space-ph↗