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Recentin situmeasurements by the MMS and Parker Solar Probe missions bring interest to small-scale plasma dynamics (waves, turbulence, magnetic reconnection) in regions where the electron thermal energy is smaller than the magnetic one. Examples of such regions are the Earth’s magnetosheath and the vicinity of the solar corona, and they are also encountered in other astrophysical systems. In this brief review, we consider simple physical models describing plasma dynamics in such low-electron-beta regimes, discuss their conservation laws and their limits of applicability.

The physical foundations of the dissipation of energy and the associated heating in weakly collisional plasmas are poorly understood. Here, we compare and contrast several measures that have been used to characterize energy dissipation and kinetic-scale conversion in plasmas by means of a suite of kinetic numerical simulations describing both magnetic reconnection and decaying plasma turbulence. We adopt three different numerical codes that can also include inter-particle collisions: the fully-kinetic particle-in-cell vpic, the fully-kinetic continuum Gkeyll, and the Eulerian Hybrid Vlasov-Maxwell (HVM) code. We differentiate between i) four energy-based parameters, whose definition is related to energy transfer in a fluid description of a plasma, and ii) four distribution function-based parameters, requiring knowledge of the particle velocity distribution function. There is overall agreement between the dissipation measures obtained in the PIC and continuum reconnection simulations, with slight differences due to the presence/absence of secondary islands in the two simulations. There are also many qualitative similarities between the signatures in the reconnection simulations and the self-consistent current sheets that form in turbulence, although the latter exhibits significant variations compared to the reconnection results. All the parameters confirm that dissipation occurs close to regions of intense magnetic stresses, thus exhibiting local correlation. The distribution function-based measures show a broader width compared to energy-based proxies, suggesting that energy transfer is co-localized at coherent structures, but can affect the particle distribution function in wider regions. The effect of inter-particle collisions on these parameters is finally discussed.

The physical foundations of the dissipation of energy and the associated heating in weakly collisional plasmas are poorly understood. Here, we compare and contrast several measures that have been used to characterize energy dissipation and kinetic-scale conversion in plasmas by means of a suite of kinetic numerical simulations describing both magnetic reconnection and decaying plasma turbulence. We adopt three different numerical codes that can also include interparticle collisions: the fully kinetic particle-in-cell VPIC, the fully kinetic continuum Gkeyll, and the Eulerian Hybrid Vlasov-Maxwell (HVM) code. We differentiate between (i) four energy-based parameters, whose definition is related to energy transfer in a fluid description of a plasma, and (ii) four distribution function-based parameters, requiring knowledge of the particle velocity distribution function. There is an overall agreement between the dissipation measures obtained in the PIC and continuum reconnection simulations, with slight differences due to the presence/absence of secondary islands in the two simulations. There are also many qualitative similarities between the signatures in the reconnection simulations and the self-consistent current sheets that form in turbulence, although the latter exhibits significant variations compared to the reconnection results. All the parameters confirm that dissipation occurs close to regions of intense magnetic stresses, thus exhibiting local correlation. The distribution function-based measures show a broader width compared to energy-based proxies, suggesting that energy transfer is co-localized at coherent structures, but can affect the particle distribution function in wider regions. The effect of interparticle collisions on these parameters is finally discussed., Accepted for publication on MNRAS

Recent time series observations of electric fields within collisionless shocks have shown that the fluctuating, electrostatic fields can be in excess of one hundred times that of the quasi-static electric fields. That is, the largest amplitude electric fields occur at high frequencies, not low. In contrast, many if not most kinetic simulations show the opposite, where the quasi-static electric fields dominate, unless they are specifically tailored to examine small-scale instabilities. Further, the shock ramp thickness is often observed to fall between the electron and ion scales while many simulations tend to produce ramp thicknesses at least at or above ion scales. This raises numerous questions about the role of small-scale instabilities and about the ability to directly compare simulations with observations.

The 1970s and 1980s were heydays for using active electron beam experiments to probe some of the fundamental physical processes that occur throughout the heliosphere and in astrophysical contexts. Electron beam experiments were used to study spacecraft charging and spacecraft-plasma coupling; beam-plasma interaction physics; magnetic bounce and drift physics; auroral physics; wave generation; and military applications. While these experiments were enormously successful, they were also limited by the technologies that were available at that time. New advances in space instrumentation, data collection, and accelerator technologies enable a revolutionary new generation of active experiments using electron beams in space. In this paper we discuss such an experiment, the Beam Plasma Interactions Experiment (Beam PIE), a sounding rocket experiment designed to (a) advance high-electron mobility transistor-based radio frequency (RF) linear accelerator electron technology for space applications and (b) study the production of whistler and X-mode waves by modulated electron beams.

We discuss the development, analysis, implementation, and numerical assessment of a spectral method for the numerical simulation of the three-dimensional Vlasov–Maxwell equations. The method is based on a spectral expansion of the velocity space with the asymmetrically weighted Hermite functions . The resulting system of time-dependent nonlinear equations is discretized by the discontinuous Galerkin (DG) method in space and by the method of lines for the time integration using explicit Runge–Kutta integrators . The resulting code, called Spectral Plasma Solver (SPS-DG), is successfully applied to standard plasma physics benchmarks to demonstrate its accuracy, robustness, and parallel scalability.

A review of the impact of the cold-ion and cold-electron populations in the Earth’s magnetosphere is presented. The cold populations are defined by total energy less than approximately 100 eV, i.e. in the energy range which is strongly affected by spacecraft charging and that often dominates the total plasma density. We also include the warm plasma cloak in the review, since it overlaps partially with the cold energy range and is a population that is still not well understood. The known impacts of cold ions and cold electrons that are discussed are: the source of hot magnetospheric plasma, solar-wind/magnetosphere coupling, magnetotail reconnection and substorms, Kelvin–Helmholtz instabilities on the magnetopause, chorus, hiss, electromagnetic-ion-cyclotron and ultra-low-frequency wave–particle interactions, aurora structuring and spacecraft charging. Other possible impacts are associated with refilling on open-drift trajectories, the remnant layer and plasmapause disruption. A discussion of the difficulty of cold-plasma measurements and the need for new measurement techniques that measure the full cold-ion and cold-electron distribution functions is also presented. There remain a lot of unknowns about the cold-ion and cold-electron populations, associated with their origin, properties, drivers and impacts. These populations will need to be fully understood before the magnetosphere–ionosphere system can be fully understood.

Electron heating and the energy inventory during asymmetric reconnection are studied in the laboratory plasma with a density ratio of about 8 across the current sheet. Features of asymmetric reconnection such as the large density gradients near the low-density side separatrices, asymmetric in-plane electric field, and bipolar out-of-plane magnetic field are observed. Unlike the symmetric case, electrons are also heated near the low-density side separatrices. The measured parallel electric field may explain the observed electron heating. Although large fluctuations driven by lower hybrid drift instabilities are also observed near the low-density side separatrices, laboratory measurements and numerical simulations reported here suggest that they do not play a major role in electron energization. The average electron temperature increase in the exhaust region is proportional to the incoming magnetic energy per an electron/ion pair but exceeds scalings of the previous space observations. This discrepancy is explained by differences in the boundary condition and system size. The profile of electron energy gain from the electric field shows that there is additional electron energy gain associated with the electron diamagnetic current besides a large energy gain near the X line. This additional energy gain increases electron enthalpy, not the electron temperature. Finally, a quantitative analysis of the energy inventory during asymmetric reconnection is conducted. Unlike the symmetric case where the ion energy gain is about twice more than the electron energy gain, electrons and ions obtain a similar amount of energy during asymmetric reconnection.

Three dimensional hybrid simulations of solar wind turbulence near the orbit of the earth are used to investigate the plasma current density over the range of scales from 0.5 proton inertial lengths to hundreds of proton inertial lengths. The data is analyzed along a simulated spacecraft trajectory in order to directly compare the results against single-spacecraft measurements. The most intense current densities are identified using an amplitude threshold technique and the properties of 5σ events identified in the true current density are compared to the properties of 5σ events identified using a proxy for the current density designed for studies of single-spacecraft solar wind measurements. The proxy is proportional to the magnitude of the directional derivative of the magnetic field along the spacecraft trajectory. The results from the simulation show that the properties of 5σ events observed in the proxy are quantitatively similar to those observed in the true current density, properties such as the spatial size of the events, the nearest neighbor distance, and the peak current density of the events. This provides some justification for the use of the proxy for the statistical analysis of solar wind data even though the simulation indicates that the occurrence times of large amplitude events in the proxy are not always a reliable indicator of the occurrence times of large amplitude events in the true current density. The physical properties of 5σ events in simulated spacecraft data show remarkable quantitative agreement with the properties of 5σ events observed in solar wind data.

We study numerically small-scale reconnection events in kinetic, low-frequency, quasi-2D turbulence (termed kinetic-Alfv\'en turbulence). Using 2D particle-in-cell simulations, we demonstrate that such turbulence generates reconnection structures where the electron dynamics do not couple to the ions, similarly to the electron-only reconnection events recently detected in the Earth's magnetosheath by Phan et al. (2018). Electron-only reconnection is thus an inherent property of kinetic-Alfv\'en turbulence, where the electron current sheets have limited anisotropy and, as a result, their sizes are smaller than the ion inertial scale. The reconnection rate of such electron-only events is found to be close to $0.1$., Comment: 8 pages, 3 figures

We study spectral features of ion velocity and magnetic field correlations in the magnetosheath and in the solar wind using data from the Magnetospheric Multiscale (MMS) spacecraft. High-resolution MMS observations enable the study of the transition of these correlations between their magnetofluid character at larger scales into the subproton kinetic range, previously unstudied in spacecraft data. Cross-helicity, angular alignment, and energy partitioning is examined over a suitable range of scales, employing measurements based on the Taylor frozen-in approximation as well as direct two-spacecraft correlation measurements. The results demonstrate signatures of alignment at large scales. As kinetic scales are approached, the alignment between $\mathbf{v}$ and $\mathbf{b}$ is destroyed by demagnetization of protons.

Spectral (transform) methods for solution of Vlasov-Maxwell system have shown significant promise as numerical methods capable of efficiently treating fluid-kinetic coupling in magnetized plasmas. We discuss SpectralPlasmaSolver (SPS), an implementation of three-dimensional, fully electromagnetic algorithm based on a decomposition of the plasma distribution function in Hermite modes in velocity space and Fourier modes in physical space. A fully-implicit time discretization is adopted for numerical stability and to ensure exact conservation laws for total mass, momentum and energy. The SPS code is parallelized using Message Passing Interface for distributed memory architectures. Application of the method to analysis of kinetic range of scales in plasma turbulence under conditions typical of the solar wind is demonstrated. With only 4 Hermite modes per velocity dimension, the algorithm yields damping rates of kinetic Alfvén waves with accuracy of 50% or better, which is sufficient to obtain a model of kinetic scales capable of reproducing many of the expected statistical properties of turbulent fluctuations. With increasing number of Hermite modes, progressively more accurate values for collisionless damping rates are obtained. Fully nonlinear simulations of decaying turbulence are presented and successfully compared with similar simulations performed using Particle-In-Cell method.

The magnetosheath flow may take the form of large amplitude, yet spatially localized, transient increases in dynamic pressure, known as “magnetosheath jets” or “plasmoids” among other denominations. Here, we describe the present state of knowledge with respect to such jets, which are a very common phenomenon downstream of the quasi-parallel bow shock. We discuss their properties as determined by satellite observations (based on both case and statistical studies), their occurrence, their relation to solar wind and foreshock conditions, and their interaction with and impact on the magnetosphere. As carriers of plasma and corresponding momentum, energy, and magnetic flux, jets bear some similarities to bursty bulk flows, which they are compared to. Based on our knowledge of jets in the near Earth environment, we discuss the expectations for jets occurring in other planetary and astrophysical environments. We conclude with an outlook, in which a number of open questions are posed and future challenges in jet research are discussed.

Recent simulations have demonstrated that coherent current sheets dominate the kinetic-scale energy dissipation in strong turbulence of magnetized plasma. Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed turbulence from a laminar state. Originally applied to neutral fluid turbulence, an iterative wavelet technique decomposes the field into coherent and incoherent contributions. In contrast to Fourier power spectra, finite time Lyapunov exponents, and simple measures of intermittency such as non-Gaussian statistics of field increments, the wavelet technique is found to provide a quantitative measure for the onset of turbulence and to track the transition to fully developed turbulence. The wavelet method makes no assumptions about the structure of the coherent current sheets or the underlying plasma model. Temporal evolution of the coherent and incoherent wavelet fluctuations is found to be highly correlated (a Pearson correlation coefficient of >0.9) with the magnetic field energy and plasma thermal energy, respectively. The onset of turbulence is identified with the rapid growth of a background of incoherent fluctuations spreading across a range of scales and a corresponding drop in the coherent components. This is suggestive of the interpretation of the coherent and incoherent wavelet fluctuations as measures of coherent structures (e.g., current sheets) and dissipation, respectively. The ratio of the incoherent to coherent fluctuations Ric is found to be fairly uniform in the turbulent state across different plasma models and provides an empirical threshold of ∼0.1 for turbulence onset. The utility of this technique is illustrated through examples. First, it is applied to the Kelvin–Helmholtz instability from different simulation models including fully kinetic, hybrid (kinetic ion/fluid electron), and Hall MHD simulations. Second, the wavelet diagnostic is applied to the development of turbulence downstream of the bowshock in a global magnetosphere simulation. Finally, the wavelet technique is also shown to be useful as a de-noising method for particle simulations.Recent simulations have demonstrated that coherent current sheets dominate the kinetic-scale energy dissipation in strong turbulence of magnetized plasma. Wavelet basis functions are a natural tool for analyzing turbulent flows containing localized coherent structures of different spatial scales. Here, wavelets are used to study the onset and subsequent transition to fully developed turbulence from a laminar state. Originally applied to neutral fluid turbulence, an iterative wavelet technique decomposes the field into coherent and incoherent contributions. In contrast to Fourier power spectra, finite time Lyapunov exponents, and simple measures of intermittency such as non-Gaussian statistics of field increments, the wavelet technique is found to provide a quantitative measure for the onset of turbulence and to track the transition to fully developed turbulence. The wavelet method makes no assumptions about the structure of the coherent current sheets or the underlying plasma model. Temporal evolution of ...

Evolution of the parametric decay instability (PDI) of a circularly polarized Alfven wave in a turbulent low-beta plasma background is investigated using 3D hybrid simulations. It is shown that the turbulence reduces the growth rate of PDI as compared to the linear theory predictions, but PDI can still exist. Interestingly, the damping rate of the ion acoustic mode (as the product of PDI) is also reduced as compared to the linear Vlasov predictions. Nonetheless, significant heating of ions in the direction parallel to the background magnetic field is observed due to resonant Landau damping of the ion acoustic waves. In low-beta turbulent plasmas, PDI can provide an important channel for energy dissipation of low-frequency Alfven waves at a scale much larger than the ion kinetic scales, different from the traditional turbulence dissipation models.

Analysis of the Vlasov-Maxwell equations from the perspective of turbulence cascade clarifies the role of electromagnetic work, and reveals the importance of the pressure-strain relation in generating internal energy. Particle-in-cell simulation demonstrates the relative importance of the several energy exchange terms, indicating that the traceless pressure-strain interaction ``Pi-D'' is of particular importance for both electrons and protons. The Pi-D interaction and the second tensor invariants of the strain are highly localized in similar spatial regions, indicating that energy transfer occurs preferentially in coherent structures. The collisionless turbulence cascade may be fruitfully explored by study of these energy transfer channels, in addition to examining transfer across spatial scales.

Kinetic plasma turbulence cascade spans multiple scales ranging from macroscopic fluid flow to sub-electron scales. Mechanisms that dissipate large scale energy, terminate the inertial range cascade and convert kinetic energy into heat are hotly debated. Here we revisit these puzzles using fully kinetic simulation. By performing scale-dependent spatial filtering on the Vlasov equation, we extract information at prescribed scales and introduce several energy transfer functions. This approach allows highly inhomogeneous energy cascade to be quantified as it proceeds down to kinetic scales. The pressure work, $-\left( \boldsymbol{P} \cdot \nabla \right) \cdot \boldsymbol{u}$, can trigger a channel of the energy conversion between fluid flow and random motions, which is a collision-free generalization of the viscous dissipation in collisional fluid. Both the energy transfer and the pressure work are strongly correlated with velocity gradients., 28 pages, 10 figures

The heliosphere is formed due to interaction between the solar wind (SW) and local interstellar medium (LISM). The shape and position of the heliospheric boundary, the heliopause, in space depend on the parameters of interacting plasma flows. The interplay between the asymmetrizing effect of the interstellar magnetic field and charge exchange between ions and neutral atoms plays an important role in the SW-LISM interaction. By performing three-dimensional, MHD plasma / kinetic neutral atom simulations, we determine the width of the outer heliosheath - the LISM plasma region affected by the presence of the heliosphere - and analyze quantitatively the distributions in front of the heliopause. It is shown that charge exchange modifies the LISM plasma to such extent that the contribution of a shock transition to the total variation of plasma parameters becomes small even if the LISM velocity exceeds the fast magnetosonic speed in the unperturbed medium. By performing adaptive mesh refinement simulations, we show that a distinct boundary layer of decreased plasma density and enhanced magnetic field should be observed on the interstellar side of the heliopause. We show that this behavior is in agreement with the plasma oscillations of increasing frequency observed by the plasma wave instrument onboard Voyager 1. We also demonstrate that Voyager observations in the inner heliosheath between the heliospheric termination shock and the heliopause are consistent with dissipation of the heliospheric magnetic field. The choice of LISM parameters in this analysis is based on the simulations that fit observations of energetic neutral atoms performed by IBEX., Comment: Accepted for publication in Astrophysical Journal

We present the design and implementation of a spectral code, called SpectralPlasmaSolver (SPS), for the solution of the multi-dimensional Vlasov-Maxwell equations. The method is based on a Hermite-Fourier decomposition of the particle distribution function. The code is written in Fortran and uses the PETSc library for solving the non-linear equations and preconditioning and the FFTW library for the convolutions. SPS is parallelized for shared- memory machines using OpenMP. As a verification example, we discuss simulations of the two-dimensional Orszag-Tang vortex problem and successfully compare them against a fully kinetic Particle-In-Cell simulation. An assessment of the performance of the code is presented, showing a significant improvement in the code running-time achieved by preconditioning, while strong scaling tests show a factor of 10 speed-up using 16 threads.

Collisionless dissipation in turbulentplasmas such as the solar wind and the solar corona has been an intensively studied subject recently, with new insights often emerging from numerical simulation. Here we report results from high resolution, fully kinetic simulations of plasma turbulence in both two (2D) and three (3D) dimensions, studying the relationship between intermittency and dissipation. The simulations show development of turbulent coherent structures, characterized by sheet-like current density structures spanning a range of scales. An approximate dissipation measure is employed, based on work done by the electromagnetic field in the local electron fluid frame. This surrogate dissipation measure is highly concentrated in small subvolumes in both 2D and 3D simulations. Fully kinetic simulations are also compared with magnetohydrodynamics(MHD) simulations in terms of coherent structures and dissipation. The interesting result emerges that the conditional averages of dissipation measure scale very similarly with normalized current densityJ in 2D and 3D particle-in-cell and in MHD. To the extent that the surrogate dissipation measure is accurate, this result implies that on average dissipation scales as ∼J2 in turbulent kinetic plasma. Multifractal intermittency is seen in the inertial range in both 2D and 3D, but at scales ∼ion inertial length, the scaling is closer to monofractal.

An unsolved problem in plasma turbulence is how energy is dissipated at small scales. Particle collisions are too infrequent in hot plasmas to provide the necessary dissipation. Simulations either treat the fluid scales and impose an ad hoc form of dissipation (e.g., resistivity) or consider dissipation arising from resonant damping of small amplitude disturbances where damping rates are found to be comparable to that predicted from linear theory. Here, we report kinetic simulations that span the macroscopic fluid scales down to the motion of electrons. We find that turbulent cascade leads to generation of coherent structures in the form of current sheets that steepen to electron scales, triggering strong localized heating of the plasma. The dominant heating mechanism is due to parallel electric fields associated with the current sheets, leading to anisotropic electron and ion distributions which can be measured with NASA's upcoming Magnetospheric Multiscale mission. The motion of coherent structures also generates waves that are emitted into the ambient plasma in form of highly oblique compressional and shear Alfven modes. In 3D, modes propagating at other angles can also be generated. This indicates that intermittent plasma turbulence will in general consist of both coherent structures and waves. However, the current sheet heating is found to be locally several orders of magnitude more efficient than wave damping and is sufficient to explain the observed heating rates in the solar wind.

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., 20 pages, 7 figures