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We derive conservative closures of the Vlasov-Poisson equations discretized in velocity via the symmetrically weighted Hermite spectral expansion. The short note analyzes the conservative closures preservation of the hyperbolicity and anti-symmetry of the Vlasov equation. Furthermore, we verify numerically the analytically derived conservative closures on simulating a classic electrostatic benchmark problem: the Langmuir wave. The numerical results and analytic analysis show that the closure by truncation is the most suitable conservative closure for the symmetrically weighted Hermite formulation.

Whistler waves propagating nearly parallel to the ambient magnetic field experience a nonlinear instability that generates oblique electrostatic waves, including whistlers near the resonance cone that resemble oblique chorus in the Earth's magnetosphere. Focusing on the generation of oblique whistlers, earlier analysis of the instability is extended to the case where low-energy background plasma consists of both a "cold" population with energy ~ eV and a "warm" electron component with energy ~100 eV. This is motivated by observations in the Earth's magnetosphere where oblique chorus waves were shown to interact resonantly with the warm electrons. The main results are: i) the instability producing oblique whistlers is sensitive to the shape of the electron distribution at low energies. In the whistler range of frequencies, two distinct peaks in the growth rate are typically present: one at low wavenumbers associated with the warm population and one at high wavenumbers associated with the cold population; ii) the instability producing oblique whistler waves persists in cases where the temperature of the cold population is relatively high, including cases where cold population is absent and only the warm population is included; iii) particle-in-cell simulations show that the instability leads to heating of the background plasma and formation of characteristic resonant plateau and beam features in the electron distribution. The plateau/beam features have been previously detected in spacecraft observations of oblique chorus waves. However, they were attributed to external sources and were proposed to be the mechanism generating oblique chorus. In the present scenario, the causality link is reversed: the instability generating oblique whistler waves is shown to be a possible mechanism to generate the plateau/beam features.

Artificial Intelligence (AI) has the potential to revolutionize space exploration by delegating several spacecraft decisions to an onboard AI instead of relying on ground control and predefined procedures. It is likely that there will be an AI/ML Processing Unit onboard the spacecraft running an inference engine. The neural-network will have pre-installed parameters that can be updated onboard by uploading, by telecommands, parameters obtained by training on the ground. However, satellite uplinks have limited bandwidth and transmissions can be costly. Furthermore, a mission operating with a suboptimal neural network will miss out on valuable scientific data. Smaller networks can thereby decrease the uplink cost, while increasing the value of the scientific data that is downloaded. In this work, we evaluate and discuss the use of reduced-precision and bare-minimum neural networks to reduce the time for upload. As an example of an AI use case, we focus on the NASA's Magnetosperic MultiScale (MMS) mission. We show how an AI onboard could be used in the Earth's magnetosphere to classify data to selectively downlink higher value data or to recognize a region-of-interest to trigger a burst-mode, collecting data at a high-rate. Using a simple filtering scheme and algorithm, we show how the start and end of a region-of-interest can be detected in on a stream of classifications. To provide the classifications, we use an established Convolutional Neural Network (CNN) trained to an accuracy >94%. We also show how the network can be reduced to a single linear layer and trained to the same accuracy as the established CNN. Thereby, reducing the overall size of the model by up to 98.9%. We further show how each network can be reduced by up to 75% of its original size, by using lower-precision formats to represent the network parameters, with a change in accuracy of less than 0.6 percentage points.

Understanding plasma turbulence requires a synthesis of experiments, observations, theory, and simulations. In the case of kinetic plasmas such as the solar wind, the lack of collisions renders the fluid closures such as viscosity meaningless and one needs to resort to higher order fluid models or kinetic models. Typically, the computational expense in such models is managed by simulating artificial values of certain parameters such as the ratio of the Alfv\'en speed to the speed of light ($v_A/c$) or the relative mass ratio of ions and electrons ($m_i/m_e$). Although, typically care is taken to use values as close as possible to realistic values within the computational constraints, these artificial values could potentially introduce unphysical effects. These unphysical effects could be significant at sub-ion scales, where kinetic effects are the most important. In this paper, we use the ten-moment fluid model in the Gkeyll framework to perform controlled numerical experiments, systematically varying the ion-electron mass ratio from a small value down to the realistic proton-electron mass ratio. We show that the unphysical mass ratio has a significant effect on the kinetic range dynamics as well as the heating of both the plasma species. The dissipative process for both ions and electrons become more compressive in nature, although the ions remain nearly incompressible in all cases. The electrons move from being dominated by incompressive viscous like heating/dissipation, to very compressive heating/dissipation dominated by compressions/rarefactions. While the heating change is significant for the electrons, a mass ratio of $m_i/m_e \sim 250$ captures the asymptotic behaviour of electron heating., Comment: 13 pages (including bibliography), 11 figures and 2 tables

The interaction of $\beta$-particles with the weakly ionized plasma background is an important mechanism for powering the kilonova transient signal from neutron star mergers. For this purpose, we present an implementation of the approximate fast-particle collision kernel, described by Inokuti (1971) following the seminal formulation of Bethe (1930), in a spectral solver of the Vlasov-Maxwell-Boltzmann equations. In particular, we expand the fast-particle plane-wave atomic excitation kernel into coefficients of the Hermite basis, and derive the relevant discrete spectral system. In this fast-particle limit, the approach permits the direct use of atomic data, including optical oscillator strengths, normally applied to photon-matter interaction. The resulting spectral matrix is implemented in the MASS-APP spectral solver framework, in a way that avoids full matrix storage per spatial zone. We numerically verify aspects of the matrix construction, and present a proof-of-principle 3D simulation of a 2D axisymmetric kilonova ejecta snapshot. Our preliminary numerical results indicate that a reasonable choice of Hermite basis parameters for $\beta$-particles in the kilonova are a bulk velocity parameter $\vec{u}=0$, a thermal velocity parameter $\vec{\alpha}=0.5c$, and a 9x9x9 mode velocity basis set (Hermite orders 0 to 8 in each dimension). For ejecta-interior sample zones, we estimate the ratio of thermalization from large-angle ($\gtrsim2.5^{\circ}$) bound excitation scattering to total thermalization is $\sim$0.002-0.003., Comment: Accepted to ApJ, 26 pages, 8 figures

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

3D kinetic-scale turbulence is studied numerically in the regime where electrons are strongly magnetized (the ratio of plasma species pressure to magnetic pressure is $\beta_e=0.1$ for electrons and $\beta_i=1$ for ions). Such a regime is relevant in the vicinity of the solar corona, the Earth's magnetosheath, and other astrophysical systems. The simulations, performed using the fluid-kinetic spectral plasma solver (SPS) code, demonstrate that the turbulent cascade in such regimes can reach scales smaller than the electron inertial scale, and results in the formation of electron-scale current sheets (ESCS). Statistical analysis of the geometrical properties of the detected ESCS is performed using an algorithm based on the medial axis transform. A typical half-thickness of the current sheets is found to be on the order of electron inertial length or below, while their half-length falls between the electron and ion inertial length. The pressure-strain interaction, used as a measure of energy dissipation, exhibits high intermittency, with the majority of the total energy exchange occurring in current structures occupying approximately 20\% of the total volume. Some of the current sheets corresponding to the largest pressure-strain interaction are found to be associated with Alfv\'enic electron jets and magnetic configurations typical of reconnection. These reconnection candidates represent about $1$\% of all the current sheets identified., Comment: 9 pages, 6 figures. Submitted for publication to MNRAS. Fixed missing references

We propose a spectral method for the 1D-1V Vlasov-Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling $\alpha$ and shifting $u$ of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of $\alpha$ and $u$ based on the numerical solution of the discrete Vlasov-Poisson system obtained at that time step. Once the new values of the Hermite parameters $\alpha$ and $u$ are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update $\alpha$ and $u$ based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion are akin to the fluid moments of a macroscopic description of the plasma, while kinetic physics is retained by adding more spectral terms. Moreover, the scheme features conservation of total mass, momentum and energy associated in the discrete, for periodic boundary conditions. A set of numerical experiments confirms that the adaptive method outperforms the non-adaptive one in terms of accuracy and stability of the numerical solution.

We study the conservation properties of the Hermite-discontinuous Galerkin (Hermite-DG) approximation of the Vlasov-Maxwell equations. In this semi-discrete formulation, the total mass is preserved independently for every plasma species. Further, an energy invariant exists if central numerical fluxes are used in the DG approximation of Maxwell's equations, while a dissipative term is present when upwind fluxes are employed. In general, traditional temporal integrators might fail to preserve invariants associated with conservation laws during the time evolution. Hence, we analyze the capability of explicit and implicit Runge-Kutta (RK) temporal integrators to preserve such invariants. Since explicit RK methods can only ensure preservation of linear invariants but do not provide any control on the system energy, we consider modified explicit RK methods in the family of relaxation Runge-Kutta methods (RRK). These methods can be tuned to preserve the energy invariant at the continuous or semi-discrete level, a distinction that is important when upwind fluxes are used in the discretization of Maxwell's equations since upwind provides a numerical source of energy dissipation that is not present when central fluxes are used. We prove that the proposed methods are able to preserve the energy invariant and to maintain the semi-discrete energy dissipation (if present) according to the discretization of Maxwell's equations. An extensive set of numerical experiments corroborates the theoretical findings. It also suggests that maintaining the semi-discrete energy dissipation when upwind fluxes are used leads to an overall better accuracy of the method relative to using upwind fluxes while forcing exact energy conservation.

Kinetic simulations and theory demonstrate that whistler waves can excite oblique, short-wavelength fluctuations through secondary drift instabilities if a population of sufficiently cold plasma is present. The excited modes lead to heating of the cold populations and damping of the primary whistler waves. The instability threshold depends on the density and temperature of the cold population and can be relatively small if the temperature of the cold population is sufficiently low. This mechanism may thus play a significant role in controlling amplitude of whistlers in the regions of the Earth's magnetosphere where cold background plasma of sufficient density is present.

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.

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 investigate the properties of the ion sky maps produced by the Dual Ion Spectrometers (DIS) from the Fast Plasma Investigation (FPI). We have trained a convolutional neural network classifier to predict four regions crossed by the MMS on the dayside magnetosphere: solar wind, ion foreshock, magnetosheath, and magnetopause using solely DIS spectrograms. The accuracy of the classifier is >98%. We use the classifier to detect mixed plasma regions, in particular to find the bow shock regions. A similar approach can be used to identify the magnetopause crossings and reveal regions prone to magnetic reconnection. Data processing through the trained classifier is fast and efficient and thus can be used for classification for the whole MMS database., Comment: Accepted to JGR: Space Physics

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., Comment: 20 pages, 7 figures

Recent observational and analytical studies suggested that a new regime of kinetic turbulence may exist in plasma environments with low electron beta (Chen and Boldyrev, 2017). Such a regime, termed inertial kinetic-Alfv\'en turbulence, is relevant for the solar corona, Earth's magnetosheath, and other astrophysical systems where the electron and ion plasma beta parameters satisfy the condition $\beta_e\ll \beta_i\lesssim 1$. In this paper we present kinetic numerical simulations that confirm existence of the iKAW regime. Specifically, the simulations demonstrate a transition at scales below electron inertial length $d_e$ when $\beta_e\ll \beta_i\lesssim 1$. Spectral slopes and other statistical properties of turbulence at sub-$d_e$ scales are consistent with the phenomenological theory of inertial kinetic-Alfv\'en turbulence proposed by Chen and Boldyrev (2017) and with the recent observations in the Earth's magnetosheath.

We prove the convergence of a spectral discretization of the Vlasov-Poisson system. The velocity term of the Vlasov equation is discretized using either Hermite functions on the infinite domain or Legendre polynomials on a bounded domain. The spatial term of the Vlasov and Poisson equations is discretized using periodic Fourier expansions. Boundary conditions are treated in weak form through a penalty type term, that can be applied also in the Hermite case. As a matter of fact, stability properties of the approximated scheme descend from this added term. The convergence analysis is carried out in details for the 1D-1V case, but results can be generalized to multidimensional domains, obtained as Cartesian product, in both space and velocity. The error estimates show the spectral convergence, under suitable regularity assumptions on the exact solution.

The Orbital-Motion-Limited (OML) theory has been modified to predict the dust charge and the results were contrasted with the Whipple approximation [Tang and Delzanno, Phys. Plasmas 21, 123708 (2014)]. To further establish its regime of applicability, in this paper the OML predictions (for a non-electron-emitting, spherical dust grain at rest in a collisionless, unmagnetized plasma) are compared with Particle-In-Cell simulations that retain the absorption radius effect. It is found that for large dust grain radius $r_d$ relative to the plasma Debye length $\lambda_D$, the revised OML theory remains a very good approximation as, for the parameters considered ($r_d/\lambda_D\le10$, equal electron and ion temperatures), it yields the dust charge to within $20\%$ accuracy. This is a substantial improvement over the Whipple approximation. The dust collected currents and energy fluxes, which remain the same in the revised and standard OML theories, are accurate to within $15-30\%$., Comment: 15 pages, 2 figures. Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Phys. Plasmas 22, 113703 (2015) and may be found at: http://scitation.aip.org/content/aip/journal/pop/22/11/10.1063/1.4935697

The foundational theory for dusty plasmas is the dust charging theory that provides the dust potential and charge arising from the dust interaction with a plasma. The most widely used dust charging theory for negatively charged dust particles is the so-called orbital motion limited (OML) theory, which predicts the dust potential and heat collection accurately for a variety of applications, but was previously found to be incapable of evaluating the dust charge and plasma response in any situation. Here we report a revised OML formulation that is able to predict the plasma response and hence the dust charge. Numerical solutions of the new OML model show that the widely-used Whipple approximation of dust charge-potential relationship agrees with OML theory in the limit of small dust radius compared with plasma Debye length, but incurs large (order-unity) deviation from the OML prediction when the dust size becomes comparable with or larger than plasma Debye length. This latter case is expected for the important application of dust particles in a tokamak plasma., Comment: 7 pages, 4 figures Copyright (2015) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Phys. Plasmas 21, 123708 (2014) and may be found at http://scitation.aip.org/content/aip/journal/pop/21/12/10.1063/1.4904404