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1. Kinetic entropy-based measures of distribution function non-Maxwellianity: theory and simulations

   https://doi.org/10.1017/S0022377820001270  

   Liang, Haoming ; Barbhuiya, M. Hasan ; Cassak, P. A. ; Pezzi, O. ; Servidio, S. ; Valentini, F. ; Zank, G. P. ( October 2020 , Journal of Plasma Physics)

   null (Ed.)

   We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e. entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow and temperature as the local distribution. First, we consider a form previously employed by Kaufmann & Paterson ( J. Geophys. Res. , vol. 114, 2009, A00D04), assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas. 

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

   Haoming Liang, Paul A. ( January 2019 , Physics of plasmas)

   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 

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3. Characterizing Velocity-Space Signatures of Electron Energization in Large-Guide-Field Collisionless Magnetic Reconnection

   McCubbin, Andrew J. ; Howes, Gregory G. ; TenBarge, Jason M. ( December 2021 , ArXivorg)

   Magnetic reconnection plays an important role in the release of magnetic energy and consequent energization of particles in collisionless plasmas. Energy transfer in collisionless magnetic reconnection is inherently a two-step process: reversible, collisionless energization of particles by the electric field, followed by collisional thermalization of that energy, leading to irreversible plasma heating. Gyrokinetic numerical simulations are used to explore the first step of electron energization, and we generate the first examples of field-particle correlation (FPC) signatures of electron energization in 2D strong-guide-field collisionless magnetic reconnection. We determine these velocity space signatures at the x-point and in the exhaust, the regions of the reconnection geometry in which the electron energization primarily occurs. Modeling of these velocity-space signatures shows that, in the strong-guide-field limit, the energization of electrons occurs through bulk acceleration of the out-of-plane electron flow by parallel electric field that drives the reconnection, a non-resonant mechanism of energization. We explore the variation of these velocity-space signatures over the plasma beta range 0.01 < beta_i < 1. Our analysis goes beyond the fluid picture of the plasma dynamics and exploits the kinetic features of electron energization in the exhaust region to propose a single-point diagnostic which can potentially identify a reconnection exhaust region using spacecraft observations. 

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4. Characterizing velocity–space signatures of electron energization in large-guide-field collisionless magnetic reconnection

   https://doi.org/10.1063/5.0082213  

   McCubbin, Andrew J. ; Howes, Gregory G. ; TenBarge, Jason M. ( May 2022 , Physics of Plasmas)

   Magnetic reconnection plays an important role in the release of magnetic energy and consequent energization of particles in collisionless plasmas. Energy transfer in collisionless magnetic reconnection is inherently a two-step process: reversible, collisionless energization of particles by the electric field, followed by collisional thermalization of that energy, leading to irreversible plasma heating. Gyrokinetic numerical simulations are used to explore the first step of electron energization, and we generate the first examples of field–particle correlation signatures of electron energization in 2D strong-guide-field collisionless magnetic reconnection. We determine these velocity space signatures at the x-point and in the exhaust, the regions of the reconnection geometry in which the electron energization primarily occurs. Modeling of these velocity–space signatures shows that, in the strong-guide-field limit, the energization of electrons occurs through bulk acceleration of the out-of-plane electron flow by the parallel electric field that drives the reconnection, a non-resonant mechanism of energization. We explore the variation of these velocity–space signatures over the plasma beta range 0.01≤βi≤1. Our analysis goes beyond the fluid picture of the plasma dynamics and exploits the kinetic features of electron energization in the exhaust region to propose a single-point diagnostic, which can potentially identify a reconnection exhaust region using spacecraft observations. 

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5. As a Matter of Dynamical Range – Scale Dependent Energy Dynamics in MHD Turbulence

   https://doi.org/10.3847/2041-8213/acaea7  

   Grete, Philipp ; O’Shea, Brian W. ; Beckwith, Kris ( January 2023 , The Astrophysical Journal Letters)

   Magnetized turbulence is ubiquitous in many astrophysical and terrestrial plasmas but no universal theory exists. Even the detailed energy dynamics in magnetohydrodynamic (MHD) turbulence are still not well understood. We present a suite of subsonic, super-Alfvénic, high plasma beta MHD turbulence simulations that only vary in their dynamical range, i.e., in their separation between the large-scale forcing and dissipation scales, and their dissipation mechanism (implicit large eddy simulation, ILES, and direct numerical simulation (DNS)). Using an energy transfer analysis framework we calculate the effective numerical viscosities and resistivities, and demonstrate that all ILES calculations of MHD turbulence are resolved and correspond to an equivalent visco-resistive MHD turbulence calculation. Increasing the number of grid points used in an ILES corresponds to lowering the dissipation coefficients, i.e., larger (kinetic and magnetic) Reynolds numbers for a constant forcing scale. Independently, we use this same framework to demonstrate that—contrary to hydrodynamic turbulence—the cross-scale energy fluxes are not constant in MHD turbulence. This applies both to different mediators (such as cascade processes or magnetic tension) for a given dynamical range as well as to a dependence on the dynamical range itself, which determines the physical properties of the flow. We do not observe any indication of convergence even at the highest resolution (largest Reynolds numbers) simulation at 2048³cells, calling into question whether an asymptotic regime in MHD turbulence exists, and, if so, what it looks like.

    

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