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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We examine velocity-space kinetic entropy, a spatially local measure of entropy for systems out of thermal equilibrium, during an encounter of an electron diffusion region at a magnetic reconnection site in Earth's magnetotail by the Magnetospheric Multiscale (MMS) mission. We start by generalizing the theory of kinetic entropy to the case of non-uniform velocity space grids and transforming the equations into spherical energy coordinates useful to experimental plasma detectors. The theory is then applied to MMS data and compared to particle-in-cell simulations of reconnection. We demonstrate that the entropy-based non-Maxwellianity measure from the MMS data is of sufficiently high precision to reliably identify non-Maxwellian distributions and therefore the measurements when kinetic effects are most significant. By comparing two different non-Maxwellian measures, we show that total entropy density suffers from “information loss” because it lacks a dependence on the velocity space grid, and so has lost information about how well a distribution function is resolved. Local velocity-space kinetic entropy density recovers this information. We quantify information loss and argue that the considerations needed to minimize it are crucial for instruments designed to measure distribution functions in situ.

Using incoherent Thomson scattering, electron heating and acceleration at the electron velocity distribution function (EVDF) level are investigated during electron-only reconnection in the PHAse Space MApping (PHASMA) facility. Reconnection arises during the merger of two kink-free flux ropes. Both push and pull type reconnection occur in a single discharge. Electron heating is localized around the separatrix, and the electron temperature increases continuously along the separatrix with distance from the X-line. The local measured gain in enthalpy flux is up to 70% of the incoming Poynting flux. Notably, non-Maxwellian EVDFs comprised of a warm bulk population and a cold beam are directly measured during the electron-only reconnection. The electron beam velocity is comparable to, and scales with, electron Alfvén speed, revealing the signature of electron acceleration caused by electron-only reconnection. The observation of oppositely directed electron beams on either side of the X-point provides “smoking-gun” evidence of the occurrence of electron-only reconnection in PHASMA. 2D particle-in-cell simulations agree well with the laboratory measurements. The measured conversion of Poynting flux into electron enthalpy is consistent with recent observations of electron-only reconnection in the magnetosheath [Phan et al., Nature 557, 202 (2018)] at similar dimensionless parameters as in the experiments. The laboratory measurements go beyond the magnetosheath observations by directly resolving the electron temperature gain.

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 analog of viscous heating referred to as [Formula: see text], which isolates the power density due to compressible and incompressible effects, respectively. It has been shown that [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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.