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Register a new userKinetic Entropy-Based Measures of Distribution Function Non-Maxwellianity: Theory and Simulations
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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 and Paterson [{it J.~Geophys.~Res.,} {bf 114}, A00D04 (2009)], 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 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.
Plasmas in Earths outer magnetosphere, magnetosheath, and solar wind are essentially collisionless. This means particle distributions are not typically in thermodynamic equilibrium and deviate significantly from Maxwellian distributions. The deviations of these distributions can be further enhanced by plasma processes, such as shocks, turbulence, and magnetic reconnection. Such distributions can be unstable to a wide variety of kinetic plasma instabilities, which in turn modify the electron distributions. In this paper the deviations of the observed electron distributions from a bi-Maxwellian distribution function is calculated and quantified using data from the Magnetospheric Multiscale (MMS) spacecraft. A statistical study from tens of millions of electron distributions shows that the primary source of the observed non-Maxwellianity are electron distributions consisting of distinct hot and cold components in Earths low-density magnetosphere. This results in large non-Maxwellianities in at low densities. However, after performing a stastical study we find regions where large non-Maxwellianities are observed for a given density. Highly non-Maxwellian distributions are routinely found are Earths bowshock, in Earths outer magnetosphere, and in the electron diffusion regions of magnetic reconnection. Enhanced non-Maxwellianities are observed in the turbulent magnetosheath, but are intermittent and are not correlated with local processes. The causes of enhanced non-Maxwellianities are investigated.
The kinetic study of plasma sheaths is critical, among other things, to understand the deposition of heat on walls, the effect of sputtering, and contamination of the plasma with detrimental impurities. The plasma sheath also provides a boundary condition and can often have a significant global impact on the bulk plasma. In this paper, kinetic studies of classical sheaths are performed with the continuum code, Gkeyll, that directly solves the Vlasov-Poisson/Maxwell equations. The code uses a novel version of the finite-element discontinuous Galerkin (DG) scheme that conserves energy in the continuous-time limit. The electrostatic field is computed using the Poisson equation. Ionization and scattering collisions are included, however, surface effects are neglected. The aim of this work is to introduce the continuum-kinetic method and compare its results to those obtained from an already established finite-volume multi-fluid model also implemented in Gkeyll. Novel boundary conditions on the fluids allow the sheath to form without specifying wall fluxes, so the fluids and fields adjust self-consistently at the wall. The work presented here demonstrates that the kinetic and fluid results are in agreement for the momentum flux, showing that in certain regimes, a multi-fluid model can be a useful approximation for simulating the plasma boundary. There are differences in the electrostatic potential between the fluid and kinetic results. Further, the direct solutions of the distribution function presented here highlight the non-Maxwellian distribution of electrons in the sheath, emphasizing the need for a kinetic model.
We evaluate various analytical models for the electron-ion energy transfer and compare the results to data from molecular dynamics (MD) simulations. The models tested includes energy transfer via strong binary collisions, Landau-Spitzer rates with different choices for the cut-off parameters in the Coulomb logarithm, rates based on Fermis golden rule (FGR) and theories taking coupled collective modes (CM) into account. In search of a model easy to apply, we first analyze different approximations of the FGR energy transfer rate. Then we investigate several numerical studies using MD simulations and try to uncover CM effects in the data obtained. Most MD data published so far show no distinct CM effects and, thus, can be interpreted within a FGR or binary collision approach. We show that this finding is related to the parameter regime, in particular the initial temperature difference, considered in these investigations.
We have performed fully-kinetic simulations of X-B and O-X-B mode conversion in one and two dimensional setups using the PIC code EPOCH. We have recovered the linear dispersion relation for electron Bernstein waves by employing relatively low amplitude incoming waves. The setups presented here can be used to study non-linear regimes of X-B and O-X-B mode conversion.
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