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

Liang, Haoming; Barbhuiya, M. Hasan; Cassak, P. A.; Pezzi, O.; Servidio, S.; Valentini, F.; Zank, G. P.

doi:10.1017/s0022377820001270

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

Journal Article · Wed Oct 21 00:00:00 EDT 2020 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s0022377820001270· OSTI ID:1755869

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Univ. of Alabama, Huntsville, AL (United States). Center for Space Plasma and Aeronomic Research; West Virginia Univ., Morgantown, WV (United States)
West Virginia Univ., Morgantown, WV (United States)
West Virginia Univ., Morgantown, WV (United States). Center for KINETIC Plasma Physics
Gran Sasso Science Inst., L’Aquila (Italy); Istituto Nazionale di Fisica Nucleare (INFN), L'aquila (Italy). Lab. Nazionali del Gran Sasso (INFN-LNGS)
Univ. della Calabria, Rende (Italy)
Univ. of Alabama, Huntsville, AL (United States). Center for Space Plasma and Aeronomic Research

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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Research Organization:: West Virginia Univ., Morgantown, WV (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES); National Science Foundation (NSF); European Union (EU)

Grant/Contract Number:: SC0020294; AC02-05CH11231; PHY-1707247; PHY-1804428; NNX16AG76G; 80NSSC19M0146

OSTI ID:: 1755869

Journal Information:: Journal of Plasma Physics, Vol. 86, Issue 5; ISSN 0022-3778

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

References (72)

Dual Phase-space Cascades in 3D Hybrid-Vlasov–Maxwell Turbulence Cerri, S. S.; Kunz, M. W.; Califano, F. The Astrophysical Journal, Vol. 856, Issue 1 https://doi.org/10.3847/2041-8213/aab557	journal	March 2018
Decomposition of plasma kinetic entropy into position and velocity space and the use of kinetic entropy in particle-in-cell simulations Liang, Haoming; Cassak, Paul A.; Servidio, Sergio Physics of Plasmas, Vol. 26, Issue 8 https://doi.org/10.1063/1.5098888	journal	August 2019
Aerodynamic aspects of the magnetospheric flow Levy, R. H.; Petschek, H. E.; Siscoe, G. L. AIAA Journal, Vol. 2, Issue 12 https://doi.org/10.2514/3.2745	journal	December 1964
Multibeam Energy Moments of Multibeam Particle Velocity Distributions Goldman, M. V.; Newman, D. L.; Eastwood, J. P. Journal of Geophysical Research: Space Physics, Vol. 125, Issue 12 https://doi.org/10.1029/2020JA028340	journal	December 2020
Turbulence, Spatial Transport, and Heating of the Solar Wind Matthaeus, W. H.; Zank, G. P.; Smith, C. W. Physical Review Letters, Vol. 82, Issue 17 https://doi.org/10.1103/PhysRevLett.82.3444	journal	April 1999
Ion heating resulting from pickup in magnetic reconnection exhausts: ION PICKUP Drake, J. F.; Swisdak, M.; Phan, T. D. Journal of Geophysical Research: Space Physics, Vol. 114, Issue A5 https://doi.org/10.1029/2008JA013701	journal	May 2009
Magnetospheric Multiscale Observation of Plasma Velocity-Space Cascade: Hermite Representation and Theory Servidio, S.; Chasapis, A.; Matthaeus, W. H. Physical Review Letters, Vol. 119, Issue 20 https://doi.org/10.1103/PhysRevLett.119.205101	journal	November 2017
Thermal disequilibration of ions and electrons by collisionless plasma turbulence Kawazura, Yohei; Barnes, Michael; Schekochihin, Alexander A. Proceedings of the National Academy of Sciences, Vol. 116, Issue 3 https://doi.org/10.1073/pnas.1812491116	journal	December 2018
Three-dimensional particle simulations of collisionless magnetic reconnection Zeiler, A. Journal of Geophysical Research, Vol. 107, Issue A9 https://doi.org/10.1029/2001JA000287	journal	January 2002
Data for Kinetic Entropy-Based Measures of Distribution Function Non-Maxwellianity: Theory and Simulations Liang, Haoming; Barbhuiya, M. Hasan; Cassak, Paul Zenodo https://doi.org/10.5281/zenodo.3951729	dataset	January 2020
Electron Heating Within the Earth's Bow Shock Feldman, W. C.; Bame, S. J.; Gary, S. P. Physical Review Letters, Vol. 49, Issue 3 https://doi.org/10.1103/PhysRevLett.49.199	journal	July 1982
Solar wind collisional heating Pezzi, Oreste Journal of Plasma Physics, Vol. 83, Issue 3 https://doi.org/10.1017/S0022377817000368	journal	May 2017
Theory and Transport of Nearly Incompressible Magnetohydrodynamic Turbulence. IV. Solar Coronal Turbulence Zank, G. P.; Adhikari, L.; Hunana, P. The Astrophysical Journal, Vol. 854, Issue 1 https://doi.org/10.3847/1538-4357/aaa763	journal	February 2018
Evolution of Entropy and Mediation of the Solar Wind by Turbulence Adhikari, L.; Zank, G. P.; Zhao, L. -L. The Astrophysical Journal, Vol. 891, Issue 1 https://doi.org/10.3847/1538-4357/ab7010	journal	March 2020
On entropy-maximized velocity distributions in circularly polarized finite amplitude Alfvén waves Nariyuki, Yasuhiro Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3590857	journal	May 2011
II. Transport of Nearly Incompressible Magnetohydrodynamic Turbulence from 1 to 75 au Adhikari, L.; Zank, G. P.; Hunana, P. The Astrophysical Journal, Vol. 841, Issue 2 https://doi.org/10.3847/1538-4357/aa6f5d	journal	May 2017
Boltzmann H function and entropy in the plasma sheet : ENTROPY IN THE PLASMA SHEET Kaufmann, Richard L.; Paterson, William R. Journal of Geophysical Research: Space Physics, Vol. 114, Issue A9 https://doi.org/10.1029/2008JA014030	journal	May 2009
Electron-scale measurements of magnetic reconnection in space Burch, J. L.; Torbert, R. B.; Phan, T. D. Science, Vol. 352, Issue 6290 https://doi.org/10.1126/science.aaf2939	journal	May 2016
Species Entropies in the Kinetic Range of Collisionless Plasma Turbulence: Particle-in-cell Simulations Gary, S. Peter; Zhao, Yinjian; Hughes, R. Scott The Astrophysical Journal, Vol. 859, Issue 2 https://doi.org/10.3847/1538-4357/aac022	journal	May 2018
Ion Acceleration at the Earth’s Bow Shock Burgess, D.; Möbius, E.; Scholer, M. Space Science Reviews, Vol. 173, Issue 1-4 https://doi.org/10.1007/s11214-012-9901-5	journal	June 2012
Entropy Generation across Earth’s Collisionless Bow Shock Parks, G. K.; Lee, E.; McCarthy, M. Physical Review Letters, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevLett.108.061102	journal	February 2012
Astrophysical Gyrokinetics: Basic Equations and Linear Theory Howes, Gregory G.; Cowley, Steven C.; Dorland, William The Astrophysical Journal, Vol. 651, Issue 1 https://doi.org/10.1086/506172	journal	November 2006
Electron-scale dynamics of the diffusion region during symmetric magnetic reconnection in space Torbert, R. B.; Burch, J. L.; Phan, T. D. Science, Vol. 362, Issue 6421 https://doi.org/10.1126/science.aat2998	journal	November 2018
Proton–Proton Collisions in the Turbulent Solar Wind: Hybrid Boltzmann–Maxwell Simulations Pezzi, O.; Perrone, D.; Servidio, S. The Astrophysical Journal, Vol. 887, Issue 2 https://doi.org/10.3847/1538-4357/ab5285	journal	December 2019
Ion and electron heating during magnetic reconnection in weakly collisional plasmas Numata, Ryusuke; Loureiro, N. F. Journal of Plasma Physics, Vol. 81, Issue 2 https://doi.org/10.1017/S002237781400107X	journal	November 2014
Fast Collisionless Reconnection and Electron Heating in Strongly Magnetized Plasmas Loureiro, N. F.; Schekochihin, A. A.; Zocco, A. Physical Review Letters, Vol. 111, Issue 2 https://doi.org/10.1103/PhysRevLett.111.025002	journal	July 2013
Fundamental issues on kappa-distributions in space plasmas and interplanetary proton distributions Leubner, M. P. Physics of Plasmas, Vol. 11, Issue 4 https://doi.org/10.1063/1.1667501	journal	April 2004
Nonlinear entropy transfer via zonal flows in gyrokinetic plasma turbulence Nakata, M.; Watanabe, T. -H.; Sugama, H. Physics of Plasmas, Vol. 19, Issue 2 https://doi.org/10.1063/1.3675855	journal	February 2012
The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox Krommes, John A.; Hu, Genze Physics of Plasmas, Vol. 1, Issue 10 https://doi.org/10.1063/1.870475	journal	October 1994
Solar Wind Turbulence Studies Using MMS Fast Plasma Investigation Data Bandyopadhyay, Riddhi; Chasapis, A.; Chhiber, R. The Astrophysical Journal, Vol. 866, Issue 2 https://doi.org/10.3847/1538-4357/aade93	journal	October 2018
MMS Observations and Hybrid Simulations of Surface Ripples at a Marginally Quasi-Parallel Shock: RIPPLES AT A QUASI-PARALLEL SHOCK Gingell, Imogen; Schwartz, Steven J.; Burgess, David Journal of Geophysical Research: Space Physics, Vol. 122, Issue 11 https://doi.org/10.1002/2017JA024538	journal	November 2017
Evidence for reconnection at Saturn's magnetopause: RECONNECTION AT SATURN'S MAGNETOPAUSE McAndrews, H. J.; Owen, C. J.; Thomsen, M. F. Journal of Geophysical Research: Space Physics, Vol. 113, Issue A4 https://doi.org/10.1029/2007JA012581	journal	April 2008
TRACE Observation of Damped Coronal Loop Oscillations: Implications for Coronal Heating Nakariakov, V. M. Science, Vol. 285, Issue 5429 https://doi.org/10.1126/science.285.5429.862	journal	August 1999
Thermal relaxation of a two-dimensional plasma in a d.c. magnetic field. Part 2. Numerical simulation Hsu, Jang-Yu; Joyce, Glenn; Montgomery, David Journal of Plasma Physics, Vol. 12, Issue 1 https://doi.org/10.1017/S0022377800024892	journal	August 1974
MESSENGER Observations of Magnetic Reconnection in Mercury's Magnetosphere Slavin, J. A.; Acuna, M. H.; Anderson, B. J. Science, Vol. 324, Issue 5927 https://doi.org/10.1126/science.1172011	journal	April 2009
Pathways to Dissipation in Weakly Collisional Plasmas Matthaeus, William H.; Yang, Yan; Wan, Minping The Astrophysical Journal, Vol. 891, Issue 1 https://doi.org/10.3847/1538-4357/ab6d6a	journal	March 2020
On Landau damping Mouhot, Clément; Villani, Cédric Acta Mathematica, Vol. 207, Issue 1 https://doi.org/10.1007/s11511-011-0068-9	journal	January 2011
MMS Observations of Electrostatic Waves in an Oblique Shock Crossing Goodrich, Katherine A.; Ergun, Robert; Schwartz, Steven J. Journal of Geophysical Research: Space Physics, Vol. 123, Issue 11 https://doi.org/10.1029/2018JA025830	journal	November 2018
Population Mixing in Asymmetric Magnetic Reconnection with a Guide Field Hesse, M.; Chen, L. J.; Liu, Y. -H. Physical Review Letters, Vol. 118, Issue 14 https://doi.org/10.1103/PhysRevLett.118.145101	journal	April 2017
Electron and Ion Energization in Relativistic Plasma Turbulence Zhdankin, Vladimir; Uzdensky, Dmitri A.; Werner, Gregory R. Physical Review Letters, Vol. 122, Issue 5 https://doi.org/10.1103/PhysRevLett.122.055101	journal	February 2019
Formation of secondary islands during magnetic reconnection Drake, J. F.; Swisdak, M.; Schoeffler, K. M. Geophysical Research Letters, Vol. 33, Issue 13 https://doi.org/10.1029/2006GL025957	journal	January 2006
On Solving the Coronal Heating Problem Klimchuk, James A. Solar Physics, Vol. 234, Issue 1 https://doi.org/10.1007/s11207-006-0055-z	journal	March 2006
Fully Kinetic versus Reduced-kinetic Modeling of Collisionless Plasma Turbulence Grošelj, Daniel; Cerri, Silvio S.; Navarro, Alejandro Bañón The Astrophysical Journal, Vol. 847, Issue 1 https://doi.org/10.3847/1538-4357/aa894d	journal	September 2017
Magnetospheric Multiscale Overview and Science Objectives Burch, J. L.; Moore, T. E.; Torbert, R. B. Space Science Reviews, Vol. 199, Issue 1-4 https://doi.org/10.1007/s11214-015-0164-9	journal	May 2015
Permutation entropy and statistical complexity analysis of turbulence in laboratory plasmas and the solar wind Weck, P. J.; Schaffner, D. A.; Brown, M. R. Physical Review E, Vol. 91, Issue 2 https://doi.org/10.1103/PhysRevE.91.023101	journal	February 2015
Electron Heating in Low-Mach-number Perpendicular Shocks. I. Heating Mechanism Guo, Xinyi; Sironi, Lorenzo; Narayan, Ramesh The Astrophysical Journal, Vol. 851, Issue 2 https://doi.org/10.3847/1538-4357/aa9b82	journal	December 2017
Energy dissipation and entropy in collisionless plasma Du, Senbei; Zank, Gary P.; Li, Xiaocan Physical Review E, Vol. 101, Issue 3 https://doi.org/10.1103/PhysRevE.101.033208	journal	March 2020
Kinetic Plasma Turbulence: Recent Insights and Open Questions From 3D3V Simulations Cerri, Silvio Sergio; Grošelj, Daniel; Franci, Luca Frontiers in Astronomy and Space Sciences, Vol. 6 https://doi.org/10.3389/fspas.2019.00064	journal	October 2019
Equations of State for Collisionless Guide-Field Reconnection Le, A.; Egedal, J.; Daughton, W. Physical Review Letters, Vol. 102, Issue 8 https://doi.org/10.1103/PhysRevLett.102.085001	journal	February 2009
Turbulence Heating ObserveR – satellite mission proposal Vaivads, A.; Retinò, A.; Soucek, J. Journal of Plasma Physics, Vol. 82, Issue 5 https://doi.org/10.1017/S0022377816000775	journal	September 2016
Entropy distribution in the plasma sheet: ENTROPY DISTRIBUTION IN THE PLASMA SHEET Kaufmann, Richard L.; Paterson, William R. Journal of Geophysical Research: Space Physics, Vol. 116, Issue A8 https://doi.org/10.1029/2010JA015667	journal	August 2011
Coronal Heating by Magnetohydrodynamic Turbulence Driven by Reflected Low-Frequency Waves Matthaeus, W. H.; Zank, G. P.; Oughton, S. The Astrophysical Journal, Vol. 523, Issue 1 https://doi.org/10.1086/312259	journal	September 1999
Hybrid-kinetic Simulations of Ion Heating in Alfvénic Turbulence Arzamasskiy, Lev; Kunz, Matthew W.; Chandran, Benjamin D. G. The Astrophysical Journal, Vol. 879, Issue 1 https://doi.org/10.3847/1538-4357/ab20cc	journal	July 2019
Collisional Relaxation of Fine Velocity Structures in Plasmas Pezzi, Oreste; Valentini, Francesco; Veltri, Pierluigi Physical Review Letters, Vol. 116, Issue 14 https://doi.org/10.1103/PhysRevLett.116.145001	journal	April 2016
Nonlinear Phase Mixing and Phase-Space Cascade of Entropy in Gyrokinetic Plasma Turbulence Tatsuno, T.; Dorland, W.; Schekochihin, A. A. Physical Review Letters, Vol. 103, Issue 1 https://doi.org/10.1103/PhysRevLett.103.015003	journal	June 2009
Dissipation of Kinetic Alfvénic Turbulence as a Function of Ion and Electron Temperature Ratios Parashar, Tulasi N.; Gary, S. Peter The Astrophysical Journal, Vol. 882, Issue 1 https://doi.org/10.3847/1538-4357/ab2fc8	journal	August 2019
A review of pressure anisotropy caused by electron trapping in collisionless plasma, and its implications for magnetic reconnection Egedal, Jan; Le, Ari; Daughton, William Physics of Plasmas, Vol. 20, Issue 6 https://doi.org/10.1063/1.4811092	journal	June 2013
Thermal Relaxation in One- and Two-Dimensional Plasma Models Montgomery, David Physics of Fluids, Vol. 13, Issue 5 https://doi.org/10.1063/1.1693081	journal	January 1970
Differential kinetic dynamics and heating of ions in the turbulent solar wind Valentini, F.; Perrone, D.; Stabile, S. New Journal of Physics, Vol. 18, Issue 12 https://doi.org/10.1088/1367-2630/18/12/125001	journal	December 2016
Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades in Magnetized Weakly Collisional Plasmas Schekochihin, A. A.; Cowley, S. C.; Dorland, W. The Astrophysical Journal Supplement Series, Vol. 182, Issue 1 https://doi.org/10.1088/0067-0049/182/1/310	journal	May 2009
Dependence of Kinetic Plasma Turbulence on Plasma β Parashar, Tulasi N.; Matthaeus, William H.; Shay, Michael A. The Astrophysical Journal, Vol. 864, Issue 1 https://doi.org/10.3847/2041-8213/aadb8b	journal	August 2018
Electron and Proton Heating in Transrelativistic Guide Field Reconnection Rowan, Michael E.; Sironi, Lorenzo; Narayan, Ramesh The Astrophysical Journal, Vol. 873, Issue 1 https://doi.org/10.3847/1538-4357/ab03d7	journal	February 2019
Permutation Entropy Analysis of Magnetic Field Turbulence at 1AU Revisited Olivier, C. P.; Engelbrecht, N. E.; Strauss, R. D. Journal of Geophysical Research: Space Physics, Vol. 124, Issue 1 https://doi.org/10.1029/2018JA026102	journal	January 2019
Entropy production and collisionless fluid closure Sarazin, Y.; Dif-Pradalier, G.; Zarzoso, D. Plasma Physics and Controlled Fusion, Vol. 51, Issue 11 https://doi.org/10.1088/0741-3335/51/11/115003	journal	October 2009
Kinetic Structure of the Electron Diffusion Region in Antiparallel Magnetic Reconnection Ng, J.; Egedal, J.; Le, A. Physical Review Letters, Vol. 106, Issue 6 https://doi.org/10.1103/PhysRevLett.106.065002	journal	February 2011
Kinetic simulation of steady states of ion temperature gradient driven turbulence with weak collisionality Watanabe, T. -H.; Sugama, H. Physics of Plasmas, Vol. 11, Issue 4 https://doi.org/10.1063/1.1669393	journal	April 2004
Jensen‐Shannon Complexity and Permutation Entropy Analysis of Geomagnetic Auroral Currents Osmane, Adnane; Dimmock, Andrew P.; Pulkkinen, Tuija I. Journal of Geophysical Research: Space Physics https://doi.org/10.1029/2018ja026248	journal	April 2019
Suppression of Magnetic Reconnection at Saturn's Low‐Latitude Magnetopause Fuselier, S. A.; Petrinec, S. M.; Sawyer, R. P. Journal of Geophysical Research: Space Physics, Vol. 125, Issue 5 https://doi.org/10.1029/2020ja027895	journal	April 2020
Current Sheets and Collisionless Damping in Kinetic Plasma Turbulence TenBarge, J. M.; Howes, G. G. The Astrophysical Journal, Vol. 771, Issue 2 https://doi.org/10.1088/2041-8205/771/2/l27	journal	June 2013
Inhomogeneous kinetic effects related to intermittent magnetic discontinuities Greco, A.; Valentini, F.; Servidio, S. Physical Review E, Vol. 86, Issue 6 https://doi.org/10.1103/physreve.86.066405	journal	December 2012
Cascades and Dissipative Anomalies in Nearly Collisionless Plasma Turbulence Eyink, Gregory L. Physical Review X, Vol. 8, Issue 4 https://doi.org/10.1103/physrevx.8.041020	journal	November 2018
Solar Wind Turbulence Studies using MMS Fast Plasma Investigation Data Bandyopadhyay, Riddhi; Chasapis, A.; Chhiber, R. arXiv https://doi.org/10.48550/arxiv.1807.06140	text	January 2018

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