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Title: Decomposition of plasma kinetic entropy into position and velocity space and the use of kinetic entropy in particle-in-cell simulations

Abstract

In this work, 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. In the beginning, 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 flnf, 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 antiparallel 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, as the position spacemore » 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.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [4];  [5];  [6]; ORCiD logo [1]; ORCiD logo [3]; ORCiD logo [7];  [8]
  1. West Virginia Univ., Morgantown, WV (United States)
  2. Univ. of Calabria (Italy)
  3. Univ. of Delaware, Newark, DE (United States)
  4. Univ. of Maryland, College Park, MD (United States)
  5. Univ. of New Hampshire, Durham, NH (United States)
  6. NASA Goddard Space Flight Center (GSFC), Greenbelt, MD (United States)
  7. Space Science Inst., Boulder, CO (United States)
  8. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States); SPACE SCIENCE INSTITUTE
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1577595
Grant/Contract Number:  
AC02-05CH11231; SC0019315
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 26; Journal Issue: 8; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Liang, Haoming, Cassak, Paul A., Servidio, Sergio, Shay, Michael A., Drake, James F., Swisdak, Marc, Argall, Matt R., Dorelli, John C., Scime, Earl E., Matthaeus, William H., Roytershteyn, Vadim, and Delzanno, Gian Luca. Decomposition of plasma kinetic entropy into position and velocity space and the use of kinetic entropy in particle-in-cell simulations. United States: N. p., 2019. Web. https://doi.org/10.1063/1.5098888.
Liang, Haoming, Cassak, Paul A., Servidio, Sergio, Shay, Michael A., Drake, James F., Swisdak, Marc, Argall, Matt R., Dorelli, John C., Scime, Earl E., Matthaeus, William H., Roytershteyn, Vadim, & Delzanno, Gian Luca. Decomposition of plasma kinetic entropy into position and velocity space and the use of kinetic entropy in particle-in-cell simulations. United States. https://doi.org/10.1063/1.5098888
Liang, Haoming, Cassak, Paul A., Servidio, Sergio, Shay, Michael A., Drake, James F., Swisdak, Marc, Argall, Matt R., Dorelli, John C., Scime, Earl E., Matthaeus, William H., Roytershteyn, Vadim, and Delzanno, Gian Luca. Fri . "Decomposition of plasma kinetic entropy into position and velocity space and the use of kinetic entropy in particle-in-cell simulations". United States. https://doi.org/10.1063/1.5098888. https://www.osti.gov/servlets/purl/1577595.
@article{osti_1577595,
title = {Decomposition of plasma kinetic entropy into position and velocity space and the use of kinetic entropy in particle-in-cell simulations},
author = {Liang, Haoming and Cassak, Paul A. and Servidio, Sergio and Shay, Michael A. and Drake, James F. and Swisdak, Marc and Argall, Matt R. and Dorelli, John C. and Scime, Earl E. and Matthaeus, William H. and Roytershteyn, Vadim and Delzanno, Gian Luca},
abstractNote = {In this work, 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. In the beginning, 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 flnf, 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 antiparallel 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, as 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.},
doi = {10.1063/1.5098888},
journal = {Physics of Plasmas},
number = 8,
volume = 26,
place = {United States},
year = {2019},
month = {8}
}

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Works referenced in this record:

Dual Phase-space Cascades in 3D Hybrid-Vlasov–Maxwell Turbulence
journal, March 2018


A Mathematical Theory of Communication
journal, July 1948


Kinetic dissipation and anisotropic heating in a turbulent collisionless plasma
journal, March 2009

  • Parashar, T. N.; Shay, M. A.; Cassak, P. A.
  • Physics of Plasmas, Vol. 16, Issue 3
  • DOI: 10.1063/1.3094062

Kinetic Dissipation Around a Dipolarization Front
journal, May 2018

  • Sitnov, M. I.; Merkin, V. G.; Roytershteyn, V.
  • Geophysical Research Letters, Vol. 45, Issue 10
  • DOI: 10.1029/2018GL077874

Estimating local plasma sheet PV 5/3 from single-spacecraft measurements
journal, January 2006

  • Wolf, R. A.; Kumar, V.; Toffoletto, F. R.
  • Journal of Geophysical Research, Vol. 111, Issue A12
  • DOI: 10.1029/2006JA012010

Three‐dimensional fluid simulations of the nonlinear drift‐resistive ballooning modes in tokamak edge plasmas
journal, October 1993

  • Guzdar, P. N.; Drake, J. F.; McCarthy, D.
  • Physics of Fluids B: Plasma Physics, Vol. 5, Issue 10
  • DOI: 10.1063/1.860842

Energy transfer channels and turbulence cascade in Vlasov-Maxwell turbulence
journal, June 2017


Laboratory space physics: Investigating the physics of space plasmas in the laboratory
journal, May 2018


Magnetospheric Multiscale Observation of Plasma Velocity-Space Cascade: Hermite Representation and Theory
journal, November 2017


A kinetic model of plasma turbulence
journal, October 2014


The Diffusion Region in Collisionless Magnetic Reconnection
journal, February 2011

  • Hesse, Michael; Neukirch, Thomas; Schindler, Karl
  • Space Science Reviews, Vol. 160, Issue 1-4
  • DOI: 10.1007/s11214-010-9740-1

Three-dimensional particle simulations of collisionless magnetic reconnection
journal, January 2002


Diagnosing collisionless energy transfer using field–particle correlations: gyrokinetic turbulence
journal, July 2017

  • Klein, Kristopher G.; Howes, Gregory G.; TenBarge, Jason M.
  • Journal of Plasma Physics, Vol. 83, Issue 4
  • DOI: 10.1017/S0022377817000563

Investigating dynamical complexity in the magnetosphere using various entropy measures: COMPLEXITY IN MAGNETOSPHERE DYNAMICS
journal, June 2009

  • Balasis, Georgios; Daglis, Ioannis A.; Papadimitriou, Constantinos
  • Journal of Geophysical Research: Space Physics, Vol. 114, Issue A9
  • DOI: 10.1029/2008JA014035

Electron Heating in Low Mach Number Perpendicular Shocks. II. Dependence on the Pre-shock Conditions
journal, May 2018

  • Guo, Xinyi; Sironi, Lorenzo; Narayan, Ramesh
  • The Astrophysical Journal, Vol. 858, Issue 2
  • DOI: 10.3847/1538-4357/aab6ad

Possible generalization of Boltzmann-Gibbs statistics
journal, July 1988

  • Tsallis, Constantino
  • Journal of Statistical Physics, Vol. 52, Issue 1-2
  • DOI: 10.1007/BF01016429

Electron and Proton Acceleration in Trans-relativistic Magnetic Reconnection: Dependence on Plasma Beta and Magnetization
journal, July 2018

  • Ball, David; Sironi, Lorenzo; Özel, Feryal
  • The Astrophysical Journal, Vol. 862, Issue 1
  • DOI: 10.3847/1538-4357/aac820

A Review of Astrophysical Jets
journal, December 2014


On the (Boltzmann) entropy of non-equilibrium systems
journal, June 2004


Phase diagram for magnetic reconnection in heliophysical, astrophysical, and laboratory plasmas
journal, November 2011

  • Ji, Hantao; Daughton, William
  • Physics of Plasmas, Vol. 18, Issue 11
  • DOI: 10.1063/1.3647505

Boltzmann H function and entropy in the plasma sheet : ENTROPY IN THE PLASMA SHEET
journal, May 2009

  • Kaufmann, Richard L.; Paterson, William R.
  • Journal of Geophysical Research: Space Physics, Vol. 114, Issue A9
  • DOI: 10.1029/2008JA014030

Intermittency, coherent structures and dissipation in plasma turbulence
journal, April 2016

  • Wan, M.; Matthaeus, W. H.; Roytershteyn, V.
  • Physics of Plasmas, Vol. 23, Issue 4
  • DOI: 10.1063/1.4945631

Electron-scale measurements of magnetic reconnection in space
journal, May 2016


Onset of reconnection in the near magnetotail: PIC simulations
journal, December 2014

  • Liu, Yi‐Hsin; Birn, Joachim; Daughton, William
  • Journal of Geophysical Research: Space Physics, Vol. 119, Issue 12
  • DOI: 10.1002/2014JA020492

Relativistic Reconnection: an Efficient Source of Non-Thermal Particles
journal, February 2014


Collisionless Damping of Nonlinear Plasma Oscillations
journal, January 1965


Forced magnetic reconnection
journal, January 2005


Entropy is in Flux V3.4
journal, April 2017


Entropy Generation across Earth’s Collisionless Bow Shock
journal, February 2012


Astrophysical Gyrokinetics: Basic Equations and Linear Theory
journal, November 2006

  • Howes, Gregory G.; Cowley, Steven C.; Dorland, William
  • The Astrophysical Journal, Vol. 651, Issue 1
  • DOI: 10.1086/506172

Ion and electron heating during magnetic reconnection in weakly collisional plasmas
journal, November 2014


Nonadiabatic heating in magnetic reconnection
journal, July 2014

  • Ma, Xuanye; Otto, Antonius
  • Journal of Geophysical Research: Space Physics, Vol. 119, Issue 7
  • DOI: 10.1002/2014JA019856

Fast Collisionless Reconnection and Electron Heating in Strongly Magnetized Plasmas
journal, July 2013


Fundamental issues on kappa-distributions in space plasmas and interplanetary proton distributions
journal, April 2004


The transport of plasma sheet material from the distant tail to geosynchronous orbit
journal, September 1998

  • Borovsky, Joseph E.; Thomsen, Michelle F.; Elphic, Richard C.
  • Journal of Geophysical Research: Space Physics, Vol. 103, Issue A9
  • DOI: 10.1029/97JA03144

The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox
journal, October 1994

  • Krommes, John A.; Hu, Genze
  • Physics of Plasmas, Vol. 1, Issue 10
  • DOI: 10.1063/1.870475

Nonlinear entropy transfer via zonal flows in gyrokinetic plasma turbulence
journal, February 2012

  • Nakata, M.; Watanabe, T. -H.; Sugama, H.
  • Physics of Plasmas, Vol. 19, Issue 2
  • DOI: 10.1063/1.3675855

Energy transfer, pressure tensor, and heating of kinetic plasma
journal, July 2017

  • Yang, Yan; Matthaeus, William H.; Parashar, Tulasi N.
  • Physics of Plasmas, Vol. 24, Issue 7
  • DOI: 10.1063/1.4990421

Inside the Black Box: Magnetic Reconnection and the Magnetospheric Multiscale Mission
journal, March 2016


Current Sheets and Collisionless Damping in Kinetic Plasma Turbulence
journal, June 2013


Supernova Remnants at High Energy
journal, September 2008


Multiscale Nature of the Dissipation Range in Gyrokinetic Simulations of Alfvénic Turbulence
journal, July 2015


Plasmoids in relativistic reconnection, from birth to adulthood: first they grow, then they go
journal, July 2016

  • Sironi, Lorenzo; Giannios, Dimitrios; Petropoulou, Maria
  • Monthly Notices of the Royal Astronomical Society, Vol. 462, Issue 1
  • DOI: 10.1093/mnras/stw1620

Electron Bulk Acceleration and Thermalization at Earth’s Quasiperpendicular Bow Shock
journal, May 2018


On Landau damping
journal, January 2011


Theory of Interstellar Shocks
journal, September 1993


Population Mixing in Asymmetric Magnetic Reconnection with a Guide Field
journal, April 2017


Energy Dissipation and Landau Damping in two- and Three-Dimensional Plasma Turbulence
journal, November 2016


Nonequilibrium Entropy in a Shock
journal, July 2017


Formation of secondary islands during magnetic reconnection
journal, January 2006

  • Drake, J. F.; Swisdak, M.; Schoeffler, K. M.
  • Geophysical Research Letters, Vol. 33, Issue 13
  • DOI: 10.1029/2006GL025957

Evidence for electron Landau damping in space plasma turbulence
journal, February 2019


On Solving the Coronal Heating Problem
journal, March 2006


On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods
journal, January 2016


Reconnection in a Striped Pulsar Wind
journal, January 2001

  • Lyubarsky, Y.; Kirk, J. G.
  • The Astrophysical Journal, Vol. 547, Issue 1
  • DOI: 10.1086/318354

Identifying the electron diffusion region in a realistic simulation of Earth's magnetotail: Identifying the EDR
journal, June 2016

  • Ashour-Abdalla, Maha; Lapenta, Giovanni; Walker, Raymond
  • Geophysical Research Letters, Vol. 43, Issue 12
  • DOI: 10.1002/2016GL069355

Fluid moment models for Landau damping with application to the ion-temperature-gradient instability
journal, June 1990


The magnetic nature of solar flares
journal, July 2001

  • Priest, E. R.; Forbes, T. G.
  • The Astronomy and Astrophysics Review, Vol. 10, Issue 4
  • DOI: 10.1007/s001590100013

Entropy conservation in simulations of magnetic reconnection
journal, September 2006

  • Birn, J.; Hesse, M.; Schindler, K.
  • Physics of Plasmas, Vol. 13, Issue 9
  • DOI: 10.1063/1.2349440

Quantifying gyrotropy in magnetic reconnection
journal, January 2016


Fully Kinetic versus Reduced-kinetic Modeling of Collisionless Plasma Turbulence
journal, September 2017

  • Grošelj, Daniel; Cerri, Silvio S.; Navarro, Alejandro Bañón
  • The Astrophysical Journal, Vol. 847, Issue 1
  • DOI: 10.3847/1538-4357/aa894d

Magnetospheric Multiscale Overview and Science Objectives
journal, May 2015


Two-Scale Structure of the Electron Dissipation Region during Collisionless Magnetic Reconnection
journal, October 2007


Role of entropy in magnetotail dynamics: ENTROPY IN TAIL DYNAMICS
journal, April 2009

  • Birn, J.; Hesse, M.; Schindler, K.
  • Journal of Geophysical Research: Space Physics, Vol. 114, Issue A9
  • DOI: 10.1029/2008JA014015

Electron Heating in Low-Mach-number Perpendicular Shocks. I. Heating Mechanism
journal, December 2017

  • Guo, Xinyi; Sironi, Lorenzo; Narayan, Ramesh
  • The Astrophysical Journal, Vol. 851, Issue 2
  • DOI: 10.3847/1538-4357/aa9b82

Turbulence Heating ObserveR – satellite mission proposal
journal, September 2016


Entropy distribution in the plasma sheet: ENTROPY DISTRIBUTION IN THE PLASMA SHEET
journal, August 2011

  • Kaufmann, Richard L.; Paterson, William R.
  • Journal of Geophysical Research: Space Physics, Vol. 116, Issue A8
  • DOI: 10.1029/2010JA015667

Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge
journal, March 2001

  • Birn, J.; Drake, J. F.; Shay, M. A.
  • Journal of Geophysical Research: Space Physics, Vol. 106, Issue A3
  • DOI: 10.1029/1999JA900449

New Measure of the Dissipation Region in Collisionless Magnetic Reconnection
journal, May 2011


A simple, analytical model of collisionless magnetic reconnection in a pair plasma
journal, October 2009

  • Hesse, Michael; Zenitani, Seiji; Kuznetsova, Masha
  • Physics of Plasmas, Vol. 16, Issue 10
  • DOI: 10.1063/1.3246005

The Evolution and Structure of Pulsar Wind Nebulae
journal, September 2006


Undamped electrostatic plasma waves
journal, September 2012

  • Valentini, F.; Perrone, D.; Califano, F.
  • Physics of Plasmas, Vol. 19, Issue 9
  • DOI: 10.1063/1.4751440

Is steady convection possible in the Earth's magnetotail?
journal, November 1980


Nonlinear Phase Mixing and Phase-Space Cascade of Entropy in Gyrokinetic Plasma Turbulence
journal, June 2009


Electron and Proton Heating in Transrelativistic Magnetic Reconnection
journal, November 2017

  • Rowan, Michael E.; Sironi, Lorenzo; Narayan, Ramesh
  • The Astrophysical Journal, Vol. 850, Issue 1
  • DOI: 10.3847/1538-4357/aa9380

Relativistic entropy and related Boltzmann kinetics
journal, May 2009


Spectral Approach to Plasma Kinetic Simulations Based on Hermite Decomposition in the Velocity Space
journal, August 2018

  • Roytershteyn, Vadim; Delzanno, Gian Luca
  • Frontiers in Astronomy and Space Sciences, Vol. 5
  • DOI: 10.3389/fspas.2018.00027

Evidence of critical balance in kinetic Alfvén wave turbulence simulations
journal, May 2012

  • TenBarge, J. M.; Howes, G. G.
  • Physics of Plasmas, Vol. 19, Issue 5
  • DOI: 10.1063/1.3693974

Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades in Magnetized Weakly Collisional Plasmas
journal, May 2009

  • Schekochihin, A. A.; Cowley, S. C.; Dorland, W.
  • The Astrophysical Journal Supplement Series, Vol. 182, Issue 1
  • DOI: 10.1088/0067-0049/182/1/310

Permutation Entropy Analysis of Magnetic Field Turbulence at 1AU Revisited
journal, January 2019

  • Olivier, C. P.; Engelbrecht, N. E.; Strauss, R. D.
  • Journal of Geophysical Research: Space Physics, Vol. 124, Issue 1
  • DOI: 10.1029/2018JA026102

Entropy production and collisionless fluid closure
journal, October 2009


Kinetic Structure of the Electron Diffusion Region in Antiparallel Magnetic Reconnection
journal, February 2011


What do we really know about collisionless shocks?
journal, January 1997


Kinetic simulation of steady states of ion temperature gradient driven turbulence with weak collisionality
journal, April 2004

  • Watanabe, T. -H.; Sugama, H.
  • Physics of Plasmas, Vol. 11, Issue 4
  • DOI: 10.1063/1.1669393

Magnetic flux and particle transport in the plasma sheet
journal, January 2006

  • Kaufmann, Richard L.; Paterson, William R.
  • Journal of Geophysical Research, Vol. 111, Issue A10
  • DOI: 10.1029/2006JA011734

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    Proton–Proton Collisions in the Turbulent Solar Wind: Hybrid Boltzmann–Maxwell Simulations
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