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Title: Self-sustaining sound in collisionless, high-β plasma

Abstract

Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $$δn/n_0≳2/β$$ (where $$β\gg1$$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves’ otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more ‘fluid-like’ than kinetic. A nonlinear fluctuation–dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels and weakly collisional thermodynamics when IAWs with $$δn/n_0≳2/β$$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3];  [4]
  1. Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  2. Univ. of Otago, Dunedin (New Zealand)
  3. Univ. of Oxford (United Kingdom); Merton College, Oxford (United Kingdom)
  4. Univ. of California, Berkeley, CA (United States)
Publication Date:
Research Org.:
Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States); University of California, Berkeley, CA (United States)
Sponsoring Org.:
USDOE; National Aeronautics and Space Administration (NASA); UK STFC; Engineering and Physical Sciences Research Council (EPSRC); National Science Foundation (NSF)
OSTI Identifier:
1814567
Alternate Identifier(s):
OSTI ID: 1984384
Grant/Contract Number:  
SC0019046; SC0019047; NNX16AK09G; UOO1727; ST/N0009/9/1; EP/M022331/1; EP/R034737/1; TG-AST130058; OCI-1053575
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Plasma Physics
Additional Journal Information:
Journal Volume: 86; Journal Issue: 6; Journal ID: ISSN 0022-3778
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; astrophysical plasmas

Citation Formats

Kunz, M. W., Squire, J., Schekochihin, A. A., and Quataert, E. Self-sustaining sound in collisionless, high-β plasma. United States: N. p., 2020. Web. doi:10.1017/s0022377820001312.
Kunz, M. W., Squire, J., Schekochihin, A. A., & Quataert, E. Self-sustaining sound in collisionless, high-β plasma. United States. https://doi.org/10.1017/s0022377820001312
Kunz, M. W., Squire, J., Schekochihin, A. A., and Quataert, E. Mon . "Self-sustaining sound in collisionless, high-β plasma". United States. https://doi.org/10.1017/s0022377820001312. https://www.osti.gov/servlets/purl/1814567.
@article{osti_1814567,
title = {Self-sustaining sound in collisionless, high-β plasma},
author = {Kunz, M. W. and Squire, J. and Schekochihin, A. A. and Quataert, E.},
abstractNote = {Using analytical theory and hybrid-kinetic numerical simulations, we demonstrate that, in a collisionless plasma, long-wavelength ion-acoustic waves (IAWs) with amplitudes $δn/n_0≳2/β$ (where $β\gg1$ is the ratio of thermal to magnetic pressure) generate sufficient pressure anisotropy to destabilize the plasma to firehose and mirror instabilities. These kinetic instabilities grow rapidly to reduce the pressure anisotropy by pitch-angle scattering and trapping particles, respectively, thereby impeding the maintenance of Landau resonances that enable such waves’ otherwise potent collisionless damping. The result is wave dynamics that evince a weakly collisional plasma: the ion distribution function is near-Maxwellian, the field-parallel flow of heat resembles its Braginskii form (except in regions where large-amplitude magnetic mirrors strongly suppress particle transport), and the relations between various thermodynamic quantities are more ‘fluid-like’ than kinetic. A nonlinear fluctuation–dissipation relation for self-sustaining IAWs is obtained by solving a plasma-kinetic Langevin problem, which demonstrates suppressed damping, enhanced fluctuation levels and weakly collisional thermodynamics when IAWs with $δn/n_0≳2/β$ are stochastically driven. We investigate how our results depend upon the scale separation between the wavelength of the IAW and the Larmor radius of the ions, and discuss briefly their implications for our understanding of turbulence and transport in the solar wind and the intracluster medium of galaxy clusters.},
doi = {10.1017/s0022377820001312},
journal = {Journal of Plasma Physics},
number = 6,
volume = 86,
place = {United States},
year = {2020},
month = {11}
}

Works referenced in this record:

Multi-Species Measurements of the Firehose and Mirror Instability Thresholds in the Solar wind
journal, July 2016


Collisionless shock waves in high β plasmas: 1
journal, July 1967


Inertial-range kinetic turbulence in pressure-anisotropic astrophysical plasmas
journal, July 2015

  • Kunz, M. W.; Schekochihin, A. A.; Chen, C. H. K.
  • Journal of Plasma Physics, Vol. 81, Issue 5
  • DOI: 10.1017/S0022377815000811

Linear Vlasov theory of a magnetised, thermally stratified atmosphere
journal, October 2016


Suppressed effective viscosity in the bulk intergalactic plasma
journal, June 2019


Viscous Shear Instability in Weakly Magnetized, Dilute Plasmas
journal, December 2004

  • Balbus, Steven A.
  • The Astrophysical Journal, Vol. 616, Issue 2
  • DOI: 10.1086/424989

Mirror instability: 1. Physical mechanism of linear instability
journal, January 1993

  • Southwood, David J.; Kivelson, Margaret G.
  • Journal of Geophysical Research, Vol. 98, Issue A6
  • DOI: 10.1029/92JA02837

Non-linear mirror instability
journal, December 2014

  • Rincon, F.; Schekochihin, A. A.; Cowley, S. C.
  • Monthly Notices of the Royal Astronomical Society: Letters, Vol. 447, Issue 1
  • DOI: 10.1093/mnrasl/slu179

Buoyancy Instabilities in Weakly Magnetized Low‐Collisionality Plasmas
journal, February 2008

  • Quataert, Eliot
  • The Astrophysical Journal, Vol. 673, Issue 2
  • DOI: 10.1086/525248

The Effect of Wave-Particle Interactions on the Propagation of Cosmic Rays
journal, May 1969

  • Kulsrud, Russell; Pearce, William P.
  • The Astrophysical Journal, Vol. 156
  • DOI: 10.1086/149981

Nonlinear Growth of Firehose and Mirror Fluctuations in Astrophysical Plasmas
journal, February 2008


Landau fluid models of collisionless magnetohydrodynamics
journal, November 1997

  • Snyder, P. B.; Hammett, G. W.; Dorland, W.
  • Physics of Plasmas, Vol. 4, Issue 11
  • DOI: 10.1063/1.872517

Comment on the linear mirror instability near the threshold
journal, August 2007


Pressure-anisotropy-driven microturbulence and magnetic-field evolution in shearing, collisionless plasma
journal, April 2016

  • Melville, Scott; Schekochihin, Alexander A.; Kunz, Matthew W.
  • Monthly Notices of the Royal Astronomical Society, Vol. 459, Issue 3
  • DOI: 10.1093/mnras/stw793

The Magnetorotational Instability in a Collisionless Plasma
journal, September 2002

  • Quataert, Eliot; Dorland, William; Hammett, Gregory W.
  • The Astrophysical Journal, Vol. 577, Issue 1
  • DOI: 10.1086/342174

On Kinetic Slow Modes, Fluid Slow Modes, and Pressure-balanced Structures in the Solar Wind
journal, May 2017

  • Verscharen, Daniel; Chen, Christopher H. K.; Wicks, Robert T.
  • The Astrophysical Journal, Vol. 840, Issue 2
  • DOI: 10.3847/1538-4357/aa6a56

A non-linear theory of the parallel firehose and gyrothermal instabilities in a weakly collisional plasma: Theory of firehose and gyrothermal instabilities
journal, March 2011


Stability, Instability, and “Backward” Transport in Stratified Fluids
journal, May 2000

  • Balbus, Steven A.
  • The Astrophysical Journal, Vol. 534, Issue 1
  • DOI: 10.1086/308732

Convective and Rotational Stability of a Dilute Plasma
journal, December 2001

  • Balbus, Steven A.
  • The Astrophysical Journal, Vol. 562, Issue 2
  • DOI: 10.1086/323875

Proton temperature-anisotropy-driven instabilities in weakly collisional plasmas: Hybrid simulations
journal, August 2014


Collisionless Isotropization of the Solar-Wind Protons by Compressive Fluctuations and Plasma Instabilities
journal, November 2016

  • Verscharen, Daniel; Chandran, Benjamin D. G.; Klein, Kristopher G.
  • The Astrophysical Journal, Vol. 831, Issue 2
  • DOI: 10.3847/0004-637X/831/2/128

The Boltzmann equation an d the one-fluid hydromagnetic equations in the absence of particle collisions
journal, July 1956

  • Chew, G. F.; Goldberger, M. L.; Low, F. E.
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 236, Issue 1204, p. 112-118
  • DOI: 10.1098/rspa.1956.0116

Wind/SWE observations of firehose constraint on solar wind proton temperature anisotropy: FIREHOSE CONSTRAINT ON PROTON ANISOTROPY
journal, September 2002

  • Kasper, Justin C.; Lazarus, Alan J.; Gary, S. Peter
  • Geophysical Research Letters, Vol. 29, Issue 17
  • DOI: 10.1029/2002GL015128

Dynamical stability of a thermally stratified intracluster medium with anisotropic momentum and heat transport: Dynamical stability of the ICM
journal, August 2011


New kinetic instability: Oblique Alfvén fire hose
journal, May 2000

  • Hellinger, P.; Matsumoto, H.
  • Journal of Geophysical Research: Space Physics, Vol. 105, Issue A5
  • DOI: 10.1029/1999JA000297

Proton fire hose instabilities in the expanding solar wind
journal, February 2017


Compressible Magnetohydrodynamic Turbulence in Interstellar Plasmas
journal, November 2001

  • Lithwick, Yoram; Goldreich, Peter
  • The Astrophysical Journal, Vol. 562, Issue 1
  • DOI: 10.1086/323470

Sound-wave instabilities in dilute plasmas with cosmic rays: implications for cosmic ray confinement and the Perseus X-ray ripples
journal, February 2020

  • Kempski, Philipp; Quataert, Eliot; Squire, Jonathan
  • Monthly Notices of the Royal Astronomical Society, Vol. 493, Issue 4
  • DOI: 10.1093/mnras/staa535

Efficient Production of Sound Waves by AGN Jets in the Intracluster Medium
journal, November 2019

  • Bambic, Christopher J.; Reynolds, Christopher S.
  • The Astrophysical Journal, Vol. 886, Issue 2
  • DOI: 10.3847/1538-4357/ab4daf

Cluster Heating by Viscous Dissipation of Sound Waves
journal, August 2004

  • Ruszkowski, Mateusz; Bruggen, Marcus; Begelman, Mitchell C.
  • The Astrophysical Journal, Vol. 611, Issue 1
  • DOI: 10.1086/422158

Drift Mirror Instability in the Magnetosphere
journal, January 1969


Thermal conduction in a mirror-unstable plasma
journal, April 2016

  • Komarov, S. V.; Churazov, E. M.; Kunz, M. W.
  • Monthly Notices of the Royal Astronomical Society, Vol. 460, Issue 1
  • DOI: 10.1093/mnras/stw963

Effect of finite ion gyroradius on the fire‐hose instability in a high beta plasma
journal, July 1993

  • Yoon, Peter H.; Wu, C. S.; de Assis, A. S.
  • Physics of Fluids B: Plasma Physics, Vol. 5, Issue 7
  • DOI: 10.1063/1.860785

Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High- β Plasma
journal, October 2017


A Stringent Limit on the Amplitude of AlfvÉNic Perturbations in High-Beta Low-Collisionality Plasmas
journal, October 2016


Firehose and Mirror Instabilities in a Collisionless Shearing Plasma
journal, May 2014


PIC Simulations of Velocity-space Instabilities in a Decreasing Magnetic Field: Viscosity and Thermal Conduction
journal, February 2018

  • Riquelme, Mario; Quataert, Eliot; Verscharen, Daniel
  • The Astrophysical Journal, Vol. 854, Issue 2
  • DOI: 10.3847/1538-4357/aaa6d1

Fluctuation-dissipation relations for a plasma-kinetic Langevin equation
journal, September 2014


Acoustic Disturbances in Galaxy Clusters
journal, April 2018

  • Zweibel, Ellen G.; Mirnov, Vladimir V.; Ruszkowski, Mateusz
  • The Astrophysical Journal, Vol. 858, Issue 1
  • DOI: 10.3847/1538-4357/aab9ae

Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence
journal, April 2016

  • Schekochihin, A. A.; Parker, J. T.; Highcock, E. G.
  • Journal of Plasma Physics, Vol. 82, Issue 2
  • DOI: 10.1017/S0022377816000374

Amplitude limits and nonlinear damping of shear-Alfvén waves in high-beta low-collisionality plasmas
journal, May 2017


On viscosity, conduction and sound waves in the intracluster medium
journal, November 2005


A deep Chandra observation of the Perseus cluster: shocks and ripples
journal, September 2003


Longitudinal Ion Oscillations in a Hot Plasma
journal, January 1961


Magnetic Fluctuation Power Near Proton Temperature Anisotropy Instability Thresholds in the Solar Wind
journal, November 2009


Solar wind proton temperature anisotropy: Linear theory and WIND/SWE observations
journal, January 2006

  • Hellinger, Petr; Trávníček, Pavel; Kasper, Justin C.
  • Geophysical Research Letters, Vol. 33, Issue 9
  • DOI: 10.1029/2006GL025925

Fluidization of collisionless plasma turbulence
journal, January 2019

  • Meyrand, Romain; Kanekar, Anjor; Dorland, William
  • Proceedings of the National Academy of Sciences, Vol. 116, Issue 4
  • DOI: 10.1073/pnas.1813913116

Do sound waves transport the AGN energy in the Perseus cluster?
journal, August 2016

  • Fabian, A. C.; Walker, S. A.; Russell, H. R.
  • Monthly Notices of the Royal Astronomical Society: Letters, Vol. 464, Issue 1
  • DOI: 10.1093/mnrasl/slw170

Particle-In-Cell Simulations of Continuously Driven Mirror and ion Cyclotron Instabilities in high beta Astrophysical and Heliospheric Plasmas
journal, February 2015

  • Riquelme, Mario A.; Quataert, Eliot; Verscharen, Daniel
  • The Astrophysical Journal, Vol. 800, Issue 1
  • DOI: 10.1088/0004-637X/800/1/27

The stability of the pinch
journal, July 1958

  • Chandrasekhar, Subrahmanyan; Kaufman, A. N.; Watson, K. M.
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 245, Issue 1243, p. 435-455
  • DOI: 10.1098/rspa.1958.0094

Dynamical Instability in an Anisotropic Ionized Gas of Low Density
journal, March 1958


Pegasus: A new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics
journal, February 2014


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

Ion Wave Instabilities
journal, January 1960

  • Bernstein, Ira B.; Kulsrud, Russell M.
  • Physics of Fluids, Vol. 3, Issue 6
  • DOI: 10.1063/1.1706161

Macroscopic Quasilinear Theory of the Garden-Hose Instability
journal, January 1968


Collisionless Damping of Hydromagnetic Waves
journal, January 1966


Stability, Instability, and “Backward” Transport in Stratified Fluids
journal, May 2000

  • Balbus, Steven A.
  • The Astrophysical Journal, Vol. 534, Issue 1
  • DOI: 10.1086/308732

Convective and Rotational Stability of a Dilute Plasma
journal, December 2001

  • Balbus, Steven A.
  • The Astrophysical Journal, Vol. 562, Issue 2
  • DOI: 10.1086/323875

Viscous Shear Instability in Weakly Magnetized, Dilute Plasmas
journal, December 2004

  • Balbus, Steven A.
  • The Astrophysical Journal, Vol. 616, Issue 2
  • DOI: 10.1086/424989

On Kinetic Slow Modes, Fluid Slow Modes, and Pressure-balanced Structures in the Solar Wind
journal, May 2017

  • Verscharen, Daniel; Chen, Christopher H. K.; Wicks, Robert T.
  • The Astrophysical Journal, Vol. 840, Issue 2
  • DOI: 10.3847/1538-4357/aa6a56

Suppression of thermal conduction in a mirror-unstable plasma
text, January 2016


Multi-Species Measurements of the Firehose and Mirror Instability Thresholds in the Solar Wind
text, January 2016


Fluidization of collisionless plasma turbulence
text, January 2018