Critical role of electron heat flux on Bohm criterion

Tang, Xianzhu; Guo, Zehua

doi:10.1063/1.4971808

Title: Critical role of electron heat flux on Bohm criterion

Abstract

Bohm criterion, originally derived for an isothermal-electron and cold-ion plasma, is often used as a rule of thumb for more general plasmas. Here, we establish a more precise determination of the Bohm criterion that are quantitatively useful for understanding and modeling collisional plasmas that still have collisional mean-free-path much greater than plasma Debye length. Specifically, it is shown that electron heat flux, rather than the isothermal electron assumption, is what sets the Bohm speed to be $$\sqrt{k_B(T_e||+3T_i||)/m_i}$$ with T_e,i∥ the electron and ion parallel temperature at the sheath entrance and m_i the ion mass.

Authors:

^[1];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Mon Dec 05 00:00:00 EST 2016

Research Org.:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Fusion Energy Sciences (FES); USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1414121

Report Number(s):: LA-UR-16-23720
Journal ID: ISSN 1070-664X; TRN: US1800647

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 23; Journal Issue: 12; 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; Magnetic Fusion Energy; Bohm criterion; electron heat flux; Plasma sheaths; Plasma temperature; Speed of sound; Plasma flows; Anisotropy

Citation Formats


                    Tang, Xianzhu, and Guo, Zehua. Critical role of electron heat flux on Bohm criterion.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4971808.

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                    Tang, Xianzhu, & Guo, Zehua. Critical role of electron heat flux on Bohm criterion.  United States.  https://doi.org/10.1063/1.4971808

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                    Tang, Xianzhu, and Guo, Zehua. Mon .  
"Critical role of electron heat flux on Bohm criterion".  United States.  https://doi.org/10.1063/1.4971808.  https://www.osti.gov/servlets/purl/1414121.

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@article{osti_1414121,

  title        = {Critical role of electron heat flux on Bohm criterion},

  author       = {Tang, Xianzhu and Guo, Zehua},

  abstractNote = {Bohm criterion, originally derived for an isothermal-electron and cold-ion plasma, is often used as a rule of thumb for more general plasmas. Here, we establish a more precise determination of the Bohm criterion that are quantitatively useful for understanding and modeling collisional plasmas that still have collisional mean-free-path much greater than plasma Debye length. Specifically, it is shown that electron heat flux, rather than the isothermal electron assumption, is what sets the Bohm speed to be $\sqrt{k_B(T_e||+3T_i||)/m_i}$ with Te,i∥ the electron and ion parallel temperature at the sheath entrance and mi the ion mass.},

  doi          = {10.1063/1.4971808},

  journal      = {Physics of Plasmas},

  number       = 12,

  volume       = 23,

  place        = {United States},

  year         = {Mon Dec 05 00:00:00 EST 2016},

  month        = {Mon Dec 05 00:00:00 EST 2016}

}

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Works referenced in this record:

Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
journal, January 1986

Zawaideh, Emad; Najmabadi, Farrokh; Conn, Robert W.
Physics of Fluids, Vol. 29, Issue 2
DOI: 10.1063/1.865731

Strongly Emitting Surfaces Unable to Float below Plasma Potential
journal, February 2016

Campanell, M. D.; Umansky, M. V.
Physical Review Letters, Vol. 116, Issue 8
DOI: 10.1103/PhysRevLett.116.085003

Charging and Heat Collection by a Positively Charged Dust Grain in a Plasma
journal, July 2014

Delzanno, Gian Luca; Tang, Xian-Zhu
Physical Review Letters, Vol. 113, Issue 3
DOI: 10.1103/PhysRevLett.113.035002

Parallel Heat Flux from Low to High Parallel Temperature along a Magnetic Field Line
journal, April 2012

Guo, Zehua; Tang, Xian-Zhu
Physical Review Letters, Vol. 108, Issue 16
DOI: 10.1103/PhysRevLett.108.165005

Principles of Plasma Discharges and Materials Processing
book, January 2005

Lieberman, Michael A.; Lichtenberg, Allan J.
DOI: 10.1002/0471724254

Particle in cell calculation of plasma force on a small grain in a non-uniform collisional sheath
journal, October 2013

Hutchinson, I. H.
Plasma Physics and Controlled Fusion, Vol. 55, Issue 11
DOI: 10.1088/0741-3335/55/11/115014

Heat Flux Dependence of Ambipolar Potential and Plasma Profile in a Long Mean-Free-Path Plasma Along Non-Uniform Open Magnetic Field Lines
journal, June 2012

Guo, Z.; Tang, X. -Z.
Contributions to Plasma Physics, Vol. 52, Issue 5-6
DOI: 10.1002/ctpp.201210043

Sheath energy transmission in a collisional plasma with collisionless sheath
journal, October 2015

Tang, Xian-Zhu; Guo, Zehua
Physics of Plasmas, Vol. 22, Issue 10
DOI: 10.1063/1.4933415

Kinetic theory of the presheath and the Bohm criterion
journal, March 2011

Baalrud, S. D.; Hegna, C. C.
Plasma Sources Science and Technology, Vol. 20, Issue 2
DOI: 10.1088/0963-0252/20/2/025013

Comment on ‘Kinetic theory of the presheath and the Bohm criterion’
journal, November 2012

Riemann, K-U
Plasma Sources Science and Technology, Vol. 21, Issue 6
DOI: 10.1088/0963-0252/21/6/068001

Where is the sheath edge ?
journal, April 2004

Franklin, R. N.
Journal of Physics D: Applied Physics, Vol. 37, Issue 9
DOI: 10.1088/0022-3727/37/9/007

Asymptotic matching of plasma and sheath in an active low pressure discharge
journal, May 1970

Franklin, R. N.; Ockendon, J. R.
Journal of Plasma Physics, Vol. 4, Issue 2
DOI: 10.1017/S0022377800005067

Extensions and applications of the Bohm criterion
journal, March 2015

Baalrud, Scott D.; Scheiner, Brett; Yee, Benjamin
Plasma Physics and Controlled Fusion, Vol. 57, Issue 4
DOI: 10.1088/0741-3335/57/4/044003

The Bohm criterion and sheath formation
journal, April 1991

Riemann, K. -U
Journal of Physics D: Applied Physics, Vol. 24, Issue 4
DOI: 10.1088/0022-3727/24/4/001

Ambipolar Transport via Trapped-Electron Whistler Instability Along Open Magnetic Field Lines
journal, September 2012

Guo, Zehua; Tang, Xian-Zhu
Physical Review Letters, Vol. 109, Issue 13
DOI: 10.1103/PhysRevLett.109.135005

Parallel transport of long mean-free-path plasmas along open magnetic field lines: Plasma profile variation
journal, August 2012

Guo, Zehua; Tang, Xian-Zhu
Physics of Plasmas, Vol. 19, Issue 8
DOI: 10.1063/1.4747167

Parallel heat flux and flow acceleration in open field line plasmas with magnetic trapping
journal, October 2014

Guo, Zehua; Tang, Xian-Zhu; McDevitt, Chris
Physics of Plasmas, Vol. 21, Issue 10
DOI: 10.1063/1.4900407

A General Theory of the Plasma of an Arc
journal, September 1929

Tonks, Lewi; Langmuir, Irving
Physical Review, Vol. 34, Issue 6
DOI: 10.1103/PhysRev.34.876

The Plasma Boundary of Magnetic Fusion Devices
book, January 2000

Stangeby, Peter C.
Plasma Physics and Controlled Fusion, Vol. 43, Issue 2
DOI: 10.1887/0750305592

The Low Pressure Plane Symmetric Discharge
journal, August 1959

Harrison, E. R.; Thompson, W. B.
Proceedings of the Physical Society, Vol. 74, Issue 2
DOI: 10.1088/0370-1328/74/2/301

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

The Interaction of Electron and Positive Ion Space Charges in Cathode Sheaths
journal, June 1929

Langmuir, Irving
Physical Review, Vol. 33, Issue 6
DOI: 10.1103/PhysRev.33.954

Kinetic model for the collisionless sheath of a collisional plasma
journal, August 2016

Tang, Xian-Zhu; Guo, Zehua
Physics of Plasmas, Vol. 23, Issue 8
DOI: 10.1063/1.4960321

Kinetic magnetic dynamo in a sheath-limited high-temperature and low-density plasma
journal, May 2011

Tang, X. Z.
Plasma Physics and Controlled Fusion, Vol. 53, Issue 8
DOI: 10.1088/0741-3335/53/8/082002

Spacecraft charging
journal, January 1979

Wrenn, Gordon L.
Nature, Vol. 277, Issue 5691
DOI: 10.1038/277011a0

The Plasma Boundary of Magnetic Fusion Devices
book, January 2000

Stangeby, P.
Series in Plasma Physics
DOI: 10.1201/9781420033328

The Plasma Boundary of Magnetic Fusion Devices
journal, January 2001

Ghendrih, Philippe
Plasma Physics and Controlled Fusion, Vol. 43, Issue 2
DOI: 10.1088/0741-3335/43/2/702

Kinetic Theory of the Presheath and the Bohm Criterion
text, January 2013

Baalrud, S. D.; Hegna, C. C.
arXiv
DOI: 10.48550/arxiv.1301.5700

Extensions and Applications of the Bohm Criterion
text, January 2014

Baalrud, Scott D.; Scheiner, Brett; Yee, Benjamin
arXiv
DOI: 10.48550/arxiv.1412.4826

Works referencing / citing this record:

Sheath formation in collisional, low pressure, and magnetized plasma
journal, April 2019

Moulick, R.; Adhikari, S.; Goswami, K. S.
Physics of Plasmas, Vol. 26, Issue 4
DOI: 10.1063/1.5090537

Plasma Power Recycling at the Divertor Surface
journal, January 2017

Tang, Xian-Zhu; Guo, Zehua
Fusion Science and Technology, Vol. 71, Issue 1
DOI: 10.13182/fst16-119

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Title: Critical role of electron heat flux on Bohm criterion

Abstract

Citation Formats

Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas journal, January 1986

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Comment on ‘Kinetic theory of the presheath and the Bohm criterion’ journal, November 2012

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Extensions and applications of the Bohm criterion journal, March 2015

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Ambipolar Transport via Trapped-Electron Whistler Instability Along Open Magnetic Field Lines journal, September 2012

Parallel transport of long mean-free-path plasmas along open magnetic field lines: Plasma profile variation journal, August 2012

Parallel heat flux and flow acceleration in open field line plasmas with magnetic trapping journal, October 2014

A General Theory of the Plasma of an Arc journal, September 1929

The Plasma Boundary of Magnetic Fusion Devices book, January 2000

The Low Pressure Plane Symmetric Discharge journal, August 1959

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

The Interaction of Electron and Positive Ion Space Charges in Cathode Sheaths journal, June 1929

Kinetic model for the collisionless sheath of a collisional plasma journal, August 2016

Kinetic magnetic dynamo in a sheath-limited high-temperature and low-density plasma journal, May 2011

Spacecraft charging journal, January 1979

The Plasma Boundary of Magnetic Fusion Devices book, January 2000

The Plasma Boundary of Magnetic Fusion Devices journal, January 2001

Kinetic Theory of the Presheath and the Bohm Criterion text, January 2013

Extensions and Applications of the Bohm Criterion text, January 2014

Sheath formation in collisional, low pressure, and magnetized plasma journal, April 2019

Plasma Power Recycling at the Divertor Surface journal, January 2017

Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas
journal, January 1986

Strongly Emitting Surfaces Unable to Float below Plasma Potential
journal, February 2016

Charging and Heat Collection by a Positively Charged Dust Grain in a Plasma
journal, July 2014

Parallel Heat Flux from Low to High Parallel Temperature along a Magnetic Field Line
journal, April 2012

Principles of Plasma Discharges and Materials Processing
book, January 2005

Particle in cell calculation of plasma force on a small grain in a non-uniform collisional sheath
journal, October 2013

Heat Flux Dependence of Ambipolar Potential and Plasma Profile in a Long Mean-Free-Path Plasma Along Non-Uniform Open Magnetic Field Lines
journal, June 2012

Sheath energy transmission in a collisional plasma with collisionless sheath
journal, October 2015

Kinetic theory of the presheath and the Bohm criterion
journal, March 2011

Comment on ‘Kinetic theory of the presheath and the Bohm criterion’
journal, November 2012

Where is the sheath edge ?
journal, April 2004

Asymptotic matching of plasma and sheath in an active low pressure discharge
journal, May 1970

Extensions and applications of the Bohm criterion
journal, March 2015

The Bohm criterion and sheath formation
journal, April 1991

Ambipolar Transport via Trapped-Electron Whistler Instability Along Open Magnetic Field Lines
journal, September 2012

Parallel transport of long mean-free-path plasmas along open magnetic field lines: Plasma profile variation
journal, August 2012

Parallel heat flux and flow acceleration in open field line plasmas with magnetic trapping
journal, October 2014

A General Theory of the Plasma of an Arc
journal, September 1929

The Plasma Boundary of Magnetic Fusion Devices
book, January 2000

The Low Pressure Plane Symmetric Discharge
journal, August 1959

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

The Interaction of Electron and Positive Ion Space Charges in Cathode Sheaths
journal, June 1929

Kinetic model for the collisionless sheath of a collisional plasma
journal, August 2016

Kinetic magnetic dynamo in a sheath-limited high-temperature and low-density plasma
journal, May 2011

Spacecraft charging
journal, January 1979

The Plasma Boundary of Magnetic Fusion Devices
book, January 2000

The Plasma Boundary of Magnetic Fusion Devices
journal, January 2001

Kinetic Theory of the Presheath and the Bohm Criterion
text, January 2013

Extensions and Applications of the Bohm Criterion
text, January 2014

Sheath formation in collisional, low pressure, and magnetized plasma
journal, April 2019

Plasma Power Recycling at the Divertor Surface
journal, January 2017