Linear theory of electron-plasma waves at arbitrary collisionality

Jorge, R.; Ricci, P.; Brunner, S.; Gamba, S.; Konovets, V.; Loureiro, N. F.; Perrone, L. M.; Teixeira, N.

doi:10.1017/s0022377819000266

Title: Linear theory of electron-plasma waves at arbitrary collisionality

Journal Article · Mon Apr 08 00:00:00 EDT 2019 · Journal of Plasma Physics

DOI:https://doi.org/10.1017/s0022377819000266· OSTI ID:1610181

^[1]; Ricci, P. ^[2]; Brunner, S. ^[2]; Gamba, S. ^[3]; Konovets, V. ^[2];

^[4]; Perrone, L. M. ^[2]; Teixeira, N. ^[5]

Ecole Polytechnique Federale Lausanne (EPFL) (Switzerland); University of Lisbon (Portugal)
Ecole Polytechnique Federale Lausanne (EPFL) (Switzerland)
Ecole Polytechnique Federale Lausanne (EPFL) (Switzerland); Politecnico di Milano (Italy)
Massachusetts Institute of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center
University of Lisbon (Portugal)

We report the dynamics of electron-plasma waves is described at arbitrary collisionality by considering the full Coulomb collision operator. The description is based on a Hermite–Laguerre decomposition of the velocity dependence of the electron distribution function. The damping rate, frequency and eigenmode spectrum of electron-plasma waves are found as functions of the collision frequency and wavelength. A comparison is made between the collisionless Landau damping limit, the Lenard–Bernstein and Dougherty collision operators and the electron–ion collision operator, finding large deviations in the damping rates and eigenmode spectra. A purely damped entropy mode, characteristic of a plasma where pitch-angle scattering effects are dominant with respect to collisionless effects, is shown to emerge numerically, and its dispersion relation is analytically derived. It is shown that such a mode is absent when simplified collision operators are used, and that like-particle collisions strongly influence the damping rate of the entropy mode.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES); Swiss National Science Foundation (SNSF); Euratom Research and Training Programme; Portuguese Fundação para a Ciência e Tecnologia

Grant/Contract Number:: FG02-91ER54109; 633053; PD/BD/105979/2014; PD/00505/2012

OSTI ID:: 1610181

Journal Information:: Journal of Plasma Physics, Vol. 85, Issue 2; ISSN 0022-3778

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 10 works

Citation information provided by
Web of Science

References (60)

Collisional losses of ring current ions Jordanova, V. K.; Kistler, L. M.; Kozyra, J. U. Journal of Geophysical Research: Space Physics, Vol. 101, Issue A1 https://doi.org/10.1029/95JA02000	journal	January 1996
Triplet Correlation for a Plasma O'Neil, Thomas; Rostoker, Norman Physics of Fluids, Vol. 8, Issue 6 https://doi.org/10.1063/1.1761361	journal	January 1965
Eigenvalue solution for the ion‐collisional effects on ion‐acoustic and entropy waves Tracy, M. D.; Williams, E. A.; Estabrook, K. G. Physics of Fluids B: Plasma Physics, Vol. 5, Issue 5 https://doi.org/10.1063/1.860883	journal	May 1993
Saturation of Gyrokinetic Turbulence through Damped Eigenmodes Hatch, D. R.; Terry, P. W.; Jenko, F. Physical Review Letters, Vol. 106, Issue 11 https://doi.org/10.1103/PhysRevLett.106.115003	journal	March 2011
Effect of electron collisions on ion‐acoustic waves and heat flow Epperlein, E. M. Physics of Plasmas, Vol. 1, Issue 1 https://doi.org/10.1063/1.870563	journal	January 1994
Damping of ion-acoustic waves in the presence of electron-ion collisions Epperlein, E. M.; Short, R. W.; Simon, A. Physical Review Letters, Vol. 69, Issue 12 https://doi.org/10.1103/PhysRevLett.69.1765	journal	September 1992
Model Fokker-Planck Equation for a Plasma and Its Solution Dougherty, J. P. Physics of Fluids, Vol. 7, Issue 11 https://doi.org/10.1063/1.2746779	journal	January 1964
Solving 0 = F(t, y(t), y′(t)) in Matlab Shampine, L. F. Journal of Numerical Mathematics, Vol. 10, Issue 4 https://doi.org/10.1515/JNMA.2002.291	journal	January 2002
New velocity-space discretization for continuum kinetic calculations and Fokker–Planck collisions Landreman, Matt; Ernst, Darin R. Journal of Computational Physics, Vol. 243 https://doi.org/10.1016/j.jcp.2013.02.041	journal	June 2013
Evidence and concepts for non-local transport Callen, J. D.; Kissick, M. W. Plasma Physics and Controlled Fusion, Vol. 39, Issue 12B https://doi.org/10.1088/0741-3335/39/12B/014	journal	December 1997
Connecting Collisionless Landau Fluid Closures to Collisional Plasma Physics Models: Connecting Collisionless Landau Fluid Closures to Collisional Plasma Physics Models Joseph, I.; Dimits, A. M. Contributions to Plasma Physics, Vol. 56, Issue 6-8 https://doi.org/10.1002/ctpp.201610043	journal	July 2016
Exact linearized Coulomb collision operator in the moment expansion Ji, Jeong-Young; Held, Eric D. Physics of Plasmas, Vol. 13, Issue 10 https://doi.org/10.1063/1.2356320	journal	October 2006
Krook collisional models of the kinetic susceptibility of plasmas Opher, M.; Morales, G. J.; Leboeuf, J. N. Physical Review E, Vol. 66, Issue 1 https://doi.org/10.1103/PhysRevE.66.016407	journal	July 2002
Theory of Plasma Oscillations. A. Origin of Medium-Like Behavior Bohm, D.; Gross, E. P. Physical Review, Vol. 75, Issue 12 https://doi.org/10.1103/PhysRev.75.1851	journal	June 1949
Dispersion of Electron Plasma Waves Malmberg, J. H.; Wharton, C. B. Physical Review Letters, Vol. 17, Issue 4 https://doi.org/10.1103/PhysRevLett.17.175	journal	July 1966
A drift-kinetic analytical model for scrape-off layer plasma dynamics at arbitrary collisionality Jorge, R.; Ricci, P.; Loureiro, N. F. Journal of Plasma Physics, Vol. 83, Issue 6 https://doi.org/10.1017/S002237781700085X	journal	November 2017
On Landau Damping Dawson, John Physics of Fluids, Vol. 4, Issue 7 https://doi.org/10.1063/1.1706419	journal	January 1961
Nonlinear Frequency Shift of an Electron Plasma Wave Morales, G. J.; O'Neil, T. M. Physical Review Letters, Vol. 28, Issue 7 https://doi.org/10.1103/PhysRevLett.28.417	journal	February 1972
Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind Qi, Feng Filomat, Vol. 28, Issue 2 https://doi.org/10.2298/FIL1402319O	journal	January 2014
Viriato : A Fourier–Hermite spectral code for strongly magnetized fluid–kinetic plasma dynamics Loureiro, N. F.; Dorland, W.; Fazendeiro, L. Computer Physics Communications, Vol. 206 https://doi.org/10.1016/j.cpc.2016.05.004	journal	September 2016
New Closures for More Precise Modeling of Landau Damping in the Fluid Framework Hunana, P.; Zank, G. P.; Laurenza, M. Physical Review Letters, Vol. 121, Issue 13 https://doi.org/10.1103/PhysRevLett.121.135101	journal	September 2018
Full- f version of GENE for turbulence in open-field-line systems Pan, Q.; Told, D.; Shi, E. L. Physics of Plasmas, Vol. 25, Issue 6 https://doi.org/10.1063/1.5008895	journal	June 2018
A 5D gyrokinetic full- $f$ global semi-Lagrangian code for flux-driven ion turbulence simulations Grandgirard, V.; Abiteboul, J.; Bigot, J. Computer Physics Communications, Vol. 207 https://doi.org/10.1016/j.cpc.2016.05.007	journal	October 2016
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
Developments in the gyrofluid approach to Tokamak turbulence simulations Hammett, G. W.; Beer, M. A.; Dorland, W. Plasma Physics and Controlled Fusion, Vol. 35, Issue 8 https://doi.org/10.1088/0741-3335/35/8/006	journal	August 1993
Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection, and electron heating in low-beta plasmas Zocco, Alessandro; Schekochihin, Alexander A. Physics of Plasmas, Vol. 18, Issue 10 https://doi.org/10.1063/1.3628639	journal	October 2011
Ion-collisional effects on ion-acoustic waves: an eigenvalue technique via moment expansion Zheng, Jian; Yu, C. X. Plasma Physics and Controlled Fusion, Vol. 42, Issue 4 https://doi.org/10.1088/0741-3335/42/4/305	journal	March 2000
Fluid moment models for Landau damping with application to the ion-temperature-gradient instability Hammett, Gregory W.; Perkins, Francis W. Physical Review Letters, Vol. 64, Issue 25 https://doi.org/10.1103/PhysRevLett.64.3019	journal	June 1990
Principles of Plasma Discharges and Materials Processing Lieberman, Michael A.; Lichtenberg, Allan J. https://doi.org/10.1002/0471724254	book	January 2005
Asymptotic Development of the Stirling Numbers of the First Kind Moser, L.; Wyman, M. Journal of the London Mathematical Society, Vol. s1-33, Issue 2 https://doi.org/10.1112/jlms/s1-33.2.133	journal	April 1958
Efficient Computation of the Complex Error Function Gautschi, Walter SIAM Journal on Numerical Analysis, Vol. 7, Issue 1 https://doi.org/10.1137/0707012	journal	March 1970
Longitudinal plasma oscillations Jackson, J. D. Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research, Vol. 1, Issue 4 https://doi.org/10.1088/0368-3281/1/4/301	journal	January 1960
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T. Journal of Plasma Physics, Vol. 83, Issue 3 https://doi.org/10.1017/S002237781700037X	journal	May 2017
Kinetic microtearing modes and reconnecting modes in strongly magnetised slab plasmas Zocco, A.; Loureiro, N. F.; Dickinson, D. Plasma Physics and Controlled Fusion, Vol. 57, Issue 6 https://doi.org/10.1088/0741-3335/57/6/065008	journal	April 2015
Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence Schekochihin, A. A.; Parker, J. T.; Highcock, E. G. Journal of Plasma Physics, Vol. 82, Issue 2 https://doi.org/10.1017/S0022377816000374	journal	April 2016
Tokamak edge turbulence: background theory and computation Scott, Bruce D. Plasma Physics and Controlled Fusion, Vol. 49, Issue 7 https://doi.org/10.1088/0741-3335/49/7/S02	journal	June 2007
Validation studies of gyrokinetic ITG and TEM turbulence simulations in a JT-60U tokamak using multiple flux matching Nakata, Motoki; Honda, Mitsuru; Yoshida, Maiko Nuclear Fusion, Vol. 56, Issue 8 https://doi.org/10.1088/0029-5515/56/8/086010	journal	July 2016
Theory of the Drift-Wave Instability at Arbitrary Collisionality Jorge, R.; Ricci, P.; Loureiro, N. F. Physical Review Letters, Vol. 121, Issue 16 https://doi.org/10.1103/PhysRevLett.121.165001	journal	October 2018
Fluid models of phase mixing, Landau damping, and nonlinear gyrokinetic dynamics Hammett, G. W.; Dorland, W.; Perkins, F. W. Physics of Fluids B: Plasma Physics, Vol. 4, Issue 7 https://doi.org/10.1063/1.860014	journal	March 1992
Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra Hatch, D. R.; Jenko, F.; Navarro, A. Bañón New Journal of Physics, Vol. 18, Issue 7 https://doi.org/10.1088/1367-2630/18/7/075018	journal	July 2016
Vlasov simulations of electron-ion collision effects on damping of electron plasma waves Banks, J. W.; Brunner, S.; Berger, R. L. Physics of Plasmas, Vol. 23, Issue 3 https://doi.org/10.1063/1.4943194	journal	March 2016
The physics basis for ignition using indirect-drive targets on the National Ignition Facility Lindl, John D.; Amendt, Peter; Berger, Richard L. Physics of Plasmas, Vol. 11, Issue 2 https://doi.org/10.1063/1.1578638	journal	February 2004
Role of stable eigenmodes in saturated local plasma turbulence Terry, P. W.; Baver, D. A.; Gupta, Sangeeta Physics of Plasmas, Vol. 13, Issue 2 https://doi.org/10.1063/1.2168453	journal	February 2006
Kinetic calculation of neoclassical transport including self-consistent electron and impurity dynamics Belli, E. A.; Candy, J. Plasma Physics and Controlled Fusion, Vol. 50, Issue 9 https://doi.org/10.1088/0741-3335/50/9/095010	journal	July 2008
Trapped-Particle Instability Leading to Bursting in Stimulated Raman Scattering Simulations Brunner, S.; Valeo, E. J. Physical Review Letters, Vol. 93, Issue 14 https://doi.org/10.1103/PhysRevLett.93.145003	journal	September 2004
Plasma Oscillations with Diffusion in Velocity Space Lenard, A.; Bernstein, Ira B. Physical Review, Vol. 112, Issue 5 https://doi.org/10.1103/PhysRev.112.1456	journal	December 1958
Complete Spectrum of Kinetic Eigenmodes for Plasma Oscillations in a Weakly Collisional Plasma Ng, C. S.; Bhattacharjee, A.; Skiff, F. Physical Review Letters, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevLett.92.065002	journal	February 2004
Laguerre–Hermite pseudo-spectral velocity formulation of gyrokinetics Mandell, N. R.; Dorland, W.; Landreman, M. Journal of Plasma Physics, Vol. 84, Issue 1 https://doi.org/10.1017/S0022377818000041	journal	January 2018
Kinetic Simulations of the Self-Focusing and Dissipation of Finite-Width Electron Plasma Waves Winjum, B. J.; Berger, R. L.; Chapman, T. Physical Review Letters, Vol. 111, Issue 10 https://doi.org/10.1103/PhysRevLett.111.105002	journal	September 2013
Kinetic Eigenmodes and Discrete Spectrum of Plasma Oscillations in a Weakly Collisional Plasma Ng, C. S.; Bhattacharjee, A.; Skiff, F. Physical Review Letters, Vol. 83, Issue 10 https://doi.org/10.1103/PhysRevLett.83.1974	journal	September 1999
Aspects of linear Landau damping in discretized systems Bratanov, Vasil; Jenko, Frank; Hatch, David Physics of Plasmas, Vol. 20, Issue 2 https://doi.org/10.1063/1.4792163	journal	February 2013
On Landau damping Mouhot, Clément; Villani, Cédric arXiv https://doi.org/10.48550/arxiv.0904.2760	text	January 2009
New velocity-space discretization for continuum kinetic calculations and Fokker-Planck collisions Landreman, Matt; Ernst, Darin R. arXiv https://doi.org/10.48550/arxiv.1210.5289	text	January 2012
Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind Qi, Feng arXiv https://doi.org/10.48550/arxiv.1301.6845	text	January 2013
Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence Schekochihin, A. A.; Parker, J. T.; Highcock, E. G. arXiv https://doi.org/10.48550/arxiv.1508.05988	text	January 2015
Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma Shi, E. L.; Hammett, G. W.; Stoltzfus-Dueck, T. arXiv https://doi.org/10.48550/arxiv.1702.03052	text	January 2017
Laguerre-Hermite Pseudo-Spectral Velocity Formulation of Gyrokinetics Mandell, N. R.; Dorland, W.; Landreman, M. arXiv https://doi.org/10.48550/arxiv.1708.04029	text	January 2017
Theory of the Drift-Wave Instability at Arbitrary Collisionality Jorge, R.; Ricci, P.; Loureiro, N. F. arXiv https://doi.org/10.48550/arxiv.1806.10538	text	January 2018
Electrostatic Response of a Two-Component Plasma with Coulomb Collisions Brantov, A. V.; Bychenkov, V. Yu.; Rozmus, W. Physical Review Letters, Vol. 108, Issue 20 https://doi.org/10.1103/physrevlett.108.205001	journal	May 2012
Stirling numbers of the second kind Moser, L.; Wyman, M. Duke Mathematical Journal, Vol. 25, Issue 1 https://doi.org/10.1215/s0012-7094-58-02504-3	journal	March 1958

Cited By (2)

Electron skin depth in low density plasmas Silveira, F. E. M.; Siqueira, B. P. Journal of Plasma Physics, Vol. 86, Issue 1 https://doi.org/10.1017/s0022377819000904	journal	January 2020
Shocks and phase space vortices driven by a density jump between two clouds of electrons and protons Moreno, Q.; Dieckmann, M. E.; Folini, D. Plasma Physics and Controlled Fusion, Vol. 62, Issue 2 https://doi.org/10.1088/1361-6587/ab5bfb	journal	December 2019

Similar Records

Linear Theory of Electron-Plasma Waves at Arbitrary Collisionality

Dataset · Tue Dec 04 00:00:00 EST 2018 · OSTI ID:1610181

Jorge, R.; Ricci, P.; Brunner, S.; +5 more

A drift-kinetic analytical model for scrape-off layer plasma dynamics at arbitrary collisionality

Journal Article · Mon Nov 20 00:00:00 EST 2017 · Journal of Plasma Physics · OSTI ID:1610181

Jorge, R.; Ricci, P.; Loureiro, N. F.

Theory of the Drift-Wave Instability at Arbitrary Collisionality

Dataset · Fri Jan 04 00:00:00 EST 2019 · OSTI ID:1610181

Jorge, R.; Ricci, P.; Loureiro, N. F.

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
plasma waves

Title: Linear theory of electron-plasma waves at arbitrary collisionality

Citation Formats

References (60)

Cited By (2)

Similar Records

Related Subjects