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Linear theory of electron-plasma waves at arbitrary collisionality

Published online by Cambridge University Press:  08 April 2019

R. Jorge Open the ORCID record for R. Jorge [Opens in a new window] ,
P. Ricci ,
S. Brunner ,
S. Gamba ,
V. Konovets ,
N. F. Loureiro Open the ORCID record for N. F. Loureiro [Opens in a new window] ,
L. M. Perrone  and
N. Teixeira
R. Jorge*
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
P. Ricci
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland
S. Brunner
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland
S. Gamba
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland Department of Energy, Politecnico di Milano, Via Ponzio 34/3, Milano, 20133, Italy
V. Konovets
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland
N. F. Loureiro
Affiliation:
Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
L. M. Perrone
Affiliation:
École Polytechnique Fédérale de Lausanne (EPFL), Swiss Plasma Center (SPC), CH-1015 Lausanne, Switzerland
N. Teixeira
Affiliation:
Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
*
†Present address: Institute for Research in Electronics and Applied Physics, University of Maryland, College Park MD 20742, USA. Email address for correspondence: [email protected]
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Abstract

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.

Keywords

plasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 2 , April 2019 , 905850211
Copyright
© The Author(s) (2019). Published by Cambridge University Press 

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References

Banks, J. W., Brunner, S., Berger, R. L., Arrighi, W. J. & Tran, T. M. 2017 Collisional damping rates for electron plasma waves reassessed. Phys. Rev. E 96 (4), 043208.Google Scholar
Banks, J. W., Brunner, S., Berger, R. L. & Tran, T. M. 2016 Vlasov simulations of electron–ion collision effects on damping of electron plasma waves. Phys. Plasmas 23 (3), 032108.Google Scholar
Belli, E. A. & Candy, J. 2008 Kinetic calculation of neoclassical transport including self-consistent electron and impurity dynamics. Plasma Phys. Control. Fusion 50 (9), 095010.Google Scholar
Bohm, D. & Gross, E. P. 1949 Theory of plasma oscillations. A. Origin of medium-like behavior. Phys. Rev. 75 (12), 1851.Google Scholar
Braginskii, S. I. 1965 Transport processes in a plasma. Rev. Plasma Phys. 1, 205.Google Scholar
Brantov, A. V., Bychenkov, V. Y. & Rozmus, W. 2012 Electrostatic response of a two-component plasma with coulomb collisions. Phys. Rev. Lett. 108 (20), 205001.Google Scholar
Bratanov, V., Jenko, F., Hatch, D. & Brunner, S. 2013 Aspects of linear Landau damping in discretized systems. Phys. Plasmas 20 (2), 022108.Google Scholar
Brunner, S. & Valeo, E. J. 2004 Trapped-particle instability leading to bursting in stimulated Raman scattering simulations. Phys. Rev. Lett. 93 (14), 145003.Google Scholar
Callen, J. D. & Kissick, M. W. 1997 Evidence and concepts for non-local transport. Plasma Phys. Control. Fusion 39 (39), 173.Google Scholar
Dawson, J. 1961 On Landau damping. Phys. Fluids 4 (7), 869.Google Scholar
Dougherty, J. P. 1964 Model Fokker–Planck equation for a plasma and its solution. Phys. Fluids 7 (11), 1788.Google Scholar
Epperlein, E. M. 1994 Effect of electron collisions on ion-acoustic waves and heat flow. Phys. Plasmas 1 (1), 109.Google Scholar
Epperlein, E. M., Short, R. W. & Simon, A. 1992 Damping of ion-acoustic waves in the presence of electron–ion collisions. Phys. Rev. Lett. 69 (12), 1765.Google Scholar
Gautschi, W. 1970 Efficient Computation of the Complex Error Function. SIAM J. Numer. Anal. 7 (1), 187.Google Scholar
Grandgirard, V., Abiteboul, J., Bigot, J., Cartier-Michaud, T., Crouseilles, N., Dif-Pradalier, G., Ehrlacher, C., Esteve, D., Garbet, X., Ghendrih, P. et al. 2016 A 5D gyrokinetic full-f global semi-Lagrangian code for flux-driven ion turbulence simulations. Comput. Phys. Commun. 207, 35.Google Scholar
Hammett, G. W., Beer, M. A., Dorland, W. D., Cowley, S. C. & Smith, S. A. 1993 Developments in the gyrofluid approach to tokamak turbulence simulations. Plasma Phys. Control. Fusion 35 (8), 973.Google Scholar
Hammett, G. W., Dorland, W. & Perkins, F. W. 1992 Fluid models of phase mixing, Landau damping, and nonlinear gyrokinetic dynamics. Phys. Fluids B 4 (7), 2052.Google Scholar
Hammett, G. W. & Perkins, F. W. 1990 Fluid moment models for Landau damping with application to the ion-temperature-gradient instability. Phys. Rev. Lett. 64 (25), 3019.Google Scholar
Hatch, D. R., Jenko, F., Navarro, A. B., Bratanov, V., Terry, P. W. & Pueschel, M. J. 2016 Linear signatures in nonlinear gyrokinetics: interpreting turbulence with pseudospectra. New J. Phys. 18 (7), 075018.Google Scholar
Hatch, D. R., Terry, P. W., Jenko, F., Merz, F. & Nevins, W. M. 2011 Saturation of gyrokinetic turbulence through damped eigenmodes. Phys. Rev. Lett. 106 (11), 115003.Google Scholar
Helander, P. & Sigmar, D. 2005 Collisional Transport in Magnetized Plasmas. Cambridge University Press.Google Scholar
Hunana, P., Zank, G. P., Laurenza, M., Tenerani, A., Webb, G. M., Goldstein, M. L., Velli, M. & Adhikari, L. 2018 New closures for more precise modeling of Landau damping in the fluid framework. Phys. Rev. Lett. 121 (13), 135101.Google Scholar
Jackson, J. D. 1960 Longitudinal plasma oscillations. J. Nuclear Energy C 1 (4), 171.Google Scholar
Ji, J.-Y. & Held, E. D. 2006 Exact linearized Coulomb collision operator in the moment expansion. Phys. Plasmas 13 (10), 102103.Google Scholar
Ji, J.-Y. & Held, E. D. 2010 Analytical solution of the kinetic equation for a uniform plasma in a magnetic field. Phys. Rev. E 82 (1), 016401.Google Scholar
Jordanova, V. K., Kistler, L. M., Kozyra, J. U., Khazanov, G. V. & Nagy, A. F. 1996 Collisional losses of ring current ions. J. Geophys. Res. 101 (A1), 111.Google Scholar
Jorge, R., Ricci, P. & Loureiro, N. F. 2017 A drift-kinetic analytical model for scrape-off layer plasma dynamics at arbitrary collisionality. J. Plasma Phys. 83 (6), 905830606.Google Scholar
Jorge, R., Ricci, P. & Loureiro, N. F. 2018 Theory of the drift-wave instability at arbitrary collisionality. Phys. Rev. Lett. 121 (16), 165001.Google Scholar
Joseph, I. & Dimits, A. M. 2016 Connecting collisionless Landau fluid closures to collisional plasma physics models. Contributions to Plasma Phys. 56 (6), 504.Google Scholar
Landau, L. D. 1946 On the vibrations of the electronic plasma. J. Phys. USSR 10 (1), 25.Google Scholar
Landreman, M. & Ernst, D. R. 2013 New velocity-space discretization for continuum kinetic calculations and Fokker–Planck collisions. J. Comput. Phys. 243 (15), 130.Google Scholar
Lenard, A. & Bernstein, I. B. 1958 Plasma oscillations with diffusion in velocity space. Phys. Rev. 112 (5), 1456.Google Scholar
Lieberman, M. A. & Lichtenberg, A. J. 2005 Principles of Plasma Discharges and Materials Processing. Wiley.Google Scholar
Lindl, J. D., Amendt, P., Berger, R. L., Glendinning, S. G., Glenzer, S. H., Haan, S. W., Kauffman, R. L., Landen, O. L. & Suter, L. J. 2004 The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. Plasmas 11 (2), 339.Google Scholar
Loureiro, N. F., Dorland, W., Fazendeiro, L., Kanekar, A., Mallet, A., Vilelas, M. S. & Zocco, A. 2016 Viriato: a Fourier–Hermite spectral code for strongly magnetized fluid-kinetic plasma dynamics. Comput. Phys. Commun. 206, 45.Google Scholar
Malmberg, J. H. & Wharton, C. B. 1966 Dispersion of electron plasma waves. Phys. Rev. Lett. 17 (4), 175.Google Scholar
Mandell, N. R., Dorland, W. & Landreman, M. 2018 Laguerre–Hermite pseudo-spectral velocity formulation of gyrokinetics. J. Plasma Phys. 84 (01), 905840108.Google Scholar
Morales, G. J. & O’Neil, T. M. 1972 Nonlinear frequency shift of an electron plasma wave. Phys. Rev. Lett. 28 (7), 417.Google Scholar
Moser, L. & Wyman, M. 1958 Asymptotic development of the stirling numbers of the first kind. J. Lond. Math. Soc. s1 (2), 133.Google Scholar
Mouhot, C. & Villani, C. 2011 On Landau damping. Acta Math. 207 (1), 29.Google Scholar
Nakata, M., Honda, M., Yoshida, M., Urano, H., Nunami, M., Maeyama, S., Watanabe, T. & Sugama, H. 2016 Validation studies of gyrokinetic ITG and TEM turbulence simulations in a JT-60U tokamak using multiple flux matching. Nucl. Fusion 56 (8), 086010.Google Scholar
Ng, C. S., Bhattacharjee, A. & Skiff, F. 1999 Kinetic eigenmodes and discrete spectrum of plasma oscillations in a weakly collisional plasma. Phys. Rev. Lett. 83 (10), 1974.Google Scholar
Ng, C. S., Bhattacharjee, A. & Skiff, F. 2004 Complete spectrum of kinetic eigenmodes for plasma oscillations in a weakly collisional plasma. Phys. Rev. Lett. 92 (6), 065002.Google Scholar
O’Neil, T. M. & Rostoker, N. 1965 Triplet correlation for a plasma. Phys. Fluids 8 (6), 1109.Google Scholar
Opher, M., Morales, G. J. & Leboeuf, J. N. 2002 Krook collisional models of the kinetic susceptibility of plasmas. Phys. Rev. E 66 (1), 016407.Google Scholar
Pan, Q., Told, D., Shi, E, Hammett, G. W. & Jenko, F. 2018 Full-f version of GENE for turbulence in open-field-line systems. Phys. Plasmas 25 (6), 062303.Google Scholar
Pueschel, M. J., Faber, B. J., Citrin, J., Hegna, C. C., Terry, P. W. & Hatch, D. R. 2016 Stellarator turbulence: subdominant eigenmodes and quasilinear modeling. Phys. Rev. Lett. 116 (8), 085001.Google Scholar
Qi, F. 2014 Explicit formulas for computing Bernoulli numbers of the second kind and stirling numbers of the first kind. Filomat 28 (2), 319.Google Scholar
Schekochihin, A. A., Parker, J. T., Highcock, E. G., Dellar, P. J., Dorland, W. & Hammett, G. W. 2016 Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence. J. Plasma Phys. 82 (2), 905820212.Google Scholar
Scott, B. D. 2007 Tokamak edge turbulence: background theory and computation. Plasma Phys. Control. Fusion 49 (7), S25.Google Scholar
Shampine, L. F. 2002 Solving $0=F(t,y(t),y^{\prime }(t))$ in matlab. J. Numer. Math. 10 (4), 291.Google Scholar
Shi, E. L., Hammett, G. W., Stoltzfus-Dueck, T. & Hakim, A. 2017 Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma. J. Plasma Phys. 83 (03), 905830304.Google Scholar
Terry, P. W., Baver, D. A. & Gupta, S. 2006 Role of stable eigenmodes in saturated local plasma turbulence. Phys. Plasmas 13 (2), 022307.Google Scholar
Tracy, M. D., Williams, E. A., Estabrook, K. G., De Groot, J. S. & Cameron, S. M. 1993 Eigenvalue solution for the ion-collisional effects on ion-acoustic and entropy waves. Phys. Fluids B 5 (5), 1430.Google Scholar
Wax, N. 1954 Selected Papers on Noise and Stochastic Processes. Dover Publications.Google Scholar
Winjum, B. J., Berger, R. L., Chapman, T., Banks, J. W. & Brunner, S. 2013 Kinetic simulations of the self-focusing and dissipation of finite-width electron plasma waves. Phys. Rev. Lett. 111 (10), 105002.Google Scholar
Zakharov, V. E. 1972 Collapse of Langmuir waves. Sov. Phys. JETP 35 (5), 908.Google Scholar
Zheng, J. & Yu, C. X. 2000 Ion-collisional effects on ion-acoustic waves: an eigenvalue technique via moment expansion. Plasma Phys. Control. Fusion 42 (4), 435.Google Scholar
Zocco, A., Loureiro, N. F., Dickinson, D., Numata, R. & Roach, C. M. 2015 Kinetic microtearing modes and reconnecting modes in strongly magnetised slab plasmas. Plasma Phys. Control. Fusion 57 (6), 065008.Google Scholar
Zocco, A. & Schekochihin, A. A. 2011 Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection, and electron heating in low-beta plasmas. Phys. Plasmas 18 (10), 102309.Google Scholar