Theory of the Drift-Wave Instability at Arbitrary Collisionality

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

doi:10.1103/physrevlett.121.165001

Theory of the Drift-Wave Instability at Arbitrary Collisionality

Journal Article · Fri Oct 19 00:00:00 EDT 2018 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.121.165001· OSTI ID:1610186

Jorge, Rogerio ^[1]; Ricci, P. ^[2]; Loureiro, N. F. ^[3]

École Polytechnique Fédérale de Lausanne (EPFL) (Switzerland); Univ. de Lisboa (Portugal); DOE/OSTI
École Polytechnique Fédérale de Lausanne (EPFL) (Switzerland)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

A numerically efficient framework that takes into account the effect of the Coulomb collision operator at arbitrary collisionalities is introduced. Such a model is based on the expansion of the distribution function on a Hermite-Laguerre polynomial basis to study the effects of collisions on magnetized plasma instabilities at arbitrary mean-free path. Focusing on the drift-wave instability, we show that our framework allows retrieving established collisional and collisionless limits. At the intermediate collisionalities relevant for present and future magnetic nuclear fusion devices, deviations with respect to collision operators used in state-of-the-art turbulence simulation codes show the need for retaining the full Coulomb operator in order to obtain both the correct instability growth rate and eigenmode spectrum, which, for example, may significantly impact quantitative predictions of transport. In conclusion, the exponential convergence of the spectral representation that we propose makes the representation of the velocity space dependence, including the full collision operator, more efficient than standard finite difference methods.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-91ER54109

OSTI ID:: 1610186

Alternate ID(s):: OSTI ID: 1478595

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 16 Vol. 121; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (62)

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
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
Physics basis and design of the ITER plasma-facing components Pitts, R. A.; Carpentier, S.; Escourbiac, F. Journal of Nuclear Materials, Vol. 415, Issue 1 https://doi.org/10.1016/j.jnucmat.2011.01.114	journal	August 2011
Fluctuation-dissipation relations for a plasma-kinetic Langevin equation Kanekar, A.; Schekochihin, A. A.; Dorland, W. Journal of Plasma Physics, Vol. 81, Issue 1 https://doi.org/10.1017/S0022377814000622	journal	September 2014
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
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
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
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
Introduction to Plasma Physics Gurnett, D. A.; Bhattacharjee, A. Cambridge University Press https://doi.org/10.1017/cbo9780511809125	book	January 2012
Theoretical interpretation of drift wave type fluctuations at the plasmapause Shukla, P. K.; Bujarbarua, S. Journal of Geophysical Research, Vol. 85, Issue A4 https://doi.org/10.1029/JA085iA04p01773	journal	January 1980
On the transition to drift turbulence in a magnetized plasma column Burin, M. J.; Tynan, G. R.; Antar, G. Y. Physics of Plasmas, Vol. 12, Issue 5 https://doi.org/10.1063/1.1889443	journal	May 2005
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
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
Eigenfunctions and eigenvalues of the Dougherty collision operator Anderson, M. W.; O’Neil, T. M. Physics of Plasmas, Vol. 14, Issue 5 https://doi.org/10.1063/1.2727463	journal	May 2007
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
Transition from drift to interchange instabilities in an open magnetic field line configuration Poli, F. M.; Ricci, P.; Fasoli, A. Physics of Plasmas, Vol. 15, Issue 3 https://doi.org/10.1063/1.2899303	journal	March 2008
Electrostatic drift waves in nonuniform quantum magnetized plasmas Wu, Zhengwei; Ren, Haijun; Cao, Jintao Physics of Plasmas, Vol. 15, Issue 8 https://doi.org/10.1063/1.2967479	journal	August 2008
Introduction to Plasma Physics Chen, F. F.; Trivelpiece, A. W. Physics Today, Vol. 29, Issue 10 https://doi.org/10.1063/1.3024417	journal	October 1976
Drift wave instability in a nonuniform quantum dusty magnetoplasma Salimullah, M.; Jamil, M.; Zeba, I. Physics of Plasmas, Vol. 16, Issue 3 https://doi.org/10.1063/1.3086861	journal	March 2009
Role of subdominant stable modes in plasma microturbulence Hatch, D. R.; Terry, P. W.; Jenko, F. Physics of Plasmas, Vol. 18, Issue 5 https://doi.org/10.1063/1.3563536	journal	May 2011
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
Drift wave dispersion relation for arbitrarily collisional plasma Angus, Justin R.; Krasheninnikov, Sergei I. Physics of Plasmas, Vol. 19, Issue 5 https://doi.org/10.1063/1.4714614	journal	May 2012
Plasma turbulence in the scrape-off layer of tokamak devices Ricci, Paolo; Rogers, B. N. Physics of Plasmas, Vol. 20, Issue 1 https://doi.org/10.1063/1.4789551	journal	January 2013
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
Turbulent regimes in the tokamak scrape-off layer Mosetto, Annamaria; Halpern, Federico D.; Jolliet, Sébastien Physics of Plasmas, Vol. 20, Issue 9 https://doi.org/10.1063/1.4821597	journal	September 2013
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
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
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
Nonlinear reduced Braginskii equations with ion thermal dynamics in toroidal plasma Zeiler, A.; Drake, J. F.; Rogers, B. Physics of Plasmas, Vol. 4, Issue 6 https://doi.org/10.1063/1.872368	journal	June 1997
Excitation of zonal flow by drift waves in toroidal plasmas Chen, Liu; Lin, Zhihong; White, Roscoe Physics of Plasmas, Vol. 7, Issue 8 https://doi.org/10.1063/1.874222	journal	August 2000
Theory-based scaling of the SOL width in circular limited tokamak plasmas Halpern, F. D.; Ricci, P.; Labit, B. Nuclear Fusion, Vol. 53, Issue 12 https://doi.org/10.1088/0029-5515/53/12/122001	journal	November 2013
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
Introduction to Plasma Physics Wesson, J. A. Plasma Physics and Controlled Fusion, Vol. 38, Issue 1 https://doi.org/10.1088/0741-3335/38/1/004	journal	January 1996
The ITER design Aymar, R.; Barabaschi, P.; Shimomura, Y. Plasma Physics and Controlled Fusion, Vol. 44, Issue 5 https://doi.org/10.1088/0741-3335/44/5/304	journal	April 2002
Simulation of plasma turbulence in scrape-off layer conditions: the GBS code, simulation results and code validation Ricci, P.; Halpern, F. D.; Jolliet, S. Plasma Physics and Controlled Fusion, Vol. 54, Issue 12 https://doi.org/10.1088/0741-3335/54/12/124047	journal	November 2012
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
Core turbulent transport in tokamak plasmas: bridging theory and experiment with QuaLiKiz Bourdelle, C.; Citrin, J.; Baiocchi, B. Plasma Physics and Controlled Fusion, Vol. 58, Issue 1 https://doi.org/10.1088/0741-3335/58/1/014036	journal	December 2015
The nonlinear drift wave instability and its role in tokamak edge turbulence Scott, Bruce D. New Journal of Physics, Vol. 4 https://doi.org/10.1088/1367-2630/4/1/352	journal	July 2002
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
Nonlinear drift waves in electron-positron-ion plasmas Saleem, H.; Haque, Q.; Vranjes̆, J. Physical Review E, Vol. 67, Issue 5 https://doi.org/10.1103/PhysRevE.67.057402	journal	May 2003
Collisional damping rates for electron plasma waves reassessed Banks, J. W.; Brunner, S.; Berger, R. L. Physical Review E, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevE.96.043208	journal	October 2017
Turbulence Phase Space in Simple Magnetized Toroidal Plasmas Ricci, Paolo; Rogers, B. N. Physical Review Letters, Vol. 104, Issue 14 https://doi.org/10.1103/PhysRevLett.104.145001	journal	April 2010
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
Gyrokinetic Fokker-Planck Collision Operator Li, B.; Ernst, D. R. Physical Review Letters, Vol. 106, Issue 19 https://doi.org/10.1103/PhysRevLett.106.195002	journal	May 2011
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
Modification of Turbulent Transport with Continuous Variation of Flow Shear in the Large Plasma Device Schaffner, D. A.; Carter, T. A.; Rossi, G. D. Physical Review Letters, Vol. 109, Issue 13 https://doi.org/10.1103/PhysRevLett.109.135002	journal	September 2012
Transition between Saturation Regimes of Gyrokinetic Turbulence Hatch, D. R.; Jenko, F.; Bañón Navarro, A. Physical Review Letters, Vol. 111, Issue 17 https://doi.org/10.1103/PhysRevLett.111.175001	journal	October 2013
Universal Instability for Wavelengths below the Ion Larmor Scale Landreman, Matt; Antonsen, Thomas M.; Dorland, William Physical Review Letters, Vol. 114, Issue 9 https://doi.org/10.1103/PhysRevLett.114.095003	journal	March 2015
Stellarator Turbulence: Subdominant Eigenmodes and Quasilinear Modeling Pueschel, M. J.; Faber, B. J.; Citrin, J. Physical Review Letters, Vol. 116, Issue 8 https://doi.org/10.1103/PhysRevLett.116.085001	journal	February 2016
Plasma Edge Turbulence Hasegawa, Akira; Wakatani, Masahiro Physical Review Letters, Vol. 50, Issue 9 https://doi.org/10.1103/PhysRevLett.50.682	journal	February 1983
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
Drift waves and transport Horton, W. Reviews of Modern Physics, Vol. 71, Issue 3 https://doi.org/10.1103/RevModPhys.71.735	journal	April 1999
The Theory of Toroidally Confined Plasmas White, Roscoe B. World Scientific https://doi.org/10.1142/p237	book	July 2001
The Theory of Toroidally Confined Plasmas White, Roscoe B. https://doi.org/10.1142/p440	book	April 2006
The Theory of Toroidally Confined Plasmas White, Roscoe B. World Scientific https://doi.org/10.1142/p916	book	January 2014
Introduction to Plasma Physics Goldston, R. J. https://doi.org/10.1201/9780367806958	book	July 2020
Introduction to Plasma Physics Goldston, Robert J.; Rutherford, Paul H. https://doi.org/10.1887/075030183X	book	January 1995
Universal instability for wavelengths below the ion Larmor scale Landreman, Matt; Antonsen, Thomas M.; Dorland, William arXiv https://doi.org/10.48550/arxiv.1411.1807	text	January 2014
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 R. Jorge, P. Ricci Harvard Dataverse https://doi.org/10.7910/dvn/cnyzc6	dataset	January 2019

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