Analysis of the Hermite spectrum in plasma turbulence

White, R. L.; Hazeltine, R. D.

doi:10.1063/1.5000518

Title: Analysis of the Hermite spectrum in plasma turbulence

Journal Article · Thu Oct 19 00:00:00 EDT 2017 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5000518· OSTI ID:1523377

^[1];

^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Univ. of Texas at Austin, Austin, TX (United States)

The properties of the Hermite spectrum associated with the linear drift-kinetic equation—as used in studies of gyrokinetic turbulence—are examined. A rigorous uniform asymptotic expression is derived for the steady-state spectrum with a Lenard-Bernstein collision operator. It is found that the spectrum is partitioned into three regions whose boundaries are determined by the ratio of the collision frequency ν to the parallel transit frequency kvth. In the regime of small Hermite index, n, with n ≲ (ν/kv_th)^2/3, collisions play no role, and the free energy decays like n^–1/2 due to phase mixing. In the previously unexplored large-n regime, n ≥ (ν/kv_th)², collisions are dominant, and the decay of the free energy spectrum is extremely steep, falling off like (n/e)^–n. Most of the free energy is dissipated in the intermediate regime, (ν/kv_th)^2/3 ≲ n << (ν/kv_th)², where the asymptotic spectrum is in close agreement with the exponentially decaying “continuization” estimate. Furthermore, our analysis shows that collisions act as a singular perturbation, giving rise to the intermediate regime, where collisions are significantly altering the spectrum well inside the general large-n asymptotic region.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-04ER54742

OSTI ID:: 1523377

Alternate ID(s):: OSTI ID: 1400334

Journal Information:: Physics of Plasmas, Vol. 24, Issue 10; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 4 works

Citation information provided by
Web of Science

References (18)

Renormalized Dissipation in Plasmas with Finite Collisionality Parker, Scott E.; Carati, Daniele Physical Review Letters, Vol. 75, Issue 3 https://doi.org/10.1103/PhysRevLett.75.441	journal	July 1995
Landau collision operators and general moment equations for an electron-ion plasma Ji, Jeong-Young; Held, Eric D. Physics of Plasmas, Vol. 15, Issue 10 https://doi.org/10.1063/1.2977983	journal	October 2008
Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit Parker, Joseph T.; Dellar, Paul J. Journal of Plasma Physics, Vol. 81, Issue 2 https://doi.org/10.1017/S0022377814001287	journal	February 2015
Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence Hatch, D. R.; Jenko, F.; Bratanov, V. Journal of Plasma Physics, Vol. 80, Issue 4 https://doi.org/10.1017/S0022377814000154	journal	May 2014
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
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
Discrete kinetic eigenmode spectra of electron plasma oscillations in weakly collisional plasma: A numerical study Black, Carrie; Germaschewski, Kai; Bhattacharjee, Amitava Physics of Plasmas, Vol. 20, Issue 1 https://doi.org/10.1063/1.4789882	journal	January 2013
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
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
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
Exact collisional moments for plasma fluid theories Pfefferlé, D.; Hirvijoki, E.; Lingam, M. Physics of Plasmas, Vol. 24, Issue 4 https://doi.org/10.1063/1.4979992	journal	April 2017
On the kinetic theory of rarefied gases Grad, Harold Communications on Pure and Applied Mathematics, Vol. 2, Issue 4 https://doi.org/10.1002/cpa.3160020403	journal	December 1949
LIII. Dynamical problems in illustration of the theory of gases Rayleigh, Lord The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 32, Issue 198 https://doi.org/10.1080/14786449108620207	journal	November 1891
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
Kinetic simulation of steady states of ion temperature gradient driven turbulence with weak collisionality Watanabe, T. -H.; Sugama, H. Physics of Plasmas, Vol. 11, Issue 4 https://doi.org/10.1063/1.1669393	journal	April 2004
Fourier-Hermite Solutions of the Vlasov Equations in the Linearized Limit Grant, Frederick C. Physics of Fluids, Vol. 10, Issue 4 https://doi.org/10.1063/1.1762177	journal	January 1967
Irreversible energy flow in forced Vlasov dynamics Plunk, Gabriel G.; Parker, Joseph T. The European Physical Journal D, Vol. 68, Issue 10 https://doi.org/10.1140/epjd/e2014-50157-8	journal	October 2014

Cited By (5)

Symmetries of a reduced fluid-gyrokinetic system White, R. L.; Hazeltine, R. D.; Loureiro, N. F. Journal of Plasma Physics, Vol. 84, Issue 2 https://doi.org/10.1017/s0022377818000247	journal	March 2018
Laboratory space physics: Investigating the physics of space plasmas in the laboratory Howes, Gregory G. Physics of Plasmas, Vol. 25, Issue 5 https://doi.org/10.1063/1.5025421	journal	May 2018
An integral transform technique for kinetic systems with collisions Heninger, J. M.; Morrison, P. J. Physics of Plasmas, Vol. 25, Issue 8 https://doi.org/10.1063/1.5046194	journal	August 2018
Laboratory Space Physics: Investigating the Physics of Space Plasmas in the Laboratory Howes, Gregory G. arXiv https://doi.org/10.48550/arxiv.1802.04154	text	January 2018
An integral transform technique for kinetic systems with collisions Heninger, Jeffrey M.; Morrison, Philip J. arXiv https://doi.org/10.48550/arxiv.1806.10203	text	January 2018

Figures / Tables (1)

FIG. 1(p. 5)

Similar Records

Stability and Conservation properties of Hermite-based approximations of the Vlasov-Poisson System

Technical Report · Fri Jun 11 00:00:00 EDT 2021 · OSTI ID:1523377

Funaro, Daniele; Manzini, Gianmarco

Linear Theory of Electron-Plasma Waves at Arbitrary Collisionality

Dataset · Tue Dec 04 00:00:00 EST 2018 · OSTI ID:1523377

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

Linear theory of electron-plasma waves at arbitrary collisionality

Journal Article · Mon Apr 08 00:00:00 EDT 2019 · Journal of Plasma Physics · OSTI ID:1523377