skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Analysis of the Hermite spectrum in plasma turbulence

Abstract

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.

Authors:
ORCiD logo [1]; ORCiD logo [2]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  2. Univ. of Texas at Austin, Austin, TX (United States)
Publication Date:
Research Org.:
Univ. of Texas, Austin, TX (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1523377
Alternate Identifier(s):
OSTI ID: 1400334
Grant/Contract Number:  
FG02-04ER54742
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 10; 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

Citation Formats

White, R. L., and Hazeltine, R. D. Analysis of the Hermite spectrum in plasma turbulence. United States: N. p., 2017. Web. doi:10.1063/1.5000518.
White, R. L., & Hazeltine, R. D. Analysis of the Hermite spectrum in plasma turbulence. United States. doi:10.1063/1.5000518.
White, R. L., and Hazeltine, R. D. Thu . "Analysis of the Hermite spectrum in plasma turbulence". United States. doi:10.1063/1.5000518. https://www.osti.gov/servlets/purl/1523377.
@article{osti_1523377,
title = {Analysis of the Hermite spectrum in plasma turbulence},
author = {White, R. L. and Hazeltine, R. D.},
abstractNote = {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/kvth)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/kvth)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/kvth)2/3 ≲ n << (ν/kvth)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.},
doi = {10.1063/1.5000518},
journal = {Physics of Plasmas},
number = 10,
volume = 24,
place = {United States},
year = {2017},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 3 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Comparison of the relative error of the continuization approximation (28), and the uniform leading order asymptotic expansion (25). Both expressions were compared to a direct numerical solution with $\barν$ = 0.05, |G1| = 1, and G1000 = 0. The negative sign implies that the numerical solution is larger.

Save / Share:

Works referenced in this record:

Renormalized Dissipation in Plasmas with Finite Collisionality
journal, July 1995


Landau collision operators and general moment equations for an electron-ion plasma
journal, October 2008

  • Ji, Jeong-Young; Held, Eric D.
  • Physics of Plasmas, Vol. 15, Issue 10
  • DOI: 10.1063/1.2977983

Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit
journal, February 2015


Phase space scales of free energy dissipation in gradient-driven gyrokinetic turbulence
journal, May 2014


Transition between Saturation Regimes of Gyrokinetic Turbulence
journal, October 2013


Fluctuation-dissipation relations for a plasma-kinetic Langevin equation
journal, September 2014


Discrete kinetic eigenmode spectra of electron plasma oscillations in weakly collisional plasma: A numerical study
journal, January 2013

  • Black, Carrie; Germaschewski, Kai; Bhattacharjee, Amitava
  • Physics of Plasmas, Vol. 20, Issue 1
  • DOI: 10.1063/1.4789882

Viriato : A Fourier–Hermite spectral code for strongly magnetized fluid–kinetic plasma dynamics
journal, September 2016


Plasma Oscillations with Diffusion in Velocity Space
journal, December 1958


Phase mixing versus nonlinear advection in drift-kinetic plasma turbulence
journal, April 2016

  • Schekochihin, A. A.; Parker, J. T.; Highcock, E. G.
  • Journal of Plasma Physics, Vol. 82, Issue 2
  • DOI: 10.1017/S0022377816000374

Exact collisional moments for plasma fluid theories
journal, April 2017

  • Pfefferlé, D.; Hirvijoki, E.; Lingam, M.
  • Physics of Plasmas, Vol. 24, Issue 4
  • DOI: 10.1063/1.4979992

On the kinetic theory of rarefied gases
journal, December 1949


LIII. Dynamical problems in illustration of the theory of gases
journal, November 1891

  • Rayleigh, Lord
  • The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 32, Issue 198
  • DOI: 10.1080/14786449108620207

Developments in the gyrofluid approach to Tokamak turbulence simulations
journal, August 1993


Reduced fluid-kinetic equations for low-frequency dynamics, magnetic reconnection, and electron heating in low-beta plasmas
journal, October 2011

  • Zocco, Alessandro; Schekochihin, Alexander A.
  • Physics of Plasmas, Vol. 18, Issue 10
  • DOI: 10.1063/1.3628639

Kinetic simulation of steady states of ion temperature gradient driven turbulence with weak collisionality
journal, April 2004

  • Watanabe, T. -H.; Sugama, H.
  • Physics of Plasmas, Vol. 11, Issue 4
  • DOI: 10.1063/1.1669393

Fourier-Hermite Solutions of the Vlasov Equations in the Linearized Limit
journal, January 1967


Irreversible energy flow in forced Vlasov dynamics
journal, October 2014


    Figures / Tables found in this record:

      Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.