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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/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.

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. https://doi.org/10.1063/1.5000518
White, R. L., and Hazeltine, R. D. Thu . "Analysis of the Hermite spectrum in plasma turbulence". United States. https://doi.org/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 = {Thu Oct 19 00:00:00 EDT 2017},
month = {Thu Oct 19 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 4 works
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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.

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Works referencing / citing this record:

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