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Title: The modulational instability in the extended Hasegawa-Mima equation with a finite Larmor radius

Abstract

The effects of the finite Larmor radius on the generation of zonal flows by the four-wave modulational instability are investigated using an extended form of the Hasegawa-Mima equation. Growth rates of the zonal mode are quantified using analytical predictions from a four-mode truncated model, as well as from direct numerical simulation of the nonlinear extended Hasegawa-Mima equation. We not only consider purely zonal flows but also examine the generic oblique case and show that, for small Larmor radii, off-axis modes may become dominant. We find a key parameter M{sub {rho}} which characterises the behaviour of the system due to changes in the Larmor radius. We find that, similarly to previous results obtained by changing the driving wave amplitude, two separate dynamical regimes can be accessed. These correspond to oscillatory energy transfer between zonal flows and a driving wave and the fully saturated zonal flow.

Authors:
; ;  [1]; ;  [2]
  1. Centre for Fusion, Space and Astrophysics, Department of Physics, Warwick University, Coventry CV4 7AL (United Kingdom)
  2. Department of Mathematics, Warwick University, Coventry CV4 7AL (United Kingdom)
Publication Date:
OSTI Identifier:
22072615
Resource Type:
Journal Article
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 19; Journal Issue: 12; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLITUDES; COMPUTERIZED SIMULATION; ENERGY TRANSFER; EQUATIONS; LARMOR RADIUS; NONLINEAR PROBLEMS; PLASMA INSTABILITY; PLASMA WAVES

Citation Formats

Gallagher, S, Hnat, B, Rowlands, G, Connaughton, C, and Nazarenko, S. The modulational instability in the extended Hasegawa-Mima equation with a finite Larmor radius. United States: N. p., 2012. Web. doi:10.1063/1.4773050.
Gallagher, S, Hnat, B, Rowlands, G, Connaughton, C, & Nazarenko, S. The modulational instability in the extended Hasegawa-Mima equation with a finite Larmor radius. United States. https://doi.org/10.1063/1.4773050
Gallagher, S, Hnat, B, Rowlands, G, Connaughton, C, and Nazarenko, S. 2012. "The modulational instability in the extended Hasegawa-Mima equation with a finite Larmor radius". United States. https://doi.org/10.1063/1.4773050.
@article{osti_22072615,
title = {The modulational instability in the extended Hasegawa-Mima equation with a finite Larmor radius},
author = {Gallagher, S and Hnat, B and Rowlands, G and Connaughton, C and Nazarenko, S},
abstractNote = {The effects of the finite Larmor radius on the generation of zonal flows by the four-wave modulational instability are investigated using an extended form of the Hasegawa-Mima equation. Growth rates of the zonal mode are quantified using analytical predictions from a four-mode truncated model, as well as from direct numerical simulation of the nonlinear extended Hasegawa-Mima equation. We not only consider purely zonal flows but also examine the generic oblique case and show that, for small Larmor radii, off-axis modes may become dominant. We find a key parameter M{sub {rho}} which characterises the behaviour of the system due to changes in the Larmor radius. We find that, similarly to previous results obtained by changing the driving wave amplitude, two separate dynamical regimes can be accessed. These correspond to oscillatory energy transfer between zonal flows and a driving wave and the fully saturated zonal flow.},
doi = {10.1063/1.4773050},
url = {https://www.osti.gov/biblio/22072615}, journal = {Physics of Plasmas},
issn = {1070-664X},
number = 12,
volume = 19,
place = {United States},
year = {Sat Dec 15 00:00:00 EST 2012},
month = {Sat Dec 15 00:00:00 EST 2012}
}