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Fluids 2018, 3(4), 89; https://doi.org/10.3390/fluids3040089

Subcritical Instabilities in Neutral Fluids and Plasmas

1
Institut Jean Lamour, CNRS UMR 7198, Université de Lorraine, F-54011 Nancy, France
2
Research Institute for Applied Mechanics, Kyushu University, Kasuga 816-8580, Japan
3
National Institute for Fusion Science, Toki 509-5292, Japan
*
Author to whom correspondence should be addressed.
Received: 28 August 2018 / Revised: 17 October 2018 / Accepted: 29 October 2018 / Published: 2 November 2018
(This article belongs to the Special Issue Modelling of Plasma Flow)
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Abstract

In neutral fluids and plasmas, the analysis of perturbations often starts with an inventory of linearly unstable modes. Then, the nonlinear steady-state is analyzed or predicted based on these linear modes. A crude analogy would be to base the study of a chair on how it responds to infinitesimaly small perturbations. One would conclude that the chair is stable at all frequencies, and cannot fall down. Of course, a chair falls down if subjected to finite-amplitude perturbations. Similarly, waves and wave-like structures in neutral fluids and plasmas can be triggered even though they are linearly stable. These subcritical instabilities are dormant until an interaction, a drive, a forcing, or random noise pushes their amplitude above some threshold. Investigating their onset conditions requires nonlinear calculations. Subcritical instabilities are ubiquitous in neutral fluids and plasmas. In plasmas, subcritical instabilities have been investigated based on analytical models and numerical simulations since the 1960s. More recently, they have been measured in laboratory and space plasmas, albeit not always directly. The topic could benefit from the much longer and richer history of subcritical instability and transition to subcritical turbulence in neutral fluids. In this tutorial introduction, we describe the fundamental aspects of subcritical instabilities in plasmas, based on systems of increasing complexity, from simple examples of a point-mass in a potential well or a box on a table, to turbulence and instabilities in neutral fluids, and finally, to modern applications in magnetized toroidal fusion plasmas. View Full-Text
Keywords: subcritical; nonlinear; instability subcritical; nonlinear; instability
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Lesur, M.; Médina, J.; Sasaki, M.; Shimizu, A. Subcritical Instabilities in Neutral Fluids and Plasmas. Fluids 2018, 3, 89.

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