How to Face the Complexity of Plasmas?

Part of the Nonlinear Systems and Complexity book series (NSCH, volume 5)


This paper has two main parts. The first part is subjective and aims at favoring a brainstorming in the plasma community. It discusses the present theoretical description of plasmas, with a focus on hot weakly collisional plasmas. It comprises two subparts. The first one deals with the present status of this description. In particular, most models used in plasma physics are shown to have feet of clay, there is no strict hierarchy between them, and a principle of simplicity dominates the modeling activity. At any moment the description of plasma complexity is provisional and results from a collective and somewhat unconscious process. The second subpart considers possible methodological improvements, some of them specific to plasma physics and some others of possible interest for other fields of science. The proposals for improving the present situation go along the following lines: improving the way papers are structured and the way scientific quality is assessed in the referral process, developing new databases, stimulating the scientific discussion of published results, diversifying the way results are made available, assessing more quality than quantity, and making available an incompressible time for creative thinking and non-purpose-oriented research. Some possible improvements for teaching are also indicated. The suggested improvement of the structure of papers would be for each paper to have a “claim section” summarizing the main results and their most relevant connection to previous literature. One of the ideas put forward is that modern nonlinear dynamics and chaos might help revisiting and unifying the overall presentation of plasma physics. The second part of this chapter is devoted to one instance where this idea has been developed for three decades: the description of Langmuir wave–electron interaction in one-dimensional plasmas by a finite-dimensional Hamiltonian. This part is more specialized and is written like a classical scientific paper. This Hamiltonian approach enables recovering Vlasovian linear theory with a mechanical understanding. The quasilinear description of the weak warm beam is discussed, and it is shown that self-consistency vanishes when the plateau forms in the tail distribution function. This leads to consider the various diffusive regimes of the dynamics of particles in a frozen spectrum of waves with random phases. A recent numerical simulation showed that diffusion is quasilinear when the plateau sets in and that the variation of the phase of a given wave with time is almost non-fluctuating for random realizations of the initial wave phases. This led to new analytical calculations of the average behavior of the self-consistent dynamics when the initial wave phases are random. Using Picard iteration technique, they confirm numerical results and exhibit a spontaneous emission of spatial inhomogeneities.


Wave Spectrum Vlasov Equation Langmuir Wave Plasma Instability Plasma Complexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



I am indebted to Y. Camenen, L. Couëdel, F. Doveil, and Y. Elskens, for a thorough reading of a first version of this paper and for providing me with an extensive feedback. My thanks also go to D. Bonfiglio, S. Cappello, and F. Sattin who did the same for a second version. Y. Elskens also helped me a lot in improving the English. F. Baldovin, M. Bécoulet, D. Bénisti, N. Bian, A. Boozer, P. Diamond, M.-C. Firpo, M. Henneaux, T. Mendonça, B. Momo, K. Razumova, S. Ruffo, M. Valisa, and F. Zolla are thanked for very useful comments and new references. I thank D. Guyomarc’h for drawing all the figures. My thanks go to M. Farge who pointed out to me reference [110]. The topic of my talk at Chaos, Complexity and Transport 2011 was about the description of self-consistent wave–particle interaction with a finite-dimensional Hamiltonian described in Sect. 4.3. However, two seminars I gave later on in the north and south campuses of Marseilles were the occasion to start developing the ideas of Sect. 4.2, in kind of an echo to Sect. 4.3. I thank the organizers of the conference for allowing me to extend the topic of my chapter beyond the original contents of my talk and to further develop my thoughts about plasma complexity and the way to tackle it.


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Authors and Affiliations

  1. 1.UMR 7345 CNRS-Aix-Marseille-UniversitéMarseille CEDEX 20France

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