How to face the complexity of plasmas?
Résumé
This paper has two main parts. The \textit{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 sub-parts. The first one deals with the present status of this description. The second one considers possible methodological improvements, in particular improving the way papers are structured and quality assessment in the referral process, and the development of new data bases. 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 \textit{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 and to shed a new light on the saturation of the weak warm beam instability.
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