Complexity and simplicity of plasmas

This paper has two main parts. The first one presents a direct path from microscopic dynamics to Debye screening, Landau damping and collisional transport. It shows there is more simplicity in microscopic plasma physics than previously thought. The second part is more subjective. It describes some difficulties in facing plasma complexity in general, suggests an inquiry about the methods used empirically to tackle complex systems, discusses the teaching of plasma physics as a physics of complexity, and proposes new directions to face the inflation of information.Comment: 13 page

Contributions of plasma physics to chaos and nonlinear dynamics

This topical review focusses on the contributions of plasma physics to chaos and nonlinear dynamics bringing new methods which are or can be used in other scientific domains. It starts with the development of the theory of Hamiltonian chaos, and then deals with order or quasi order, for instance adiabatic and soliton theories. It ends with a shorter account of dissipative and high dimensional Hamiltonian dynamics, and of quantum chaos. Most of these contributions are a spin-off of the research on thermonuclear fusion by magnetic confinement, which started in the fifties. Their presentation is both exhaustive and compact. [15 April 2016

Self-consistency vanishes in the plateau regime of the bump-on-tail instability

Using the Vlasov-wave formalism, it is shown that self-consistency vanishes in the plateau regime of the bump-on-tail instability if the plateau is broad enough. This shows that, in contrast with the "turbulent trapping" Ansatz, a renormalization of the Landau growth rate or of the quasilinear diffusion coefficient is not necessarily related to the limit where the Landau growth time becomes large with respect to the time of spreading of the particle positions due to velocity diffusion

How to face the complexity of plasmas?

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

Basic microscopic plasma physics unified and simplified by N-body classical mechanics

Debye shielding, collisional transport, Landau damping of Langmuir waves, and spontaneous emission of these waves are introduced, in typical plasma physics textbooks, in different chapters. This paper provides a compact unified introduction to these phenomena without appealing to fluid or kinetic models, but by using Newton's second law for a system of $N$ electrons in a periodic box with a neutralizing ionic background. A rigorous equation is derived for the electrostatic potential. Its linearization and a first smoothing reveal this potential to be the sum of the shielded Coulomb potentials of the individual particles. Smoothing this sum yields the classical Vlasovian expression including initial conditions in Landau contour calculations of Langmuir wave growth or damping. The theory is extended to accommodate a correct description of trapping or chaos due to Langmuir waves. In the linear regime, the amplitude of such a wave is found to be ruled by Landau growth or damping and by spontaneous emission. Using the shielded potential, the collisional diffusion coefficient is computed for the first time by a convergent expression including the correct calculation of deflections for all impact parameters. Shielding and collisional transport are found to be two related aspects of the repulsive deflections of electrons

What is a reversed field pinch?

The reversed field pinch (RFP) is a magnetic configuration germane to the tokamak, that produces most of its magnetic field by the currents flowing inside the plasma; external coils provide only a small edge toroidal field whose sign is reversed with respect to the central one. Because of the presence of magnetic turbulence and chaos, the RFP had been considered for a long period as a terrible confinement configuration. Then strong enhancements were triggered in the RFX-mod RFP in Padua (Italy): a self-organized helical state with an internal transport barrier develops, and a broad zone of the plasma becomes hot (above 1 keV for a central magnetic field above 0.8 T). The possibility of this helical state and of the corresponding improvement in confinement had been theoretically predicted by three-dimensional nonlinear visco-resistive magnetohydrodynamic (MHD) simulations. This course summarizes the present experimental and theoretical knowledge about this helical state, in particular with the following issues: Lawson criterion, dynamo, MHD and magnetic field bifurcations, analytical description, analogy with the nonlinear tearing mode, attractiveness of the RFP configuration for a reactor, usefulness for fusion science and dynamo physics. The new paradigm for the RFP supports its reappraisal as a low-external field, non-disruptive, ohmically heated approach to magnetic fusion, exploiting both self-organization and technological simplicity

Uniform derivation of Coulomb collisional transport thanks to Debye shielding

The effective potential acting on particles in plasmas being essentially the Debye-shielded Coulomb potential, the particles collisional transport in thermal equilibrium is calculated for all impact parameters $b$, with a convergent expression reducing to Rutherford scattering for small $b$. No cutoff at the Debye length scale is needed, and the Coulomb logarithm is only slightly modified.Comment: arXiv admin note: text overlap with arXiv:1210.1546, arXiv:1310.309

New foundations and unification of basic plasma physics by means of classical mechanics

The derivation of Debye shielding and Landau damping from the $N$-body description of plasmas requires many pages of heavy kinetic calculations in classical textbooks and is done in distinct, unrelated chapters. Using Newton's second law for the $N$-body system, we perform this derivation in a few steps with elementary calculations using standard tools of calculus, and no probabilistic setting. Unexpectedly, Debye shielding is encountered on the way to Landau damping. The theory is extended to accommodate a correct description of trapping or chaos due to Langmuir waves, and to avoid the small amplitude assumption for the electrostatic potential. Using the shielded potential, collisional transport is computed for the first time by a convergent expression including the correct calculation of deflections for all impact parameters. Shielding and collisional transport are found to be two related aspects of the repulsive deflections of electrons.Comment: 28 pages, revTeX. arXiv admin note: substantial text overlap with arXiv:1210.154