Basic microscopic plasma physics from N-body mechanics

Computing is not understanding. This is exemplified by the multiple and discordant interpretations of Landau damping still present after seventy years. For long deemed impossible, the mechanical N-body description of this damping, not only enables its rigorous and simple calculation, but makes unequivocal and intuitive its interpretation as the synchronization of almost resonant passing particles. This synchronization justifies mechanically why a single formula applies to both Landau growth and damping. As to the electrostatic potential, the phase mixing of many beam modes produces Landau damping, but it is unexpectedly essential for Landau growth too. Moreover, collisions play an essential role in collisionless plasmas. In particular, Debye shielding results from a cooperative dynamical self-organization process, where collisional deflections due to a given electron diminish the apparent number of charges about it. The finite value of exponentiation rates due to collisions is crucial for the equivalent of the van Kampen phase mixing to occur in the N-body system. The N-body approach incorporates spontaneous emission naturally, whose compound effect with Landau damping drives a thermalization of Langmuir waves. ONeils damping with trapping typical of initially large enough Langmuir waves results from a phase transition. As to collisional transport, there is a smooth connection between impact parameters where the two-body Rutherford picture is correct, and those where a collective description is mandatory. The N-body approach reveals two important features of the Vlasovian limit: it is singular and it corresponds to a renormalized description of the actual N-body dynamics.

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]

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.

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 Newtons 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.