Direct path from microscopic mechanics to Debye shielding, Landau damping and wave-particle interaction
The derivation of Debye shielding and Landau damping from the N-body description of plasmas is performed directly by using Newton’s second law for the N-body system. This is done in a few steps with elementary calculations using standard tools of calculus and no probabilistic setting. Unexpectedly, Debye shielding is encountered together with Landau damping. This approach is shown to be justified in the one-dimensional case when the number of particles in a Debye sphere becomes large. The theory is extended to accommodate a correct description of trapping and chaos due to Langmuir waves. On top of their well-known production of collisional transport, the repulsive deflections of electrons are shown to produce shielding, in such a way that each particle is shielded by all other ones, while keeping in uninterrupted motion.
Summary of the fundamental plasma physics session in the first AAPPS-DPP conference
Understanding of fundamental plasma physics contributes to progress in plasma science in many fields, such as magnetic confinement fusion, solar/space physics and application of plasma techniques. Intersecting common fundamental problems stimulate cross-fertilization of different topical areas. This paper summarizes the highlights of progress reported in the Fundamental Plasma Physics Session of the first conference of the Association of Asia Pacific Physical Societies-Division of plasma physics. Progress in the following fields is reviewed: (1) basic plasma theory; (2) self-organization; (3) reconnection and particle acceleration; (4) magneto-hydrodynamic instabilities and energetic particle physics; (5) magnetic confinement physics fundamentals; and (6) exploiting fundamentals for performance.
Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations
We prove asymptotic stability of shear flows close to the planar Couette flow in the 2D inviscid Euler equations on T×R. That is, given an initial perturbation of the Couette flow small in a suitable regularity class, specifically Gevrey space of class smaller than 2, the velocity converges strongly in L2 to a shear flow which is also close to the Couette flow. The vorticity is asymptotically driven to small scales by a linear evolution and weakly converges as t→±∞. The strong convergence of the velocity field is sometimes referred to as inviscid damping, due to the relationship with Landau damping in the Vlasov equations. This convergence was formally derived at the linear level by Kelvin in 1887 and it occurs at an algebraic rate first computed by Orr in 1907; our work appears to be the first rigorous confirmation of this behavior on the nonlinear level.