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Register a new userN-body description of Debye shielding and Landau damping
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D.F. Escande
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This paper brings further insight into the recently published N-body description of Debye shielding and Landau damping [Escande D F, Elskens Y and Doveil F 2014 Plasma Phys. Control. Fusion 57 025017]. Its fundamental equation for the electrostatic potential is derived in a simpler and more rigorous way. Various physical consequences of the new approach are discussed, and this approach is compared with the seminal one by Pines and Bohm [Pines D and Bohm D 1952 Phys. Rev. 85 338--353].
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The derivation of Debye shielding and Landau damping from the $N$-body description of plasmas is performed directly by using Newtons 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. Shielding and collisional transport are found to be two related aspects of the repulsive deflections of electrons, in such a way that each particle is shielded by all other ones while keeping in uninterrupted motion.
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.
To model momentum exchange in nonlinear wave-particle interaction, as in amplification devices like traveling-wave tubes, we use an $N$-body self-consistent hamiltonian description based on Kuznetsovs discrete model, and we provide new formulations for the electromagnetic power and the conserved momentum. This approach leads to fast and accurate numerical simulations in time domain and in one dimensional space.
We discuss the self-consistent dynamics of plasmas by means of hamiltonian formalism for a system of $N$ near-resonant electrons interacting with a single Langmuir wave. The connection with the Vlasov description is revisited through the numerical calculation of the van Kampen-like eigenfrequencies of the linearized dynamics for many degrees of freedom. Both the exponential-like growth as well as damping of the Langmuir wave are shown to emerge from a phase mixing effect among beam modes, revealing unexpected similarities between the stable and unstable regimes.
Kinetic treatments of drift-tearing modes that match an inner resonant layer solution to an external MHD region solution, characterised by $Delta^{prime}$, fail to properly match the ideal MHD boundary condition on the parallel electric field, $E_{parallel}.$ In this paper we demonstrate how consideration of ion sound and ion Landau damping effects achieves this and place the theory on a firm footing. As a consequence, these effects contribute quite significantly to the critical value of $Delta^{prime}$ for instability of drift-tearing modes and play a key role in determining the minimum value for this threshold.
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