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Register a new userPhase mixing importance for both Landau instability and damping
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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.
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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.
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].
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.
Incorporation of kinetic effects such as Landau damping into a fluid framework was pioneered by Hammett and Perkins PRL 1990, by obtaining closures of the fluid hierarchy, where the gyrotropic heat flux fluctuations or the deviation of the 4th-order gyrotropic fluid moment, are expressed through lower-order fluid moments. To obtain a closure of a fluid model expanded around a bi-Maxwellian distribution function, the usual plasma dispersion function $Z(zeta)$ that appears in kinetic theory or the associated plasma response function $R(zeta)=1 + zeta Z(zeta)$, have to be approximated with a suitable Pade approximant in such a way, that the closure is valid for all $zeta$ values. Such closures are rare, and the original closures of Hammett and Perkins are often employed. Here we present a complete mapping of all plausible Landau fluid closures that can be constructed at the level of 4th-order moments in the gyrotropic limit and we identify the most precise closures. Furthermore, by considering 1D closures at higher-order moments, we show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing convergence of the fluid and collisionless kinetic descriptions.
Turbulence is thought to play a role in the heating of the solar wind plasma, though many questions remain to be solved regarding the exact nature of the mechanisms driving this process in the heliosphere. In particular, the physics of the collisionl
ess interactions between particles and turbulent electromagnetic fields in the kinetic dissipation range of the turbulent cascade remains incompletely understood. A recent analysis of an interval of Magnetosphere Multiscale (MMS) observations has used the field-particle correlation technique to demonstrate that electron Landau damping is involved in the dissipation of turbulence in the Earths magnetosheath. Motivated by this discovery, we perform a high-resolution gyrokinetic numerical simulation of the turbulence in the MMS interval to investigate the role of electron Landau damping in the dissipation of turbulent energy. We employ the field-particle correlation technique on our simulation data, compare our results to the known velocity-space signatures of Landau damping outside the dissipation range, and evaluate the net electron energization. We find qualitative agreement between the numerical and observational results for some key aspects of the energization and speculate on the nature of disagreements in light of experimental factors, such as differences in resolution, and of developing insights into the nature of field-particle interactions in the presence of dispersive kinetic Alfven waves.
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