Collisionless Damping of Electrostatic Plasma Waves

Malmberg, J. H.; Wharton, C. B.

doi:10.1103/physrevlett.13.184

Cited by 175 publications

(100 citation statements)

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“…Of particular note is the behavior known as Landau damping -the rapid decay of the electric field despite the lack of dissipative mechanisms [35,49,16,40]. Landau damping was discovered first for the linearized equations by Landau in 1946 [35] and was later observed in experiments [38,39], and is now a fundamentally important property of collisionless plasmas (see e.g. [49,16,51,40]).…”

Section: Msc: 35b35 35b34 35b40 35q83 35q84mentioning

confidence: 99%

Suppression of Plasma Echoes and Landau Damping in Sobolev Spaces by Weak Collisions in a Vlasov-Fokker-Planck Equation

Bedrossian

2017

Ann. PDE

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In this paper, we study Landau damping in the weakly collisional limit of a Vlasov-FokkerPlanck equation with nonlinear collisions in the phase-space (x, v) ∈ T n x × R n v . The goal is four-fold: (A) to understand how collisions suppress plasma echoes and enable Landau damping in agreement with linearized theory in Sobolev spaces, (B) to understand how phase mixing accelerates collisional relaxation, (C) to understand better how the plasma returns to global equilibrium during Landau damping, and (D) to rule out that collision-driven nonlinear instabilities dominate. We give an estimate for the scaling law between Knudsen number and the maximal size of the perturbation necessary for linear theory to be accurate in Sobolev regularity. We conjecture this scaling to be sharp (up to logarithmic corrections) due to potential nonlinear echoes in the collisionless model.

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Section: Msc: 35b35 35b34 35b40 35q83 35q84mentioning

confidence: 99%

Suppression of Plasma Echoes and Landau Damping in Sobolev Spaces by Weak Collisions in a Vlasov-Fokker-Planck Equation

Bedrossian

2017

Ann. PDE

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“…Additionally, it is shown analytically that any even power of velocity space hyperdiffusion also produces a Case-Van Kampen spectrum which, in the limit of zero hyperdiffusivity, matches the collisionless Landau solutions. First predicted analytically 1 and later observed experimentally, 2 collisionless Landau damping is one of the most well known phenomena in plasma physics. The Landau solutions, all of which are damped for electrostatic Langmuir waves, arise after a Laplace transform with respect to time of the linearized governing equations and dominate the solution for large times.…”

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confidence: 99%

Aspects of linear Landau damping in discretized systems

et al. 2013

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Discrete kinetic eigenmode spectra of electron plasma oscillations in weakly collisional plasma: A numerical study Phys. Plasmas 20, 012125 (2013) Non-planar ion-acoustic solitary waves and their head-on collision in a plasma with nonthermal electrons and warm adiabatic ions Phys. Plasmas 20, 012122 (2013) The incomplete plasma dispersion function: Properties and application to waves in bounded plasmas Phys. Plasmas 20, 012118 (2013) Effect of ion temperature on ion-acoustic solitary waves in a magnetized plasma in presence of superthermal electrons Phys. Plasmas 20, 012306 (2013) Additional information on Phys. Plasmas Basic linear eigenmode spectra for electrostatic Langmuir waves and drift-kinetic slab ion temperature gradient modes are examined in a series of scenarios. Collisions are modeled via a Lenard-Bernstein collision operator which fundamentally alters the linear spectrum even for infinitesimal collisionality [Ng et al., Phys. Rev. Lett. 83, 1974(1999. A comparison between different discretization schemes reveals that a Hermite representation is superior for accurately resolving the spectra compared to a finite differences scheme using an equidistant velocity grid. Additionally, it is shown analytically that any even power of velocity space hyperdiffusion also produces a Case-Van Kampen spectrum which, in the limit of zero hyperdiffusivity, matches the collisionless Landau solutions. V C 2013 American Institute of Physics. [http://dx

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“…This is absent in the Vlasovian description and has two important consequences. First, because of its lack of intuitive contents, the reality of collisionless Landau damping was fully recognized only after its experimental observation in 1964 by Malmberg and Wharton [93], almost two decades after its prediction. Second, textbooks are forced to come up with complementary models to try and explain intuitively the way Landau effect works.…”

Section: A Recovering Vlasovian Linear Theory With a Mechanical Undementioning

confidence: 99%

How to Face the Complexity of Plasmas?

Escande

2013

Nonlinear Systems and Complexity

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This paper has two main parts. The 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. In particular, most models used in plasma physics are shown to have feet of clay, there is no strict hierarchy between them, and a principle of simplicity dominates the modeling activity. At any moment the description of plasma complexity is provisional and results from a collective and somewhat unconscious process. The second sub-part considers possible methodological improvements, some of them specific to plasma physics, some others of possible interest for other fields of science. The proposals for improving the present situation go along the following lines: improving the way papers are structured and the way scientific quality is assessed in the referral process, developing new data bases, stimulating the scientific discussion of published results, diversifying the way results are made available, assessing more quality than quantity, making available an incompressible time for creative thinking and non purpose-oriented research. Some possible improvements for teaching are also indicated. 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 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. The quasilinear description of the weak warm beam is discussed, and it is shown that self-consistency vanishes when the plateau forms in the tail distribution function. This leads to consider the various diffusive regimes of the dynamics of particles in a frozen spectrum of waves with random phases. A recent numerical simulation showed that diffusion is quasilinear when the plateau sets in, and that the variation of the phase of a given wave with time is almost non fluctuating for random realizations of the initial wave phases. This led to new analytical calculations of the average behavior of the self-consistent dynamics when the initial wave phases are random. Using Picard iteration technique, they confirm numerical results, and exhibit a spontaneous emission of spatial inhomogeneities.Non quia difficilia sunt, non audemus, sed quia non audemus, difficilia sunt. It is not because things are difficult that we do not dare, it is because we do not dare that things a...

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Collisionless Damping of Electrostatic Plasma Waves

Cited by 175 publications

References 4 publications

Suppression of Plasma Echoes and Landau Damping in Sobolev Spaces by Weak Collisions in a Vlasov-Fokker-Planck Equation

Suppression of Plasma Echoes and Landau Damping in Sobolev Spaces by Weak Collisions in a Vlasov-Fokker-Planck Equation

Aspects of linear Landau damping in discretized systems

How to Face the Complexity of Plasmas?

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