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Landau damping
About: Landau damping is a research topic. Over the lifetime, 3788 publications have been published within this topic receiving 76459 citations.
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Book•
01 Jan 1974
TL;DR: In this article, the authors define the concept of debye shielding and define a set of criteria for plasmas in terms of temperature, debye Shielding, and debye shielding.
Abstract: 1. Introduction.- Occurrence of Plasmas in Nature.- Definition of Plasma.- Concept of Temperature.- Debye Shielding.- The Plasma Parameter.- Criteria for Plasmas.- Applications of Plasma Physics.- 2. Single-Particle Motions.- Uniform E and B Field.- Nonuniform B Field.- Nonuniform E Field.- TimeVarying E Field.- Time-Varying B Field.- Summary of Guiding Center Drifts.- Adiabatic Invariants.- 3. Plasmas as Fluids.- Relation of Plasma Physics to Ordinary Electromagnetics.- The Fluid Equation of Motion.- Fluid Drifts Perpendicular to B.- Fluid Drifts Parallel to B.- The Plasma Approximation.- 4. Waves in Plasmas.- Representation of Waves.- Group Velocity.- Plasma Oscillations.- Electron Plasma Waves.- Sound Waves.- Ion Waves.- Validity of the Plasma Approximation.- Comparison of Ion and Electron Waves.- Electrostatic Electron Oscillations Perpendicular to B.- Electrostatic Ion Waves Perpendicular to B.- The Lower Hybrid Frequency.- Electromagnetic Waves with B0 =.- Experimental Applications.- Electromagnetic Waves Perpendicular to B0.- Cutoffs and Resonances.- Electromagnetic Waves Parallel to B0.- Experimental Consequences.- Hydromagnetic Wave.- Magnetosonic Waves.- Summary of Elementary Plasma Waves.- The CMA Diagram.- 5. Diffusion and Resistivity.- Diffusion and Mobility in Weakly Ionized Gases.- Decay of a Plasma by Diffusion.- Steady State Solutions.- Recombination.- Diffusion Across a Magnetic Field.- Collisions in Fully Ionized Plasmas.- The Single-Fluid MHD Equations.- Diffusion in Fully Ionized Plasmas.- Solutions of the Diffusion Equation.- Bohm Diffusion and Neoclassical Diffusion.- 6. Equilibrium and Stability.- Introductio.- Hydromagnetic Equilibrium.- The Concept of ss.- Diffusion of Magnetic Field into a Plasma.- Classification of Instabilities.- Two-Stream Instability.- The "Gravitational" Instability.- Resistive Drift Waves.- 7. Introduction to Kinetic Theory.- The Meaning off(v).- Equations of Kinetic Theory.- Derivation of the Fluid Equations.- Plasma Oscillations and Landau Damping.- The Meaning of Landau Damping.- A Physical Derivation of Landau Damping.- BGK and Van Kampen Modes.- Experimental Verification.- Ion Landau Damping.- 8. Nonlinear Effects.- Sheaths.- Ion Acoustic Shock Waves.- The Ponderomotive Force.- Parametric Instabilities.- Plasma Echoes.- Nonlinear Landau Damping.- 9. Introduction to Controlled Fusion.- The Problem of Controlled Fusion.- Magnetic Confinement: Toruses.- Mirrors.- Pinches.- Laser-Fusion.- Plasma Heating.- Fusion Technology.- Summary.- Units.- Useful Constants and Formulas.- Useful Vector Relations.
1,415 citations
Book•
15 Jan 1993
TL;DR: Wake Fields and Impedances. Landau Damping and Perturbation Formalism. as discussed by the authors Theoretical analysis of linear accelerators. But they do not consider the effects of linear acceleration on linear models.
Abstract: Wake Fields and Impedances. Instabilities in Linear Accelerators. Macroparticle Models. Landau Damping. Perturbation Formalism. Index.
1,231 citations
TL;DR: In this paper, it is shown that, by adding appropriate numbers of particles trapped in the potential energy troughs, essentially arbitrary traveling wave solutions can be constructed, and the possible existence of such waves in an actual plasma will depend on factors ignored in this paper, as in most previous works, namely interparticle collisions and the stability of the solutions against various types of perturbations.
Abstract: The problem of a one-dimensional stationary nonlinear electrostatic wave in a plasma free from interparticle collisions is solved exactly by elementary means. It is demonstrated that, by adding appropriate numbers of particles trapped in the potential-energy troughs, essentially arbitrary traveling wave solutions can be constructed.When one passes to the limit of small-amplitude waves it turns out that the distribution function does not possess an expansion whose first term is linear in the amplitude, as is conventionally assumed. This disparity is associated with the trapped particles. It is possible, however, to salvage the usual linearized theory by admitting singular distribution functions. These, of course, do not exhibit Landau damping, which is associated with the restriction to well-behaved distribution functions.The possible existence of such waves in an actual plasma will depend on factors ignored in this paper, as in most previous works, namely interparticle collisions, and the stability of the solutions against various types of perturbations.
1,171 citations
TL;DR: In this article, the Laplace transform method was used to study the small oscillations of a fully ionized plasma, in which collisions are negligible, in a constant external magnetic field, and the full set of Maxwell equations was employed and the ion dynamics were included.
Abstract: The small oscillations of a fully ionized plasma, in which collisions are negligible, in a constant external magnetic field, is treated by the Laplace transform method. The full set of Maxwell equations is employed and the ion dynamics are included. Various limiting cases are considered. It is shown that self-excitation of waves around thermal equilibrium is impossible. It is also demonstrated that for longitudinal electron oscillations propagating perpendicular to the constant magnetic field, there are gaps in the spectrum of allowed frequencies at multiples of the electron gyration frequency, but zero Landau damping. These particular waves are also associated with a nonuniformity of convergence in the limit of vanishing magnetic field which phenomenon, however, is of no physical consequence. When the ion dynamics are included, two classes of low frequency oscillations are found, the existence of both of which has been predicted by the simple hydrodynamic theory, namely longitudinal ion waves, and transverse hydromagnetic waves. The well known results for the propagation of electromagnetic waves in an ionized atmosphere are also recovered, as well as the effects on such waves in various limiting cases of the magnetic field and particle motion. These calculations indicate that in many cases the transport equations are capable of yielding correct results, apart from such things as Landau damping, for a wide class of waves in a collision-free plasma.
808 citations
TL;DR: A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed in this paper.
Abstract: A nonlinear gyrokinetic formalism for low‐frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed The nonlinear equations thus derived are valid in the strong‐turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magnetic field geometries The specific case of axisymmetric tokamaks is then considered and a model nonlinear equation is derived for electrostatic drift waves Also, applying the formalism to the shear Alfven wave heating scheme, it is found that nonlinear ion Landau damping of kinetic shear‐Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects In particular, wave energy is found to cascade in wavenumber instead of frequency
763 citations