Electron oscillations in a plasma: Effect of collisions on Landau damping

Summary Electron oscillations in a plasma are analysed starting from the integral form of Boltzmann-Vlasov equation. The effects of collisions on Landau damping are shown. The conditions for Landau damping existence are derived.

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Riassunto Onde elettrostatiche in un plasma sono studiate ricorrendo alla forma integrale dell'equazione di Boltzmann-Vlasov. In particolare, sono stati evidenziati gli effetti prodotti sul Landau damping dalle collisioni. Si è ricavato che in certe condizioni le collisioni possono impedire il Landau damping e si sono ottenuti i valori di soglia.

     

Vlasov equation for photons and quasi-particles in a plasma

We show that, in quite general conditions, a Vlasov equation can be derived for photons in a medium. The same is true for other quasi-particles, such as plasmons, phonons or driftons, associated with other wave modes in a plasma. The range of validity of this equation is discussed. We also discuss the Landau resonance, and its relation with photon acceleration. Exact and approximate expressions for photon and quasi-particle Landau damping are stated. Photon and quasi-particle acceleration and trapping is also discussed. Specific applications to laser-plasma interaction, and to magnetic fusion turbulence, are considered as illustrations of the general approach.     

量子等离子体中波的色散关系以及朗道阻尼

利用动理学理论研究量子等离子体中波的色散关系和电子朗道阻尼.从电子的量子流体动力学方程和动理学描述下的光子运动方程出发,研究量子效应对光子朗道阻尼的修正.研究发现量子效应只对纵波模式,即电子等离子体波的色散关系有修正,对横向电磁波的色散关系没有影响.量子效应减小了朗道阻尼,起着朗道增长的作用. 关键词： 量子等离子体 朗道阻尼 电子等离子体波 色散关系     

Thermoelastic vibrations in micro-/nano-scale beam resonators with voids

In this paper the closed form expressions for the transverse vibrations of a homogenous isotropic, thermoelastic thin beam with voids, based on Euler-Bernoulli theory have been derived. The effects of voids, relaxation times, thermomechanical coupling, surface conditions and beam dimensions on energy dissipation induced by thermoelastic damping in (micro-electromechanical systems) MEMS/(nano-electromechanical systems) NEMS resonators are investigated for beams under clamped and simply supported conditions. Analytical expressions for deflection, temperature change, frequency shifts and thermoelastic damping in the beam have been derived. Some numerical results with the help of MATLAB programming software in case of magnesium like material have also been presented. The computer simulated results in respect of damping factor and frequency shift have been presented graphically.     

Phase transition in the collisionless damping regime for wave-particle interaction

Gibbs statistical mechanics is derived for the Hamiltonian system coupling a wave to N particles self-consistently. This identifies Landau damping with a regime where a second order phase transition occurs. For nonequilibrium initial data with warm particles, a critical initial wave intensity is found: above it, thermodynamics predicts a finite wave amplitude in the limit N-->infinity; below it, the equilibrium amplitude vanishes. Simulations support these predictions providing new insight into the long-time nonlinear fate of the wave due to Landau damping in plasmas.     

Study of dust ion-acoustic wave propagation in the Lorentzian magnetized dusty plasma

Dust ion-acoustic waves propagation in the magnetized dusty plasma including ions, electrons and dust particulates are studied by using kinetic equation. For unbounded and collisionless plasma and in the presence of uniform external magnetic field B₀, electrons and ions with Lorentzian distribution function and dust particles with Maxwellian one are considered. Calculating dielectric tensor through the Vlasov equation solution, in the parallel propagation, dispersion relation is derived and suprathermal particle effects on the Landau damping is studied. It is shown that the Landau damping effect vanishes for parallel propagation.     

Effects of suprathermal particles on the dust ion-acoustic waves in a complex plasma

Dust ion-acoustic waves propagating in a complex plasma containing dusty particles and suprathermal electrons and ions are kinetically analyzed. The suprathermal particles are effectively modeled by the Lorentzian (kappa) velocity distribution function. For a collisionless and unmagnetized plasma, the full spectrum of the dispersion relation is obtained and the suprathermal particle effects on the wave frequency and the Landau damping are investigated. For a given wave number, the wave frequency decreases as the spectral index κ decreases, especially very rapidly in the low κ region. The Landau damping of the wave and its maximum are derived. They are found to be enhanced by the increase of suprathermal particles. The ion-to-electron density ratio also enhances the damping rate greatly.     

激励Brillouin散射非线性致稳过程的阻尼效应

本文研究了由非线性引起的Brillouin散射致稳效应。我们主要兴趣是Landau阻尼对非线性致稳的影响。我们求解了时间、空间和时-空有关的方程,得到了场能密度、场幅、饱和时间和空间大小等随物理参量变化的近似解析表达式。 关键词：     

Unstable mode of ion-acoustic waves with two temperature q-nonextensive distributed electrons

The linear characteristics of the unstable mode of ion-acoustic waves are examined in an electrostatic electron-ion plasma composed of streaming hot electrons, non-streaming cold electrons and dynamical positive ions. The plasma under consideration is modeled by using a non-gyrotropic nonextensive q-distribution function in which the free energy source for wave excitation is provided by the relative directed motion of streaming hot electrons with respect to the other plasma species. In the frame work of kinetic model, a linearized set of Vlasov–Poisson's equations are solved to obtain the analytical expressions for dispersion relation and Landau damping rate. The threshold condition for the unstable ionacoustic wave is derived to assess the stability of the wave in the presence of nonextensive effects. Growth in the wave spectrum and nontrivial effects of q-nonextensive parameter on the ion-acoustic waves can be of interest for the readers in the regions of Saturns' s magnetosphere.     

Ion-acoustic soliton-like waves undergoing Landau damping

Effects of Landau damping on ion-acoustic soliton-like waves are investigated experimentally and numerically. Landau damping is enhanced by increasing the ion temperature in the experiments. A ramp which is composed of resonant ions is observed in front of a soliton-like wave. The ramp is also seen in numerical simulations of an extended Korteweg–de Vries equation with a term of Landau damping. Experimental results of the height of the ramp are found to agree with numerical ones.     

Landau damping in a dipolar Bose–Fermi mixture in the Bose–Einstein condensation(BEC) limit

By using a mean-field approximation which describes the coupled oscillations of condensate and noncondensate atoms in the collisionless regime, Landau damping in a dilute dipolar Bose–Fermi mixture in the BEC limit where Fermi superfluid is treated as tightly bounded molecules, is investigated. In the case of a uniform quasi-two-dimensional(2D)case, the results for the Landau damping due to the Bose–Fermi interaction are obtained at low and high temperatures. It is shown that at low temperatures, the Landau damping rate is exponentially suppressed. By increasing the strength of dipolar interaction, and the energy of boson quasiparticles, Landau damping is suppressed over a broader temperature range.     

Wave Trajectories and Damping of Lower Hybrid Wave in Tokamak Plasmas

Incident lower hybrid waves (LHW) propagate toward the center of the plasma in a spiral form in the poloidal and the toroidal sections, and finally are absorbed by the ion Landau damping (ILD) and/or the electron Landau damping (ELD) in accordance with the refractive index parallel to the magnetic field N?, which is varied considerably along the trajectory because of the toroidicity and the rotational transform. We propose the scaling law of the wave trajectories on plasma parameters, which shows that the control of N? or the applied frequency is necessary during the lower hybrid heating (LHH).     

雪茄形铷原子玻色-爱因斯坦凝聚中单极子模的朗道阻尼和频移

采用含时哈特里-福克-博戈留波夫近似研究雪茄形铷原子玻色-爱因斯坦凝聚中单极子模的朗道阻尼和频移. 通过考虑元激发的实际弛豫及其各弛豫间的正交关系改进原有方法, 并由此给出计算朗道阻尼和频移的新公式. 此外, 令凝聚体边界处动能密度为零代替令基态能量极小以改进原消除三模耦合矩阵元的方法. 通过这些改进, 同时计算阻尼和频移, 并讨论它们的温度依赖, 所得理论结果都与实验符合. 关键词： 玻色-爱因斯坦凝聚 朗道阻尼和频移 哈特里-福克-博戈留波夫近似 托马斯-费米近似     

Effective Coulomb interaction among electrons in cuprates

Analytical expressions for the charge susceptibility and permittivity of cuprates are obtained using the singlet-correlated conduction band model. The screening parameter caused by interband transitions is refined using experimental plasmon frequencies. A new branch of acoustic plasmons is predicted. The range of values in which acoustic plasmons do not experience Landau damping is determined for wave vectors in the Brillouin zone. Fourier images of the effective Coulomb interaction among charge carriers is calculated for different wave vectors.     

Effects of Landau damping and collision on stimulated Raman scattering with various phase-space distributions

Stimulated Raman scattering (SRS) is one of the main instabilities affecting success of fusion ignition. Here, we study the relationship between Raman growth and Landau damping with various distribution functions combining the analytic formulas and Vlasov simulations. The Landau damping obtained by Vlasov-Poisson simulation and Raman growth rate obtained by Vlasov-Maxwell simulation are anti-correlated, which is consistent with our theoretical analysis quantitatively. Maxwellian distribution, flattened distribution, and bi-Maxwellian distribution are studied in detail, which represent three typical stages of SRS. We also demonstrate the effects of plateau width, hot-electron fraction, hot-to-cold electron temperature ratio, and collisional damping on the Landau damping and growth rate. They gives us a deep understanding of SRS and possible ways to mitigate SRS through manipulating distribution functions to a high Landau damping regime.     

离子回旋共振加热的电子加热

理论分析和实验结果都证明在离子回旋共振加热情况下,电子能直接从波吸收能量,其能量吸收机制是郎道阻尼和飞行时间磁泵阻尼。本文从线性化波的一般理论,导出了电子吸收功率和吸收特征长度的解析表示式,与其他结果进行了比较并做了简短的讨论。     

On the theory of Langmuir waves in a quantum plasma

Nonlinear quantum-mechanical equations are derived for Langmuir waves in an isotropic electron collisionless plasma. A general analysis of dispersion relations is carried out for complex spectra of Langmuir waves and van Kampen waves in a quantum plasma with an arbitrary electron momentum distribution. Quantum nonlinear collisionless Landau damping in Maxwellian and degenerate plasmas is studied. It is shown that collisionless damping of Langmuir waves (including zero sound) occurs in collisionless plasmas due to quantum correction in the Cherenkov absorption condition, which is a purely quantum effect. Solutions to the quantum dispersion equation are obtained for a degenerate plasma.     

Measurement of Landau damping and the evolution to a BGK equilibrium

Linear Landau damping and nonlinear wave-particle trapping oscillations are observed with standing plasma waves in a trapped pure electron plasma. For low wave amplitudes, the measured linear damping rate agrees quantitatively with linear Landau damping theory. At larger amplitudes, the wave initially damps at the Landau rate, then regrows and oscillates, approaching a steady state, as predicted by O'Neil in 1965 [Phys. Fluids 8, 2255 (1965)]]. This BGK equilibrium is observed to decay slowly due to external dissipation.     

Nuclear collective motions in a self-consistent Landau-Vlasov approach

A semiclassical theory of nuclear collective motions based on the Vlasov equation is extended to take into account self-consistency effects provided by the residual interaction. Using separable forces a correlated response function is derived which has several striking similarities with fully quantum results. Explicit spin-orbit terms are also included through a clear WKB correspondence with the quantum response. Finite temperature effects are analysed showing little change in the strength distribution. Through a relaxation time approach two-body collision terms are introduced. This is essential to account for the damping widths of isoscalar quadrupole and octupole giant resonances. However a quite important interplay between self-consistent (Landau damping) and collisional damping is also revealed.     

Influence of Generalized (r, q) Distribution Function on Electrostatic Waves

Non-Maxwellian particle distribution functions possessing high energy tail and shoulder in the profile of distribution function considerably change the damping characteristics of the waves. In the present paper Landau damping of electron plasma (Langmuir) waves and ion-acoustic waves in a hot, isotropic, unmagnetized plasma is studied with the generalized (r,q) distribution function. The results show that for the Langmuir oscillations Landau damping becomes severe as the spectral index r or q reduces. However, for the ion-acoustic waves Landau damping is more sensitive to the ion temperature than the spectral indices.