Landau damping
Landau damping is calculated using real variables, clarifying the physical mechanism.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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Transverse Wakefield Damping (BNS - Landau Damping) in the SLC Linac
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Seeman, J.↗
ENERGY DISSIPATION AND LANDAU DAMPING IN TWO- AND THREE-DIMENSIONAL PLASMA TURBULENCE
Plasma turbulence is ubiquitous in space and astrophysical plasmas, playing an important role in plasma energization, but the physical mechanisms leading to dissipation of the turbulent energy remain to be definitively identified. Kinetic simulations in two dimensions (2D) have been extensively used to study the dissipation process. How the limitation to 2D affects energy dissipation remains unclear. This work provides a model of comparison between two- and three-dimensional (3D) plasma turbulence using gyrokinetic simulations; it also explores the dynamics of distribution functions during the dissipation process. It is found that both 2D and 3D nonlinear gyrokinetic simulations of a low-beta plasma generate electron velocity-space structures with the same characteristics as that of the linear Landau damping of Alfvén waves in a 3D linear simulation. The continual occurrence of the velocity-space structures throughout the turbulence simulations suggests that the action of Landau damping may be responsible for the turbulent energy transfer to electrons in both 2D and 3D, and makes possible the subsequent irreversible heating of the plasma through collisional smoothing of the velocity-space fluctuations. Although, in the 2D case where variation along the equilibrium magnetic field is absent, it may be expected that Landau damping is not possible, a common trigonometric factor appears in the 2D resonant denominator, leaving the resonance condition unchanged from the 3D case. The evolution of the 2D and 3D cases is qualitatively similar. However, quantitatively, the nonlinear energy cascade and subsequent dissipation is significantly slower in the 2D case.
79 ASTRONOMY AND ASTROPHYSICS↗
Landau damping effects and evolutions of energy spread in small isochronous ring
This paper presents the Landau damping effects on the microwave instability of a coasting long bunch in an isochronous ring due to finite energy spread and emittance. Our two-dimensional (2D) dispersion relation gives more accurate predictions of the microwave instability growth rates of short-wavelength perturbations than the conventional 1D formula. The long-term evolution of energy spread is also studied by measurements and simulations.
Li, Yingjie↗
Investigation of the validity of quasilinear theory for electron Landau damping in a tokamak using a broad-band wave effect
The quasilinear diffusion coefficient assuming a constant magnetic field along the electron orbit is widely used to describe electron Landau damping of waves in a tokamak where the magnitude of the magnetic field varies on a flux surface. To understand the impact of violating the constant magnetic field assumption, we introduce the effect of a broad-bandwidth wave spectrum which has been used in the past to validate quasilinear theory for the fast decorrelation process between resonances. By the reevaluation of the diffusion coefficient through the level of the phase integral for the tokamak geometry with the broad-band wave effect included, we identify the three acceptable errors for the use of the quasilinear diffusion coefficient.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Landau Damping and Debye Shielding
Landau damping in collisionless plasma - Debye shielding of electrostatic plasma perturbation
ELECTROSTATIC SHIELDING↗
Landau damping in space plasmas
The Landau damping of electrostatic Langmuir waves and ion-acoustic waves in a hot, isotropic, nonmagnetized, generalized Lorentzian plasma is analyzed using the modified plasma dispersion function. Numerical solutions for the real and imaginary parts of the wave frequency omega sub 0 - (i)(gamma) have been obtained as a function of the normalized wave number (k)(lambda sub D), where lambda sub D is the electron Debye length. For both particle distributions the electrostatic modes are found to be strongly damped at short wavelengths. At long wavelengths, this damping becomes less severe, but the attenuation of Langmuir waves is much stronger for a generalized Lorentzian plasma than for a Maxwellian plasma. It is concluded that Landau damping of ion-acoustic waves is only slightly affected by the presence of a high energy tail, but is strongly dependent on the ion temperature.
Thorne, Richard M.↗
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Landau damping
Section 2.5.8 of the Handbook of Accelerator Physics and Engineering on Landau damping is rewritten. An solvable example is first given to demonstrate the interplay between Landau damping and decoherence. This example is an actual one when the beam oscillatory motion is driven by a wake force. The dispersion relation is derived and its implication on Landau damping is illustrated. The rest of the article touches on the Landau damping of transverse and longitudinal beam oscillations. The stability criteria are given for a bunched beam and the changes of the criteria when the beam is lengthened and becomes unbunched.
43 PARTICLE ACCELERATORS↗
Nonlinear Landau damping and Alfven wave dissipation
Nonlinear Landau damping has been often suggested to be the cause of the dissipation of Alfven waves in the solar wind as well as the mechanism for ion heating and selective preacceleration in solar flares. We discuss the viability of these processes in light of our theoretical and numerical results. We present one-dimensional hybrid plasma simulations of the nonlinear Landau damping of parallel Alfven waves. In this scenario, two Alfven waves nonresonantly combine to create second-order magnetic field pressure gradients, which then drive density fluctuations, which in turn drive a second-order longitudinal electric field. Under certain conditions, this electric field strongly interacts with the ambient ions via the Landau resonance which leads to a rapid dissipation of the Alfven wave energy. While there is a net flux of energy from the waves to the ions, one of the Alfven waves will grow if both have the same polarization. We compare damping and growth rates from plasma simulations with those predicted by Lee and Volk (1973), and also discuss the evolution of the ambient ion distribution. We then consider this nonlinear interaction in the presence of a spectrum of Alfven waves, and discuss the spectrum's influence on the growth or damping of a single wave. We also discuss the implications for wave dissipation and ion heating in the solar wind.
Vinas, Adolfo F.↗
Test particle study of Landau damping of steepening magnetosonic waves
A test particle study of Landau damping of steepening large-amplitude magnetosonic waves is made. Motions of test particles in a model of a steepening large-amplitude magnetosonic wave are traced. The kinetic energy change of the ensemble of test particles is computed to estimate the effective Landau damping rate of the magnetosonic wave. The numerical results are compared with the linear kinetic theory of Landau damping and interpreted in terms of a simple physical picture for particle trapping.
Matsumoto, H.↗
Landau damping in a turbulent setting
To address the problem of Landau damping in kinetic turbulence, we consider the forcing of the linearized Vlasov equation by a stationary random source. It is found that the time-asymptotic density response is dominated by resonant particle interactions that are synchronized with the source. The energy consumption of this response is calculated, implying an effective damping rate, which is the main result of this paper. Evaluating several cases, it is found that the effective damping rate can differ from the Landau damping rate in magnitude and also, remarkably, in sign. A limit is demonstrated in which the density and current become phase-locked, which causes the effective damping to be negligible; this result offers a fresh perspective from which to reconsider recent observations of kinetic turbulence satisfying critical balance.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Landau damping effects on dust-acoustic solitary waves in a dusty negative-ion plasma
The nonlinear theory of dust-acoustic waves (DAWs) with Landau damping is studied in an unmagnetized dusty negative-ion plasma in the extreme conditions when the free electrons are absent. The cold massive charged dusts are described by fluid equations, whereas the two-species of ions (positive and negative) are described by the kinetic Vlasov equations. A Korteweg-de Vries (KdV) equation with Landau damping, governing the dynamics of weakly nonlinear and weakly dispersive DAWs, is derived following Ott and Sudan [Phys. Fluids 12, 2388 (1969)]. It is shown that for some typical laboratory and space plasmas, the Landau damping (and the nonlinear) effects are more pronounced than the finite Debye length (dispersive) effects for which the KdV soliton theory is not applicable to DAWs in dusty pair-ion plasmas. The properties of the linear phase velocity, solitary wave amplitudes (in presence and absence of the Landau damping) as well as the Landau damping rate are studied with the effects of the positive ion to dust density ratio (μ{sub pd}) as well as the ratios of positive to negative ion temperatures (σ) and masses (m)
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The first radial-mode Lorentzian Landau damping of dust acoustic space-charge waves
The dispersion properties and the first radial-mode Lorentzian Landau damping of a dust acoustic space-charge wave propagating in a cylindrical waveguide dusty plasma which contains nonthermal electrons and ions are investigated by employing the normal mode analysis and the method of separation of variables. It is found that the frequency of dust acoustic space-charge wave increases as the wave number increases as well as the radius of cylindrical plasma does. However, the nonthermal property of the Lorentzian plasma is found to suppress the wave frequency of the dust acoustic space-charge wave. The Landau damping rate of the dust acoustic space-charge wave is derived in a cylindrical waveguide dusty plasma. The damping of the space-charge wave is found to be enhanced as the radius of cylindrical plasma and the nonthermal property increase. The maximum Lorentzian Landau damping rate is also found in a cylindrical waveguide dusty plasma. The variation of the wave frequency and the Landau damping rate due to the nonthermal character and geometric effects are also discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Landau damping of auroral hiss
Auroral hiss is observed to propagate over distances comparable to an Earth radius from its source in the auroral oval. The role of Landau damping is investigated for upward propagating auroral hiss. By using a ray tracing code and a simplified model of the distribution function, the effect of Landau damping is calculated for auroral hiss propagation through the environment around the auroral oval. Landau damping is found to be the likely mechanism for explaining some of the one-sided auroral hiss funnels observed by Dynamics Explorer 1. It is also found that Landau damping puts a lower limit on the wavelength of auroral hiss. Poleward of the auroral oval, Landau damping is found in a typical case to limit omega/k(sub parallel) to values of 3.4 x 10(exp 4) km/s or greater, corresponding to resonance energies of 3.2 keV or greater and wavelengths of 2 km or greater. For equatorward propagation, omega/k(sub parallel) is limited to values greater than 6.8 x 10(exp 4) km/s, corresponding to resonance energies greater than 13 keV and wavelengths greater than 3 km. Independent estimates based on measured ratios of the magnetic to electric field intensity also show that omega/k(sub parallel) corresponds to resonance energies greater than 1 keV and wavelengths greater than 1 km. These results lead to the difficulty that upgoing electron beams sufficiently energetic to directly generate auroral hiss of the inferred wavelength are not usually observed. A partial transmission mechanism utilizing density discontinuities oblique to the magnetic field is proposed for converting auroral hiss to wavelengths long enough to avoid damping of the wave over long distances. Numerous reflections of the wave in an upwardly flared density cavity could convert waves to significantly increased wavelengths and resonance velocities.
Morgan, D. D.↗
Landau damping of the dust-acoustic surface waves in a Lorentzian dusty plasma slab
Landau damping of a dust-acoustic surface wave propagating at the interfaces of generalized Lorentzian dusty plasma slab bounded by a vacuum is kinetically derived as the surface wave displays the symmetric and the anti-symmetric mode in a plasma slab. In the limiting case of small scaled wave number, we have found that Landau damping is enhanced as the slab thickness is increased. In particular, the damping of anti-symmetric mode is much stronger for a Lorentzian plasma than for a Maxwellian plasma. We have also found that the damping is more affected by superthermal particles in a Lorentzian plasma than by a Maxwellian plasma for both of the symmetric and the anti-symmetric cases. The variations of Landau damping with various parameters are also discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Three-dimensional Simulations and Spacecraft Observations of Sub-ion Scale Turbulence in the Solar Wind: Influence of Landau Damping
Three-dimensional nonlinear finite Larmor radius (FLR)–Landau fluid simulations, which include some small-scale (k{sub ⊥}ρ{sub i}≳1) kinetic effects, are performed to explore the nature of the sub-ion scale turbulence in the solar wind and to investigate the role of Landau damping and FLR corrections. The resulting steady-state magnetic power spectrum in the dispersive range display exponents that vary within a range of values compatible with statistical results reported from in situ spacecraft measurements of solar wind turbulence as well as from gyrokinetic simulations. The spectral slopes are shown to depend on the strength of the nonlinear effects and on the scale at which turbulent fluctuations are driven in the simulations. The influence of Landau damping is addressed by comparison with simulations where the double-adiabatic closure is imposed. The role of FLR corrections is also analyzed. Comparison with in situ observations in the solar wind are performed to enlighten the influence of the fluctuations power at different scales on the spectral slopes in the sub-ion range. Using diagnosis of both magnetic compressibility and frequency-wavenumber spectra, it is shown that in spite of the evidence of the presence of fast-magnetosonic modes, the magnetic energy is mostly distributed around the kinetic Alfvén waves and the slow modes, in agreement with solar wind measurements. The observed large broadening about the linear dispersion relations may reflect the presence of coherent structures.
79 ASTRONOMY AND ASTROPHYSICS↗