Collisionless Plasma Oscillations, Their Residual Presentation and the Mechanism of Landau Damping

The description of the electron oscillations of a collisionless plasma by the usual residual presentation is insufficient in the initial phase of time development and for perturbations of small velocity spread. We derived criteria for the number of residual terms which have to be taken into account and obtain analytic expressions for the remaining integral. Decomposing the initial perturbation into velocity beams we show that Landau damping is due to phase mixing caused by free streaming of particle beams modified through the response of the main plasma body.

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Fluidization of collisionless plasma turbulence

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1813913116 ◽

2019 ◽

Vol 116 (4) ◽

pp. 1185-1194 ◽

Cited By ~ 13

Author(s):

Romain Meyrand ◽

Anjor Kanekar ◽

William Dorland ◽

Alexander A. Schekochihin

Keyword(s):

Solar Wind ◽

Power Law ◽

Collisionless Plasma ◽

Plasma Turbulence ◽

Magnetized Plasma ◽

Landau Damping ◽

Astrophysical Plasmas ◽

Phase Mixing ◽

Fluid Turbulence ◽

Collisionless Plasmas

In a collisionless, magnetized plasma, particles may stream freely along magnetic field lines, leading to “phase mixing” of their distribution function and consequently, to smoothing out of any “compressive” fluctuations (of density, pressure, etc.). This rapid mixing underlies Landau damping of these fluctuations in a quiescent plasma—one of the most fundamental physical phenomena that makes plasma different from a conventional fluid. Nevertheless, broad power law spectra of compressive fluctuations are observed in turbulent astrophysical plasmas (most vividly, in the solar wind) under conditions conducive to strong Landau damping. Elsewhere in nature, such spectra are normally associated with fluid turbulence, where energy cannot be dissipated in the inertial-scale range and is, therefore, cascaded from large scales to small. By direct numerical simulations and theoretical arguments, it is shown here that turbulence of compressive fluctuations in collisionless plasmas strongly resembles one in a collisional fluid and does have broad power law spectra. This “fluidization” of collisionless plasmas occurs, because phase mixing is strongly suppressed on average by “stochastic echoes,” arising due to nonlinear advection of the particle distribution by turbulent motions. Other than resolving the long-standing puzzle of observed compressive fluctuations in the solar wind, our results suggest a conceptual shift for understanding kinetic plasma turbulence generally: rather than being a system where Landau damping plays the role of dissipation, a collisionless plasma is effectively dissipationless, except at very small scales. The universality of “fluid” turbulence physics is thus reaffirmed even for a kinetic, collisionless system.

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Landau Damping and the Velocity Fourier Transform of the Initial Perturbation

The Physics of Fluids ◽

10.1063/1.1761508 ◽

1966 ◽

Vol 9 (1) ◽

pp. 134 ◽

Cited By ~ 4

Author(s):

J. Denavit

Keyword(s):

Fourier Transform ◽

Initial Perturbation ◽

Landau Damping

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Interplay between intermittency and dissipation in collisionless plasma turbulence

Journal of Plasma Physics ◽

10.1017/s0022377819000357 ◽

2019 ◽

Vol 85 (3) ◽

Cited By ~ 9

Author(s):

Alfred Mallet ◽

Kristopher G. Klein ◽

Benjamin D. G. Chandran ◽

Daniel Grošelj ◽

Ian W. Hoppock ◽

...

Keyword(s):

Narrow Range ◽

Collisionless Plasma ◽

Plasma Turbulence ◽

Landau Damping ◽

Intermittent Turbulence ◽

Stochastic Heating ◽

Overall Efficiency

We study the damping of collisionless Alfvénic turbulence in a strongly magnetised plasma by two mechanisms: stochastic heating (whose efficiency depends on the local turbulence amplitude $\unicode[STIX]{x1D6FF}z_{\unicode[STIX]{x1D706}}$ ) and linear Landau damping (whose efficiency is independent of $\unicode[STIX]{x1D6FF}z_{\unicode[STIX]{x1D706}}$ ), describing in detail how they affect and are affected by intermittency. The overall efficiency of linear Landau damping is not affected by intermittency in critically balanced turbulence, while stochastic heating is much more efficient in the presence of intermittent turbulence. Moreover, stochastic heating leads to a drop in the scale-dependent kurtosis over a narrow range of scales around the ion gyroscale.

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Quantum-like description of modulational and instability and Landau damping in the longitudinal dynamics of high-energy charged-particle beams

10.1063/1.58411 ◽

1999 ◽

Cited By ~ 1

Author(s):

D. Anderson ◽

R. Fedele ◽

V. G. Vaccaro ◽

M. Lisak ◽

A. Berntson ◽

...

Keyword(s):

Charged Particle ◽

High Energy ◽

Landau Damping ◽

Particle Beams ◽

Longitudinal Dynamics ◽

Charged Particle Beams

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Saturation and damping of collisionless plasma wave echoes

Journal of Plasma Physics ◽

10.1017/s0022377800004657 ◽

1969 ◽

Vol 3 (4) ◽

pp. 603-610 ◽

Cited By ~ 8

Author(s):

J. Coste ◽

J. Peyraud

Keyword(s):

Plasma Wave ◽

Collisionless Plasma ◽

Time Interval ◽

Phase Mixing ◽

Mixing Effect ◽

Applied Pulse ◽

Comparable Amplitude

We point out in this paper that when one increases the intensity of the second applied pulse or the time interval between the two pulses, the amplitude of the first echo saturates and multiple echoes of comparable amplitude appear. Moreover, we predict a damping of the echoes which is due to a phase mixing effect; that is collisionless.

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The growth and decay of resonant plasma oscillations excited by a small pulsed dipole

Journal of Plasma Physics ◽

10.1017/s0022377800004335 ◽

1969 ◽

Vol 3 (2) ◽

pp. 227-241 ◽

Cited By ~ 11

Author(s):

J. A. Fejer ◽

Wai-Mao Yu

Keyword(s):

Time Delays ◽

Cyclotron Frequency ◽

Plasma Frequency ◽

Practical Interest ◽

Observation Point ◽

Landau Damping ◽

Plasma Oscillations ◽

Fixed Distance ◽

The Mean ◽

Thermal Speed

The application of integration by the method of stationary phase to resonant oscillations excited by a small pulsed dipole is outlined. Both the growth and the decay of the oscillations near the plasma frequency are determined by this method at a fixed distance from the dipole, first in the absence and then in the presence of an external magnetic field. It is shown that Landau damping must be taken into account in the calculation of the growth but not of the decay. The oscillations are shown to spread out with a speed that is about half the mean thermal speed of electrons.Only the decay, not the growth, of the oscifiations near harmonics of the cyclotron frequency can be calculated by the same method. It is shown, moreover, that the amplitude, calculated for an observation point that moves away with sateffite velocity in an ionospheric environment, is only valid for time delays longer than about a minute. Such a result is therefore of no practical interest because the resonances observed from sateffites only last a few milliseconds. The erroneous nature of using such a result and the need for a different approach, such as that used in earlier work by the first author, are thus demonstrated.

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Landau damping of surface waves at a plasma— vacuum interface

Journal of Plasma Physics ◽

10.1017/s0022377800025629 ◽

1975 ◽

Vol 14 (1) ◽

pp. 179-194 ◽

Cited By ~ 4

Author(s):

P. C. Clemmow ◽

J. N. Elgin

Keyword(s):

Distribution Function ◽

Surface Wave ◽

Dispersion Relation ◽

Fluid Model ◽

Velocity Distribution Function ◽

Landau Damping ◽

Velocity Spread ◽

Equilibrium Distribution Function ◽

Elementary Functions ◽

Surface Wave Dispersion

The exact surface-wave dispersion relation is expressed in terms of elementary functions for a plasma characterized by a ‘resonance’ velocity distribution function. An approximate form of the relation is derived for the case when the thermal velocity spread is much less than c. The pure surface wave obtained by dropping the term responsible for Landau damping is compared with that predicted on the basis of a fluid model of the plasma. The effect of Landau damping is then investigated, both by analytic approximations and by computation. Two branches of the solution to the dispersion relation are found; and it is shown that the surface wave suffers increasingly severe damping as the frequency grows beyond 1/ √ 2 times the plasma frequency. It is argued that qualitatively similar damping would be present were the plasma to have a Maxwellian equilibrium distribution function.

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