Combined action of phase-mixing and Landau damping causing strong decay of geodesic acoustic modes

2016 ◽  
Vol 115 (1) ◽  
pp. 15001 ◽  
Author(s):  
F. Palermo ◽  
A. Biancalani ◽  
C. Angioni ◽  
F. Zonca ◽  
A. Bottino
2016 ◽  
Vol 23 (11) ◽  
pp. 112115 ◽  
Author(s):  
A. Biancalani ◽  
F. Palermo ◽  
C. Angioni ◽  
A. Bottino ◽  
F. Zonca

2014 ◽  
Vol 81 (1) ◽  
Author(s):  
A. Kanekar ◽  
A. A. Schekochihin ◽  
W. Dorland ◽  
N. F. Loureiro

A linearised kinetic equation describing electrostatic perturbations of a Maxwellian equilibrium in a weakly collisional plasma forced by a random source is considered. The problem is treated as a kinetic analogue of the Langevin equation and the corresponding fluctuation-dissipation relations are derived. The kinetic fluctuation-dissipation relation reduces to the standard “fluid” one in the regime where the Landau damping rate is small and the system has no real frequency; in this case the simplest possible Landau-fluid closure of the kinetic equation coincides with the standard Langevin equation. Phase mixing of density fluctuations and emergence of fine scales in velocity space is diagnosed as a constant flux of free energy in Hermite space; the fluctuation-dissipation relations for the perturbations of the distribution function are derived, in the form of a universal expression for the Hermite spectrum of the free energy. Finite-collisionality effects are included. This work is aimed at establishing the simplest fluctuation-dissipation relations for a kinetic plasma, clarifying the connection between Landau and Hermite-space formalisms, and setting a benchmark case for a study of phase mixing in turbulent plasmas.


1992 ◽  
Vol 4 (7) ◽  
pp. 2052-2061 ◽  
Author(s):  
G. W. Hammett ◽  
W. Dorland ◽  
F. W. Perkins

2015 ◽  
Vol 81 (2) ◽  
Author(s):  
Joseph T. Parker ◽  
Paul J. Dellar

We study Landau damping in the 1+1D Vlasov–Poisson system using a Fourier–Hermite spectral representation. We describe the propagation of free energy in Fourier–Hermite phase space using forwards and backwards propagating Hermite modes recently developed for gyrokinetic theory. We derive a free energy equation that relates the change in the electric field to the net Hermite flux out of the zeroth Hermite mode. In linear Landau damping, decay in the electric field corresponds to forward propagating Hermite modes; in nonlinear damping, the initial decay is followed by a growth phase characterized by the generation of backwards propagating Hermite modes by the nonlinear term. The free energy content of the backwards propagating modes increases exponentially until balancing that of the forward propagating modes. Thereafter there is no systematic net Hermite flux, so the electric field cannot decay and the nonlinearity effectively suppresses Landau damping. These simulations are performed using the fully-spectral 5D gyrokinetics code SpectroGK, modified to solve the 1+1D Vlasov–Poisson system. This captures Landau damping via Hou–Li filtering in velocity space. Therefore the code is applicable even in regimes where phase mixing and filamentation are dominant.


2019 ◽  
Vol 116 (4) ◽  
pp. 1185-1194 ◽  
Author(s):  
Romain Meyrand ◽  
Anjor Kanekar ◽  
William Dorland ◽  
Alexander A. Schekochihin

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.


2016 ◽  
Vol 82 (2) ◽  
Author(s):  
A. A. Schekochihin ◽  
J. T. Parker ◽  
E. G. Highcock ◽  
P. J. Dellar ◽  
W. Dorland ◽  
...  

A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g. drift-wave turbulence driven by ion temperature gradients) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating $\boldsymbol{E}\times \boldsymbol{B}$ flows and of its phase mixing, which is caused by the streaming of the particles along the mean magnetic field and, in a linear problem, would lead to Landau damping. It is found that it is possible to construct a consistent theory in which very little free energy leaks into high velocity moments of the distribution function, rendering the turbulent cascade in the energetically relevant part of the wavenumber space essentially fluid-like. The velocity-space spectra of free energy expressed in terms of Hermite-moment orders are steep power laws and so the free-energy content of the phase space does not diverge at infinitesimal collisionality (while it does for a linear problem); collisional heating due to long-wavelength perturbations vanishes in this limit (also in contrast with the linear problem, in which it occurs at the finite rate equal to the Landau damping rate). The ability of the free energy to stay in the low velocity moments of the distribution function is facilitated by the ‘anti-phase-mixing’ effect, whose presence in the nonlinear system is due to the stochastic version of the plasma echo (the advecting velocity couples the phase-mixing and anti-phase-mixing perturbations). The partitioning of the wavenumber space between the (energetically dominant) region where this is the case and the region where linear phase mixing wins its competition with nonlinear advection is governed by the ‘critical balance’ between linear and nonlinear time scales (which for high Hermite moments splits into two thresholds, one demarcating the wavenumber region where phase mixing predominates, the other where plasma echo does).


1974 ◽  
Vol 29 (12) ◽  
pp. 1863-1873
Author(s):  
G. Ecker ◽  
G. Frömling

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.


2013 ◽  
Vol 20 (9) ◽  
pp. 092107 ◽  
Author(s):  
C. P. Hung ◽  
A. B. Hassam
Keyword(s):  

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