Collisional damping of Langmuir waves in the collisionless limit

Auerbach, Steven P.

doi:10.1063/1.861801

Cited by 31 publications

(35 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This fast collision time can act to ruin plateau formation in the electron velocity distribution function and continuously force the electron distribution function back to a Maxwellian form. This collisional process has been quantified for plateau formation owing to the electron Landau damping of Langmuir waves [Zakharov and Karpman, 1963;Denavit et al, 1968;Johnston, 1971;Auerbach, 1977;Bilato and Brambilla, 2008]. Similar arguments about collisions have been made for the electron Landau damping of Alfvén waves [Potapenko et al, 2000] and of nonlinearly steepened Alfvén waves [Medvedev et al, 1998;Medvedev, 1999].…”

Section: Introductionmentioning

confidence: 72%

Electron-ion Coulomb scattering and the electron Landau damping of Alfvén waves in the solar wind

Borovsky

Gary

2011

J. Geophys. Res.

View full text Add to dashboard Cite

[1] All Alfvén waves in the solar wind have parallel electric fields, which enable Landau damping. The Alfvén waves' Landau resonate with very low energy electrons; low-energy electrons are easily trapped in the Alfvén waves, and at low energies electron-ion Coulomb scattering is very rapid. Analytic fluid theory and numerical solutions to the linear Vlasov equation are used to determine the properties of Alfvén waves (and kinetic Alfvén waves) in the solar wind. Electrostatic potentials associated with the waves' parallel electric fields are found to be relatively large. Owing to the large potentials, electrons over a broad range of velocities interact with the wave to produce Landau damping. Because of this broad range, linear Vlasov theory is invalid and the Landau-damping rates computed via linear Vlasov theory may not be accurate. Electron velocity diffusion owed to electron-ion Coulomb scattering is analyzed. Electron diffusion times in the Alfvén wave Landau resonance are calculated and are found to be faster than wave periods and much faster than Landau-damping time scales. Coulomb collisions should prevent the electron distribution function from evolving away from a Maxwellian form, and thereby Coulomb collisions act to maintain Landau damping (although at a rate different than that given by linear Vlasov theory). Some complications of this Landau-damping picture arise from the interplanetary electric field competing with the Alfvén wave parallel electric fields and from ion beams near the Landau resonance.Citation: Borovsky, J. E., and S. P. Gary (2011), Electron-ion Coulomb scattering and the electron Landau damping of Alfvén waves in the solar wind,

show abstract

Section: Introductionmentioning

confidence: 72%

Electron-ion Coulomb scattering and the electron Landau damping of Alfvén waves in the solar wind

Borovsky

Gary

2011

J. Geophys. Res.

View full text Add to dashboard Cite

show abstract

“…The influence of weak collisions on linear Landau damping has previously been considered by Ref. [6]. Basically the result is that the linear damping rate is unaffected by the collisions, although the distribution function is significantly affected in the resonance region.…”

Section: G Brodinmentioning

confidence: 95%

“…In particular, both linear (e.g., Refs. [4][5][6]) and nonlinear (e.g., Refs. [7][8][9][10][11][12][13][14][15][16]) Landau damping have been discussed extensively in the literature.…”

Section: G Brodinmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Landau Damping

Brodin

1997

Phys. Rev. Lett.

View full text Add to dashboard Cite

We present a new description of nonlinear Landau damping, applicable to wave propagation in a weakly collisional as well as a collisionless plasma. We derive a set of equations with a simple energy conservation law which is useful for understanding the evolution of the system. A numerical investigation shows significant differences as compared to previous studies. The reasons for the deviations from the earlier results are explained. [S0031-9007 (97)02399-5] PACS numbers: 52.35.Mw, 52.25.Dg, 52.35.Sb Wave-particle interaction processes are of fundamental interest in plasma physics. Besides the purely theoretical interest, they are important for many applications-for example, for the supplementary heating of magnetically confined fusion plasmas [1], for the absorption of laser radiation in inertial fusion experiments [2], and for particle acceleration by means of plasma accelerators [3]. In particular, both linear (e.g., Refs. [4-6]) and nonlinear (e.g., Refs. [7-16]) Landau damping have been discussed extensively in the literature. The problem of nonlinear Landau damping has been investigated for more than two decades, experimentally [7], analytically [8], with computer aided calculations [9], and with intermediate approaches [10]. Furthermore, the presentation given in recent textbooks (e.g., ) agrees with the early results. Basically, the picture of nonlinear Landau damping is the following: If the bounce frequency v B of the particles trapped in the wave field is comparable to the linear damping rate g L , the initial decay of the wave amplitude will soon turn into nonlinear oscillations around a value somewhat lower than the initial value. After a few oscillations the amplitude will approach a steady value, and the wave becomes a Bernstein-GreekKruskal (BGK) mode (e.g., Refs. [12,14]). However, our picture differs significantly: According to our calculations the amplitude never settles to a steady value, although the nonlinearities obstruct the linear decay. Instead the energy of the resonant particles diffuses slowly into higher harmonics. Furthermore, a flat distribution of the trapped particles corresponding to the BGK modes never develops. The discrepancy with previous analytical work [8] is due to a lack of self-consistency in that paper. In particular, the neglect of the dynamics associated with the trappinguntrapping transitions of particles is crucial. The calculations made in Ref.[10] are self-consistent on the other hand, but use the assumption that the amplitude of the electric field deviates only slightly from a final steady value. This is fulfilled neither in experiments [7] nor in our calculations for any value of g L ͞v B . Furthermore, previous numerical work starting from the basic equations [9] has used a too low resolution [17] to describe the excitation of high harmonics of resonant particle oscillations. Finally, experimental results [7] show an average decay of the large amplitude waves not predicted by previous theories [18], but in agreement with the results of the present Letter.From ...

show abstract

“…This effect on electron Landau damping in homogeneous plasmas was amply discussed in Ref. 8. In this case, only one pole exists in the perturbed distribution function and the analysis of the weak collision effect is very simple.…”

Section: Introductionmentioning

confidence: 92%

The Coulomb scattering effect on trapped particles bounce-resonance dissipation in magnetized toroidal plasmas

et al. 1999

View full text Add to dashboard Cite

The solution of the Vlasov equation with a simplified Fokker-Planck collision operator is presented for axially symmetric tokamak plasmas with a circular cross section of magnetic surfaces. The analytical expression for the parallel component of the dielectric permittivity tensor of trapped particles is obtained. This expression is used for theoretical analyses of the collision effect on the bounce-resonance wave dissipation. Conditions for a collisionless description of radio-frequency ͑rf͒ oscillations are found. This dielectric tensor components can be used for computer calculations of the rf field structure and the rf dissipated power related to trapped electrons in tokamak plasmas.

show abstract

Collisional damping of Langmuir waves in the collisionless limit

Cited by 31 publications

References 11 publications

Electron-ion Coulomb scattering and the electron Landau damping of Alfvén waves in the solar wind

Electron-ion Coulomb scattering and the electron Landau damping of Alfvén waves in the solar wind

Nonlinear Landau Damping

The Coulomb scattering effect on trapped particles bounce-resonance dissipation in magnetized toroidal plasmas

Contact Info

Product

Resources

About