EFFECTS OF COULOMB COLLISIONS ON LONGITUDINAL PLASMA OSCILLATIONS

1964 ◽  
Vol 42 (1) ◽  
pp. 193-199 ◽  
Author(s):  
T. W. Johnston ◽  
I. P. Shkarofsky
Keyword(s):  
Collision Frequency ◽  
Low Frequency ◽  
Planck Equation ◽  
Landau Damping ◽  
Ion Temperature ◽  
Coulomb Collisions ◽  
Coulomb Damping ◽  
Specific Heats ◽  
Longitudinal Plasma ◽  
Ion Collision

This theoretical analysis shows that the Fokker–Planck equation can be applied to obtain identical wavelength-dependent (k2) damping as previously derived from the much more complicated Liouville equation approach. It is also noted that electron (ω ~ ωp) and ion (ω ~ Ωp) oscillations are only slightly damped by Coulomb collisions. The k2 dependent damping is difficult to observe for electron oscillations but perhaps not for ion oscillations (where it is the only Coulomb damping) if Landau damping effects do not obscure the observation and if the electron temperature is not too high compared with the ion temperature. The electron and ion oscillations are effectively free (the ratio of specific heats γ multiplying the temperature is effectively 3). The low-frequency sound oscillations [Formula: see text] are isothermal for electrons (γ = 1) and can be adiabatic (γ = 5/3) or free (γ = 3) for ions as the ion–ion collision frequency is much more or less than ω.

New low-frequency waves and negative mass instability in dusty plasmas

2010 ◽  
Vol 76 (6) ◽  
pp. 929-937
Author(s):  
D. P. RESENDES ◽  
R. BINGHAM ◽  
S. MOTA ◽  
V. N. TSYTOVICH
Keyword(s):  
Electron Temperature ◽  
Free Path ◽  
Collision Frequency ◽  
Low Frequency ◽  
Mean Free Path ◽  
Sound Waves ◽  
Ion Temperature ◽  
Plasma Particle ◽  
Charging Mode ◽  
Dust Charging

AbstractLow-frequency dusty plasma waves with frequencies much smaller than the frequency of charging collisions of plasma particles with dust particles are considered taking into account elastic and charging collisions of plasma particles with dust and neutrals. The usual dust sound waves with an upper frequency equal to the dust plasma frequency are found to be present only for wavelengths much smaller than the plasma particle effective mean free path due to the effective collision frequency. The effectice collision frequency is found to be inversely proportional to the square root of the product of the charging frequency and the frequency of particle momentum losses, involving processes due to elastic plasma particle–dust collisions and collisions with neutrals. It is shown that when the wavelength of the wave is much larger than the mean free path for effective collisions, the properties of the waves are different from those considered previously. A negative mass instability is found in this domain of frequencies when the effective mean free path of ions is larger than the effective mean free path of electrons. In the absence of neutrals, this appears to be possible only if the temperature of ions exceeds the electron temperature. This can occur in laboratory experiments and space plasmas but not in plasma-etching experiments. In the absence of instability, a new dust oscillation, a dust charging mode, is found, whose frequency is almost constant over a certain range of wave numbers. It is inversely proportional to the dust mass and charging frequency of the dust. A new dust electron sound wave is found for frequencies less than the frequency of the dust charging mode. The velocity of the dust electron sound wave is determined by the electron temperature but not the ion temperature, as for the usual dust sound waves, with the electron temperature substantially exceeding the ion temperature.

CARTESIAN TENSOR EXPANSION OF THE FOKKER–PLANCK EQUATION

1963 ◽  
Vol 41 (11) ◽  
pp. 1753-1775 ◽  
Author(s):  
I. P. Shkarofsky
Keyword(s):  
Relaxation Times ◽  
Low Frequency ◽  
Planck Equation ◽  
Ion Distribution ◽  
Arbitrary Mass ◽  
Fokker Planck Equation ◽  
Energy Equipartition ◽  
Tensor Part ◽  
Ion Collision ◽  
Fokker Planck

The Fokker–Planck equation is expanded via Cartesian tensors. The results, valid for arbitrary mass ratio, reduce to known expressions for the f0, (isotropic) and f1 (directional) parts of the distribution. The same analysis also gives the relation for the f2 (tensor) part of the distribution. Nonlinear and recoil terms are also investigated. The f0 relation yields relaxation times and energy equipartition times for arbitrary velocity distributions. The ion recoil term is important for low-frequency waves in the electron f1 equation but is negligible in the electron f2 equation. The electron–electron contributions to the f1 and f2 collisional terms are of the same order as the electron–ion contributions. Except for momentum transfer calculations, the ion–ion collisional terms dominate over the ion–electron terms in the ion collision equations referring to the directional (F1) and tensor (F2) parts of the ion distribution.

Effects of temperature and electron collision frequency on the elastic electron–ion collisions in a collisional plasma

2013 ◽  
Vol 79 (5) ◽  
pp. 553-558 ◽  
Author(s):  
YOUNG-DAE JUNG ◽  
WOO-PYO HONG
Keyword(s):  
Phase Shift ◽  
Temperature Effect ◽  
Cross Section ◽  
Collision Frequency ◽  
Electron Collision ◽  
Elastic Electron ◽  
Dynamic Temperature ◽  
Electron Collision Frequency ◽  
Dynamic Screening ◽  
Ion Collision

AbstractThe effects of dynamic temperature and electron–electron collisions on the elastic electron–ion collision are investigated in a collisional plasma. The second-order eikonal analysis and the velocity-dependent screening length are employed to derive the eikonal phase shift and eikonal cross section as functions of collision energy, electron collision frequency, Debye length, impact parameter, and thermal energy. It is interesting to find out that the electron–electron collision effect would be vanished; however, the dynamic temperature effect is included in the first-order approximation. We have found that the dynamic temperature effect strongly enhances the eikonal phase shift as well as the eikonal cross section for electron–ion collision since the dynamic screening increases the effective shielding distance. In addition, the detailed characteristic behavior of the dynamic screening function is also discussed.

Local kinetic analysis of low-frequency electrostatic modes in tokamaks

1991 ◽  
Vol 69 (2) ◽  
pp. 102-106
Author(s):  
A. Hirose
Keyword(s):  
Dispersion Relation ◽  
Kinetic Analysis ◽  
Low Frequency ◽  
Acoustic Mode ◽  
Landau Damping ◽  
Trapped Electrons ◽  
Ion Acoustic ◽  
Transit Frequency

Analysis, based on a local kinetic dispersion relation in the tokamak magnetic geometry incorporating the ion transit frequency and trapped electrons, indicates that modes with positive frequencies are predominant. Unstable "drift"-type modes can have frequencies well above the diamagnetic frequency. They have been identified as the destabilized ion acoustic mode suffering little ion Landau damping even when [Formula: see text].

Electronic transport coefficients in plasmas using an effective energy-dependent electron-ion collision-frequency

2017 ◽  
Vol 24 (10) ◽  
pp. 102701
Author(s):  
G. Faussurier ◽  
C. Blancard ◽  
P. Combis ◽  
A. Decoster ◽  
L. Videau
Keyword(s):  
Electronic Transport ◽  
Collision Frequency ◽  
Transport Coefficients ◽  
Effective Energy ◽  
Energy Dependent ◽  
Ion Collision

scholarly journals Two-temperature magnetohydrodynamic simulations for sub-relativistic active galactic nucleus jets: dependence on the fraction of the electron heating

2020 ◽  
Vol 493 (4) ◽  
pp. 5761-5772 ◽  
Author(s):  
Takumi Ohmura ◽  
Mami Machida ◽  
Kenji Nakamura ◽  
Yuki Kudoh ◽  
Ryoji Matsumoto
Keyword(s):  
Electron Temperature ◽  
X Rays ◽  
Ion Temperature ◽  
Temperature Plasma ◽  
Electron Heating ◽  
Coulomb Collisions ◽  
X Ray ◽  
Jet Plasma ◽  
Magnetohydrodynamic Simulations ◽  
Two Temperature

ABSTRACT We present the results of two-temperature magnetohydrodynamic simulations of the propagation of sub-relativistic jets of active galactic nuclei. The dependence of the electron and ion temperature distributions on the fraction of electron heating, fe, at the shock front is studied for fe = 0, 0.05, and 0.2. Numerical results indicate that in sub-relativistic, rarefied jets, the jet plasma crossing the terminal shock forms a hot, two-temperature plasma in which the ion temperature is higher than the electron temperature. The two-temperature plasma expands and forms a backflow referred to as a cocoon, in which the ion temperature remains higher than the electron temperature for longer than 100 Myr. Electrons in the cocoon are continuously heated by ions through Coulomb collisions, and the electron temperature thus remains at Te > 109 K in the cocoon. X-ray emissions from the cocoon are weak because the electron number density is low. Meanwhile, X-rays are emitted from the shocked intracluster medium (ICM) surrounding the cocoon. Mixing of the jet plasma and the shocked ICM through the Kelvin–Helmholtz instability at the interface enhances X-ray emissions around the contact discontinuity between the cocoon and shocked ICM.

scholarly journals The stimulated emission of Bremsstrahlung in a fully ionized plasma

1988 ◽  
Vol 6 (3) ◽  
pp. 513-523 ◽  
Author(s):  
W. B. Thompson
Keyword(s):  
Electron Distribution ◽  
Collision Frequency ◽  
Stimulated Emission ◽  
Radiation Frequency ◽  
Numerical Factor ◽  
Gain Rate ◽  
Ion Collision

The process of induced bremsstrahlung is studied and it is found that anisotropy in the electron distribution can lead to the amplification of radiation. The gain rate is ,Λ where ν is the electron-ion collision frequency, ωp and ω the plasma and radiation frequency, and Λ a numerical factor which is positive only for anisotropic distributions.

scholarly journals An introductory guide to fluid models with anisotropic temperatures. Part 2. Kinetic theory, Padé approximants and Landau fluid closures

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
P. Hunana ◽  
A. Tenerani ◽  
G. P. Zank ◽  
M. L. Goldstein ◽  
G. M. Webb ◽  
...  
Keyword(s):  
Kinetic Theory ◽  
Fourth Order ◽  
Low Frequency ◽  
Padé Approximants ◽  
Landau Damping ◽  
Order Moment ◽  
Fluid Models ◽  
Frequency Limit ◽  
Long Wavelength ◽  
Pade Approximants

In Part 2 of our guide to collisionless fluid models, we concentrate on Landau fluid closures. These closures were pioneered by Hammett and Perkins and allow for the rigorous incorporation of collisionless Landau damping into a fluid framework. It is Landau damping that sharply separates traditional fluid models and collisionless kinetic theory, and is the main reason why the usual fluid models do not converge to the kinetic description, even in the long-wavelength low-frequency limit. We start with a brief introduction to kinetic theory, where we discuss in detail the plasma dispersion function $Z(\unicode[STIX]{x1D701})$ , and the associated plasma response function $R(\unicode[STIX]{x1D701})=1+\unicode[STIX]{x1D701}Z(\unicode[STIX]{x1D701})=-Z^{\prime }(\unicode[STIX]{x1D701})/2$ . We then consider a one-dimensional (1-D) (electrostatic) geometry and make a significant effort to map all possible Landau fluid closures that can be constructed at the fourth-order moment level. These closures for parallel moments have general validity from the largest astrophysical scales down to the Debye length, and we verify their validity by considering examples of the (proton and electron) Landau damping of the ion-acoustic mode, and the electron Landau damping of the Langmuir mode. We proceed by considering 1-D closures at higher-order moments than the fourth order, and as was concluded in Part 1, this is not possible without Landau fluid closures. We show that it is possible to reproduce linear Landau damping in the fluid framework to any desired precision, thus showing the convergence of the fluid and collisionless kinetic descriptions. We then consider a 3-D (electromagnetic) geometry in the gyrotropic (long-wavelength low-frequency) limit and map all closures that are available at the fourth-order moment level. In appendix A, we provide comprehensive tables with Padé approximants of $R(\unicode[STIX]{x1D701})$ up to the eighth-pole order, with many given in an analytic form.

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