Dominant Effects of Coulomb Collisions on Maintenance of Landau Damping

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.

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A possible excitation mechanism for a longitudinal wave instability in a plasma by a quasi-static electric field

Journal of Plasma Physics ◽

10.1017/s0022377800018109 ◽

1995 ◽

Vol 53 (2) ◽

pp. 169-184 ◽

Cited By ~ 7

Author(s):

A. N. Kryshtal ◽

V. P. Kuchernko

Keyword(s):

Electric Field ◽

Longitudinal Wave ◽

Landau Damping ◽

Excitation Mechanism ◽

Static Electric Field ◽

Wave Instability ◽

Plasma Parameters ◽

Langmuir Waves ◽

Coulomb Collisions ◽

Ion Acoustic

A specific type of longitudinal wave instability in a plasma due entirely to an external quasi-static electric field E0 is considered for the cases of ion-acoustic and Langmuir waves. The quasi-static time variation of the field leads to a relatively simple mechanism for the development of instability. For frequency ranges typical of ion-acoustic and Langmuir waves dispersion relations are obtained, with Landau damping and pair Coulomb collisions taken into account in addition to E0. The model integral of Bhatnagar, Gross & Krook is used to describe collisions. Two methods for taking account of the influence of the electric field on development of the instability are compared: that of Pines & Schrieffer and that of Brinca and Dysthe. Expressions are obtained for the growth rates in the framework of linear theory. Numerical simulations of both types of instabilities are performed for specific values of the plasma parameters.

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Stopping-power determination for compound by EELS

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100172474 ◽

1994 ◽

Vol 52 ◽

pp. 948-949 ◽

Cited By ~ 1

Author(s):

David C. Joy ◽

Suichu Luo ◽

John R. Dunlap ◽

Dick Williams ◽

Siqi Cao

Keyword(s):

Energy Loss ◽

Electron Energy ◽

Electron Energy Loss Spectroscopy ◽

Materials Science ◽

Average Energy ◽

Stopping Power ◽

Accurate Information ◽

Power Calculation ◽

Coulomb Collisions ◽

Electron Energy Loss

In Physics, Chemistry, Materials Science, Biology and Medicine, it is very important to have accurate information about the stopping power of various media for electrons, that is the average energy loss per unit pathlength due to inelastic Coulomb collisions with atomic electrons of the specimen along their trajectories. Techniques such as photoemission spectroscopy, Auger electron spectroscopy, and electron energy loss spectroscopy have been used in the measurements of electron-solid interaction. In this paper we present a comprehensive technique which combines experimental and theoretical work to determine the electron stopping power for various materials by electron energy loss spectroscopy (EELS ). As an example, we measured stopping power for Si, C, and their compound SiC. The method, results and discussion are described briefly as below.The stopping power calculation is based on the modified Bethe formula at low energy:where Neff and Ieff are the effective values of the mean ionization potential, and the number of electrons participating in the process respectively. Neff and Ieff can be obtained from the sum rule relations as we discussed before3 using the energy loss function Im(−1/ε).

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