The anisotropic plasma fluid stress tensor and its dispersion relation

1986 ◽  
Vol 29 (9) ◽  
pp. 2914-2918
Author(s):  
E. A. Evangelidis ◽  
J. D. Neethling
Keyword(s):  
Dispersion Relation ◽  
Stress Tensor ◽  
Anisotropic Plasma

Oblique whistler-mode propagation in a hot anisotropic plasma

1982 ◽  
Vol 27 (2) ◽  
pp. 199-204 ◽  
Author(s):  
S. S. Sazhin ◽  
E. M. Sazhina
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Plasma Temperature ◽  
Anisotropic Plasma ◽  
Mode Propagation ◽  
Whistler Mode ◽  
Energy Focusing ◽  
Wave Normal ◽  
The Magnetic Field ◽  
Normal Angle

An approximate dispersion relation is obtained for quasi-longitudinal whistler mode propagation in the hot anisotropic plasma. The influence of plasma temperature and anisotropy on whistler energy focusing along the magnetic field and whistler trapping in the magnetospheric ducts are considered for the case when the whistler wave normal angle is not equal to zero.

Effect of Hall current on the instability of an anisotropic plasma jet

1974 ◽  
Vol 12 (1) ◽  
pp. 33-43 ◽  
Author(s):  
K. M. Srivastava
Keyword(s):  
Dispersion Relation ◽  
Plasma Density ◽  
Hall Current ◽  
Surrounding Medium ◽  
Plasma Jet ◽  
Cylindrical Geometry ◽  
Anisotropic Plasma ◽  
Wave Numbers ◽  
Critical Wavenumber

The modified Chew—Goldberger—Low (CGL) equations are applied to the effect of Hall current on the instability of an incompressible plasma jet surrounded by non-conducting, compressible matter. The dispersion relation is obtained and discussed. The following is found. (i) When λ (the ratio of plasma density to the density of surrounding medium) is much greater than unity, the plasma jet is unstable for all wavenumbers for which k* = Küα < [(4R22 – 1)ü(1 + V2α)], where R2 = p∥/p⊥, V2α = H2/4αρ, K = (l2 + α2)½. Also, the jet is unstable for R2 > 1 + V2α. (ii) When λ ≪ 1, the critical wavenumber ratio for the instability to set in is k* < [(V2α + 3R2)ü(1 + V2α)½. Also, the jet becomes unstable for R2 < ⅓. (iii) When either l = 0 or α= 0, we must have R2 > 1 + V2α for instability. It is established that the Hall current has a destabilizing effect for certain wave- numbers. The dispersion relation for the incompressible plasma jet in cylindrical geometry is solved numerically on a computer.

Anisotropic Plasma ChemicalVapor Deposition of Copper Films in Trenches

2003 ◽  
Vol 766 ◽  
Author(s):  
Kosuke Takenaka ◽  
Masao Onishi ◽  
Manabu Takenshita ◽  
Toshio Kinoshita ◽  
Kazunori Koga ◽  
...  
Keyword(s):  
Chemical Vapor Deposition ◽  
Deposition Rate ◽  
Vapor Deposition ◽  
Chemical Vapor ◽  
Anisotropic Plasma ◽  
Bottom Surface ◽  
Chemical Vapor Deposition Method ◽  
Copper Films ◽  
Deposition Method ◽  
Via Holes

AbstractAn ion-assisted chemical vapor deposition method by which Cu is deposited preferentially from the bottom of trenches (anisotropic CVD) has been proposed in order to fill small via holes and trenches. By using Ar + H2 + C2H5OH[Cu(hfac)2] discharges with a ratio H2 / (H2 + Ar) = 83%, Cu is filled preferentially from the bottom of trenches without deposition on the sidewall and top surfaces. The deposition rate on the bottom surface of trenches is experimentally found to increase with decreasing its width.

Gluing Solutions

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Stress Tensor ◽  
Compact Support ◽  
Smooth Solution ◽  
Continuous Solution ◽  
Total Momentum ◽  
Frame Of Reference ◽  
Galilean Transformation ◽  
Hölder Continuous ◽  
Pressure Form ◽  
Original Frame

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor

2011 ◽  
Vol 56 (2) ◽  
pp. 503-508 ◽  
Author(s):  
R. Pęcherski ◽  
P. Szeptyński ◽  
M. Nowak
Keyword(s):  
Stress Tensor ◽  
Elastic Energy ◽  
Yield Condition ◽  
The Third ◽  
Third Invariant ◽  
Lode Angle

An Extension of Burzyński Hypothesis of Material Effort Accounting for the Third Invariant of Stress Tensor The aim of the paper is to propose an extension of the Burzyński hypothesis of material effort to account for the influence of the third invariant of stress tensor deviator. In the proposed formulation the contribution of the density of elastic energy of distortion in material effort is controlled by Lode angle. The resulted yield condition is analyzed and possible applications and comparison with the results known in the literature are discussed.

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