scholarly journals Resonance, Particle Trapping, and Landau Damping in Finite Amplitude Obliquely Propagating Waves

1972 ◽  
Vol 15 (11) ◽  
pp. 2006 ◽  
Author(s):  
P. J. Palmadesso
Keyword(s):  
Finite Amplitude ◽  
Landau Damping ◽  
Particle Trapping ◽  
Propagating Waves ◽  
Resonance Particle

Asymptotic Theory of Nonlinear Landau Damping and Particle Trapping in Waves of Finite Amplitude

1998 ◽  
Vol 81 (26) ◽  
pp. 5824-5827 ◽  
Author(s):  
M. V. Medvedev ◽  
P. H. Diamond ◽  
M. N. Rosenbluth ◽  
V. I. Shevchenko
Keyword(s):  
Asymptotic Theory ◽  
Finite Amplitude ◽  
Landau Damping ◽  
Particle Trapping ◽  
Nonlinear Landau Damping

Higher order approximations in the theory of longitudinal plasma oscillations. II

1970 ◽  
Vol 4 (4) ◽  
pp. 819-824
Author(s):  
F. Einaudi ◽  
W. I. Axford
Keyword(s):  
Distribution Function ◽  
Time Scale ◽  
Asymptotic Series ◽  
Finite Amplitude ◽  
Landau Damping ◽  
Multiple Time ◽  
Complex Frequency ◽  
Previous Note ◽  
Non Linear ◽  
Independent Variable

In this note we comment and extend the results of a previous analysis in which the non-linear behaviour of one-dimensional electrostatic oscillations in a homogeneous, unbounded, collisionless and fully ionized plasma was considered. The evolution of a monochromatic wave of small, but finite amplitude is studied by expanding the dependent variables as well as the independent variable tin the form of asymptotic series; an ordering parameter e proportional to the initial amplitude of the electric field is introduced. The expansion of the independent variable in such a series allows us to eliminate secular terms from the part of the distribution function which does not depend on the free-streaming terms. This, in turn, allows us to determine corrections to the complex frequency a. Results of a previous note on non-linear Landau damping for an initially Maxwellian. distribution function are confirmed, but it is indicated that they apply to values of time up to a value τ1 rather than for all times. One can proceed to larger values of time in the manner of the multiple time-scale method. In particular it is found that the Landau damping is increased with respect to the linear value only initially during the first time scale.

Instabilities of the upstream meniscus in directional viscous fingering

1996 ◽  
Vol 312 ◽  
pp. 125-148 ◽  
Author(s):  
Sylvain Michalland ◽  
Marc Rabaud ◽  
Yves Couder
Keyword(s):  
Viscous Fluid ◽  
Viscous Fingering ◽  
Finite Amplitude ◽  
Dynamical Behaviour ◽  
Solid Surfaces ◽  
Time Dependent ◽  
Narrow Gap ◽  
Propagating Waves ◽  
Spatio Temporal ◽  
Set Up

New instabilities affecting the meniscus of a viscous fluid are presented. They occur in an experimental set-up introduced previously by Rabaud et al. (1990) in which a small quantity of a viscous fluid is placed in the narrow gap between two rotating cylinders. In this geometry the downstream meniscus located in the region where the two solid surfaces move away from each other is known to be unstable and to exhibit directional viscous fingering. In the present article it is shown that the upstream meniscus can also be unstable. Two types of instabilities are observed. In the first supercritical transition the front becomes time-dependent with either standing or propagating waves. In a second transition, which is subcritical, parallel fingers of finite amplitude are formed. The various types of spatio-temporal dynamical behaviour are discussed.

Finite Amplitude Effects on Landau Damping and Diminished Transportation of Trapped Electrons

2014 ◽  
Vol 83 (7) ◽  
pp. 074502
Author(s):  
Chang Woo Myung ◽  
Im Hee Won ◽  
Ho Young Kim ◽  
Jeong-Soo Lee ◽  
Gun Su Yun ◽  
...  
Keyword(s):  
Finite Amplitude ◽  
Landau Damping ◽  
Trapped Electrons
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