scholarly journals Interpretation of dispersion relations for bounded systems

1972 ◽  
Vol 7 (1) ◽  
pp. 13-48 ◽  
Author(s):  
T. D. Rognlien ◽  
S. A. Self
Keyword(s):  
Dispersion Relation ◽  
Boundary Conditions ◽  
Normal Modes ◽  
Plasma Waves ◽  
Axial Current ◽  
Linear Dispersion ◽  
Linear Dispersion Relation ◽  
End Plate ◽  
Cylindrical Form ◽  
Bounded System

A treatment is given of the problem of constructing normal modes for anarbitrarily bounded system from roots of the linear dispersion relationD( ω, k) = 0 for the corresponding infinite or periodically bounded system. For a system described by continuous macroscopic variables, and of general cylindrical form (uniform along an axisz, say), each transverse eigenmode gives rise to a set of axial normal modes constructed from a pair of dominant rootskαz(ω) ofD= 0 satisfying the boundary conditions which are characterized by complex reflexion coefficients for the dominant waves. The implications of the results for the interpretation of experiments on plasma waves and instabilities on finite cylinders are discussed, with particular reference to the effects of end-plate damping and axial current onQ-machines.

scholarly journals Effect of Streaming and Finite Geometry on a Resonance-like Phenomenon in Beam-Plasma Systems

1993 ◽  
Vol 46 (6) ◽  
pp. 807
Author(s):  
J Mukhopadhyay ◽  
K Roy Chowdhury ◽  
A Roy Chowdhury
Keyword(s):  
Dispersion Relation ◽  
Solitary Wave ◽  
Finite Geometry ◽  
Plasma System ◽  
Linear Dispersion ◽  
Ion Density ◽  
Linear Dispersion Relation ◽  
Beam Plasma ◽  
Streaming Velocity ◽  
Bounded System

We have analysed the effect of finite geometry and streaming on a resonance-like phenomenon in a beam-plasma system placed in an infinite magentic field. The resonance-like phenomenon is displayed through a variation of the amplitude of the soliton with respect to a (the ratio of electron to ion density). It is shown that this event is very prominent in the case of an infinite plasma, but for a bounded system the effect is not so significant. As such, an effect of this type will be difficult to observe experimentally unless the dimension of the containment system is considerable. Furthermore, the peak of the resonance varies considerably with the streaming velocity and other parameters of the plasma. The whole phenomenon is crucially dependent on the phase velocity of the solitary wave, whose variation is also considered in detail. Lastly, it is demonstrated that the existence of a resonance-like phenomenon can also be ascertained from an analysis of the linear dispersion relation.

Higher Order Corrections to the Soliton-Velocity and the Linear Dispersion Relation

1979 ◽  
Vol 20 (3-4) ◽  
pp. 486-489 ◽  
Author(s):  
Yuji Kodama ◽  
Tosiya Taniuti
Keyword(s):  
Dispersion Relation ◽  
Higher Order ◽  
Linear Dispersion ◽  
Linear Dispersion Relation ◽  
Higher Order Corrections

Electromagnetic linear dispersion relation for plasma with a drift across magnetic field revisited

2018 ◽  
Vol 25 (10) ◽  
pp. 102109 ◽  
Author(s):  
Takayuki Umeda ◽  
Takuma K. M. Nakamura
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Linear Dispersion ◽  
Linear Dispersion Relation

Linear dispersion relation for a fluid of light in an atomic vapor

2017 ◽  
Author(s):  
Quentin Fontaine ◽  
Agostino Apra ◽  
Giovanni Lerario ◽  
Elisabeth Giacobino ◽  
Alberto Bramati ◽  
...  
Keyword(s):  
Dispersion Relation ◽  
Atomic Vapor ◽  
Linear Dispersion ◽  
Linear Dispersion Relation

scholarly journals Dispersive magnetized waves in the solar wind plasma

2010 ◽  
Vol 77 (3) ◽  
pp. 357-365 ◽  
Author(s):  
B. DASGUPTA ◽  
DASTGEER SHAIKH ◽  
P. K. SHUKLA
Keyword(s):  
Solar Wind ◽  
Dispersion Relation ◽  
Fluid Model ◽  
Phase Speed ◽  
Solar Wind Plasma ◽  
Small Scale ◽  
Linear Dispersion ◽  
Length Scales ◽  
Linear Dispersion Relation ◽  
Two Fluid Model

AbstractWe derive a generalized linear dispersion relation of waves in a strongly magnetized, compressible, homogeneous and isotropic quasi-neutral plasma. Starting from a two-fluid model, describing distinguishable electron and ion fluids, we obtain a six-order linear dispersion relation of magnetized waves that contains effects due to electron and ion inertia, finite plasma beta and angular dependence of phase speed. We investigate propagation characteristics of these magnetized waves in a regime where scale lengths are comparable with electron and ion inertial length scales. This regime corresponds essentially to the solar wind plasma, where length scales, comparable with ion cyclotron frequency, lead to dispersive effects. These scales in conjunction with linear waves present a great deal of challenges in understanding the high-frequency, small-scale dynamics of turbulent fluctuations in the solar wind plasma.

scholarly journals Measurement of the dispersion relation for random surface gravity waves

2015 ◽  
Vol 766 ◽  
pp. 326-336 ◽  
Author(s):  
Tore Magnus A. Taklo ◽  
Karsten Trulsen ◽  
Odin Gramstad ◽  
Harald E. Krogstad ◽  
Atle Jensen
Keyword(s):  
Dispersion Relation ◽  
Gravity Waves ◽  
Laboratory Experiments ◽  
Surface Gravity ◽  
Linear Dispersion ◽  
Random Surface ◽  
Zakharov Equation ◽  
Surface Gravity Waves ◽  
Linear Dispersion Relation ◽  
Jonswap Spectrum

AbstractWe report laboratory experiments and numerical simulations of the Zakharov equation, designed to have sufficient resolution in space and time to measure the dispersion relation for random surface gravity waves. The experiments and simulations are carried out for a JONSWAP spectrum and Gaussian spectra of various bandwidths on deep water. It is found that the measured dispersion relation deviates from the linear dispersion relation above the spectral peak when the bandwidth is sufficiently narrow.

scholarly journals A linear dispersion relation for the hybrid kinetic-ion/fluid-electron model of plasma physics

2016 ◽  
Vol 18 (7) ◽  
pp. 075001 ◽  
Author(s):  
D Told ◽  
J Cookmeyer ◽  
P Astfalk ◽  
F Jenko
Keyword(s):  
Dispersion Relation ◽  
Plasma Physics ◽  
Linear Dispersion ◽  
Electron Model ◽  
Linear Dispersion Relation

Terahertz planar waveguide devices based on graphene

2017 ◽  
Vol 31 (05) ◽  
pp. 1750045
Author(s):  
Yizhe Yuan ◽  
Xiaoyong Guo ◽  
Liqun An ◽  
Wen Xu
Keyword(s):  
Dispersion Relation ◽  
Planar Waveguide ◽  
Theoretical Study ◽  
Transmission Characteristics ◽  
Linear Dispersion ◽  
Linear Dispersion Relation ◽  
Planar Structures ◽  
Waveguide Devices

We present a theoretical study on graphene-semiconductor planar structures. The frequency of the photonic modes in the structure, which can be efficiently tuned via varying the sample parameters, is within the terahertz (THz) bandwidth. Furthermore, it is found that a roughly linear dispersion relation can be obtained for photonic modes in the THz region. Hence, the proposed graphene-semiconductor planar structures can be served as THz waveguide with desirable transmission characteristics.

The Growth of Localized Disturbances in Unstable Flows

1982 ◽  
Vol 49 (2) ◽  
pp. 284-290 ◽  
Author(s):  
A. D. D. Craik
Keyword(s):  
Dispersion Relation ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Computational Effort ◽  
Plane Poiseuille Flow ◽  
Linear Dispersion ◽  
Linear Dispersion Relation ◽  
Practical Possibility ◽  
Proposed Model ◽  
Axis Of Symmetry

The development of three-dimensional localized disturbances in unstable flows was recently studied by Craik [1] using a model dispersion relation. The adoption of such an approximate formula for the linear dispersion relation allows a dramatic reduction in computational effort, in comparison with more precise calculations (e.g., Gaster [3], [5]), yet may still yield quite accurate results. Craik [1] gives simple analytical solutions for various limiting cases of his chosen model. Here, this model is further investigated. Numerical results are given which are free of previous scaling assumptions and the accuracy of the proposed model is assessed by comparison with known exact computations for plane Poiseuille flow. Certain improvements are made by including further terms in the model dispersion relation and the influence of these additional terms is determined. A further model is investigated which yields “splitting” of the wave packet into two regions of greatest amplitude, one on either side of the axis of symmetry. Such behavior may be characteristic of many flows at sufficiently large Reynolds numbers. Extension of this work to three-dimensional and slowly varying flows seems a practical possibility.

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