Modification of a turbulent spectrum through the injection of a monochromatic wave Part 2. The dispersion relation

1977 ◽  
Vol 17 (1) ◽  
pp. 1-11
Author(s):  
Armando L. Brinca
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Frequency Shift ◽  
Dispersion Equation ◽  
Monochromatic Wave ◽  
Nonlinear Dispersion ◽  
Linear Dispersion ◽  
Real Frequency ◽  
Nonlinear Dispersion Relation ◽  
Turbulent Spectrum

Analysis of the influence of an injected monochromatic wave on a turbulent spectrum shows that the resulting nonlinear dispersion relation for the stochastic modes displays a real frequency shift and a corrected growth rate when contrasted with the classical quasi-linear dispersion equation.

Plasma maser theory of the extraordinary mode in the presence of Langmuir turbulence

1991 ◽  
Vol 46 (2) ◽  
pp. 331-346 ◽  
Author(s):  
S. N. Sarma ◽  
K. K. Sarma ◽  
M. Nambu
Keyword(s):  
Growth Rate ◽  
Electron Beam ◽  
Dispersion Relation ◽  
Space Plasma ◽  
Conversion Process ◽  
Nonlinear Dispersion ◽  
Langmuir Turbulence ◽  
Nonlinear Dispersion Relation ◽  
Maser Effect ◽  
Scope Of Application

The emission of extraordinary mode radiation in a plasma with Langmuir turbulence driven by an electron beam is considered. The process of emission considered in this paper is the plasma maser effect, which is essentially an energy up-conversion process. The energy necessary for the growth of the extraordinary mode is derived from the Langmuir turbulence. The nonlinear dispersion relation of the extraordinary mode in the presence of Langmuir turbulence is obtained and its growth rate calculated. The scope of application of the results to space-plasma observation is then stressed.

Parametric decay in a two-electron-temperature plasma

1990 ◽  
Vol 43 (3) ◽  
pp. 451-456
Author(s):  
S. Guha ◽  
Meenu Asthana
Keyword(s):  
Growth Rate ◽  
Dispersion Relation ◽  
Electron Temperature ◽  
Pump Wave ◽  
Nonlinear Dispersion ◽  
Hybrid Wave ◽  
Temperature Plasma ◽  
Parametric Decay ◽  
Electromagnetic Pump ◽  
Nonlinear Dispersion Relation

Nonlinear decay of an ordinary electromagnetic pump wave into an electro-acoustic wave and an upper-hybrid wave in a two-electron-temperature plasma has been investigated analytically. In contrast with the work of Sharma, Ramamurthy & Yu (1984), it is found that the decay can take place in the absence of the restrictive condition Ti ≫ Te and the plasma be magnetized. Using a hydrodynamical model of the plasma, the nonlinear dispersion relation and growth rate are obtained. A comparison of the present investigation is made with earlier work, and its possible application to the ELMO bumpy torus is discussed.

Electrostatic plasma turbulence Part 2. The nonlinear dispersion relation and fluctuation spectrum

1977 ◽  
Vol 17 (3) ◽  
pp. 503-517 ◽  
Author(s):  
H. C. Barr ◽  
T. J. M. Boyd
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Diffusion Tensor ◽  
Nonlinear Dispersion ◽  
Fluctuation Spectrum ◽  
Nonlinear Dispersion Relation ◽  
Turbulent Spectrum ◽  
Self Consistent ◽  
Ion Acoustic ◽  
The Magnetic Field

This paper complements an earlier one in which we considered the diffusion and drift across a magnetic field induced by a turbulent spectrum of fluctuations. We examine here the effects of these on the propagation of an unstable spectrum of modes. In the first paper a nonlinear dispersion relation is derived in a general closed form. This is then examined in the limint of short wavelengths (i.e.wavelengths much less than the gyroradii) and results of other authors are retrieved. In particular it is found that modes supported by the magnetic field are quashed whenever a particle may diffuse a wavelength per gyroperiod. For instance, in the context of current-driven instabilities (current across the magnetic field), electron cyclotron instabilities are quashed but not the ion-acoustic. The dispersion characteristics of the latter are unchanged except in that the drift which sustains the instability is altered by the presence of a turbulent (E × B) type drift. Depending on the level of fluctuations and magnetic field strength, this may amount simply to a rotation of the cone of unstable modes or may form a countercurrent which in turn suppresses the original current driving the instability.In the second half of the paper the problem of calculating the fluctuation spectrum of the electric field is addressed since this is essential for a self-consistent computation of the diffusion tensor and turbulent drift appearing in the nonlinear dispersion relation.

scholarly journals Thermodynamical Extension of a Symplectic Numerical Scheme with Half Space and Time Shifts Demonstrated on Rheological Waves in Solids

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 155 ◽  
Author(s):  
Tamás Fülöp ◽  
Róbert Kovács ◽  
Mátyás Szücs ◽  
Mohammad Fawaier
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Dispersion Relation ◽  
Half Space ◽  
Numerical Stability ◽  
Numerical Scheme ◽  
Nonlinear Dispersion ◽  
Finite Element Software ◽  
Space And Time ◽  
Nonlinear Dispersion Relation

On the example of the Poynting–Thomson–Zener rheological model for solids, which exhibits both dissipation and wave propagation, with nonlinear dispersion relation, we introduce and investigate a finite difference numerical scheme. Our goal is to demonstrate its properties and to ease the computations in later applications for continuum thermodynamical problems. The key element is the positioning of the discretized quantities with shifts by half space and time steps with respect to each other. The arrangement is chosen according to the spacetime properties of the quantities and of the equations governing them. Numerical stability, dissipative error, and dispersive error are analyzed in detail. With the best settings found, the scheme is capable of making precise and fast predictions. Finally, the proposed scheme is compared to a commercial finite element software, COMSOL, which demonstrates essential differences even on the simplest—elastic—level of modeling.

scholarly journals Nonlinear Bloch waves and balance between hardening and softening dispersion

2018 ◽  
Vol 474 (2217) ◽  
pp. 20180173 ◽  
Author(s):  
M. I. Hussein ◽  
R. Khajehtourian
Keyword(s):  
Dispersion Relation ◽  
Cell Size ◽  
Unit Cell ◽  
Homogeneous Layer ◽  
Nonlinear Dispersion ◽  
Elastic Band ◽  
Bloch Waves ◽  
Unit Cell Size ◽  
Nonlinear Dispersion Relation ◽  
Hardening And Softening

The introduction of nonlinearity alters the dispersion of elastic waves in solid media. In this paper, we present an analytical formulation for the treatment of finite-strain Bloch waves in one-dimensional phononic crystals consisting of layers with alternating material properties. Considering longitudinal waves and ignoring lateral effects, the exact nonlinear dispersion relation in each homogeneous layer is first obtained and subsequently used within the transfer matrix method to derive an approximate nonlinear dispersion relation for the overall periodic medium. The result is an amplitude-dependent elastic band structure that upon verification by numerical simulations is accurate for up to an amplitude-to-unit-cell length ratio of one-eighth. The derived dispersion relation allows us to interpret the formation of spatial invariance in the wave profile as a balance between hardening and softening effects in the dispersion that emerge due to the nonlinearity and the periodicity, respectively. For example, for a wave amplitude of the order of one-eighth of the unit-cell size in a demonstrative structure, the two effects are practically in balance for wavelengths as small as roughly three times the unit-cell size.

scholarly journals Nonlinear dispersion relation in anharmonic periodic mass-spring and mass-in-mass systems

2019 ◽  
Vol 462 ◽  
pp. 114929 ◽  
Author(s):  
R. Zivieri ◽  
F. Garescì ◽  
B. Azzerboni ◽  
M. Chiappini ◽  
G. Finocchio
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Dispersion ◽  
Nonlinear Dispersion Relation ◽  
Mass Spring

Envelope solitons of surface waves in a plasma column

1987 ◽  
Vol 38 (3) ◽  
pp. 427-437 ◽  
Author(s):  
D. Grozev ◽  
A. Shivarova ◽  
A. D. Boardman
Keyword(s):  
Dispersion Relation ◽  
Surface Waves ◽  
Plasma Column ◽  
Soliton Solutions ◽  
Elliptic Functions ◽  
Nonlinear Dispersion ◽  
Dark Solitons ◽  
Envelope Solitons ◽  
Nonlinear Dispersion Relation ◽  
Universal Procedure

The problem of envelope solitons of surface waves is considered on the basis of results for the nonlinear dispersion relation of the waves in a plasma column. The soliton solutions are derived as particular cases of the general solutions obtained by a universal procedure and expressed in terms of Jacobi elliptic functions. Since the two types of interactions, namely the (ω + ω) – ω and the (ω – ω) + ω interactions (where ω is the frequency of the carrier wave) included in the nonlinear dispersion relation act in opposite ways, existence both of bright and dark solitons is shown to be possible. The effect of the ponderomotive force that in our case is expressed through the contribution of the (ω – ω) + ω interaction leads to the formation of dark solitons. The effect of the losses is also considered.

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