Theory of stimulated scattering of large-amplitude waves

1999 ◽  
Vol 61 (1) ◽  
pp. 129-134 ◽  
Author(s):  
L. STENFLO
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Large Amplitude ◽  
Pump Wave ◽  
Low Frequency ◽  
Nonlinear Dispersion ◽  
Stimulated Scattering ◽  
Nonlinear Dispersion Relation

A nonlinear dispersion relation that governs the interaction between a high-frequency pump wave and the low-frequency modes in a plasma is derived. Previous results are generalized and discussed.

Theory of stimulated scattering of large-amplitude waves

1995 ◽  
Vol 53 (2) ◽  
pp. 213-222 ◽  
Author(s):  
L. Stenflo
Keyword(s):  
Dispersion Relation ◽  
Large Amplitude ◽  
Pump Wave ◽  
Low Frequency ◽  
Wave Frequency ◽  
Nonlinear Coupling ◽  
Stimulated Scattering ◽  
Pump Wave Frequency ◽  
General Dispersion ◽  
Electron Gyrofrequency

By means of the standard fluid equations, we consider the nonlinear coupling between a large-amplitude pump wave and the low-frequency modes in a collisional plasma. We derive the general dispersion relation in order to discuss the case where the pump-wave frequency is not much larger than the electron gyrofrequency.

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.

Scattering of electromagnetic waves by hybrid waves in a two-electron-temperature plasma

1991 ◽  
Vol 46 (1) ◽  
pp. 99-106 ◽  
Author(s):  
S. K. Sharma ◽  
A. Sudarshan
Keyword(s):  
Growth Rate ◽  
Electron Temperature ◽  
High Frequency ◽  
Electromagnetic Waves ◽  
Low Frequency ◽  
Lower Hybrid ◽  
Stimulated Scattering ◽  
Coupled Modes ◽  
Temperature Plasma ◽  
Electrostatic Perturbation

In this paper, we use the hydrodynamic approach to study the stimulated scattering of high-frequency electromagnetic waves by a low-frequency electrostatic perturbation that is either an upper- or lower-hybrid wave in a two-electron-temperature plasma. Considering the four-wave interaction between a strong high-frequency pump and the low-frequency electrostatic perturbation (LHW or UHW), we obtain the dispersion relation for the scattered wave, which is then solved to obtain an explicit expression for the growth rate of the coupled modes. For a typical Q-machine plasma, results show that in both cases the growth rate increases with noh/noc. This is in contrast with the results of Guha & Asthana (1989), who predicted that, for scattering by a UHW perturbation, the growth rate should decrease with increasing noh/noc.

Ion-cyclotron modes in weakly relativistic plasmas

1994 ◽  
Vol 51 (3) ◽  
pp. 371-379 ◽  
Author(s):  
Chandu Venugopal ◽  
P. J. Kurian ◽  
G. Renuka
Keyword(s):  
Dispersion Relation ◽  
High Frequency ◽  
Low Frequency ◽  
Dispersion Relations ◽  
The Other ◽  
Larmor Radius ◽  
Relativistic Plasmas ◽  
Ion Plasma ◽  
Maxwellian Plasma ◽  
Relativistic Dispersion

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

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
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