Nonlinear coupling of two three-wave systems in plasma

1983 ◽  
Vol 30 (3) ◽  
pp. 345-357
Author(s):  
Shukla Basu (De) ◽  
R. K. Roychowdhury
Keyword(s):  
Longitudinal Wave ◽  
Nonlinear Interaction ◽  
Initial Conditions ◽  
Coupling Factor ◽  
Negative Energy ◽  
Relative Strength ◽  
Nonlinear Coupling ◽  
Longitudinal Waves ◽  
Frequency Mismatch ◽  
Linear Damping

The nonlinear interaction of two three-wave systems, including the possibility of negative energy waves in the presence of linear damping or growth and frequency mismatch, is investigated in a plasma, where one system of two transverse and one longitudinal wave interacts with a system of three longitudinal waves, and one of the longitudinal waves introduces coupling between the two subsystems. The solutions are analysed under various initial conditions and it is shown that, if one triplet be explosively unstable by itself, the presence of the second triplet can stabilize the solutions, depending on the relative strength of the coupling factor.

Nonlinear coupling of three waves in non-uniform plasma

1979 ◽  
Vol 22 (2) ◽  
pp. 353-359 ◽  
Author(s):  
G. C. Pramanik
Keyword(s):  
Nonlinear Interaction ◽  
Electron Plasma ◽  
Coupled Mode Theory ◽  
Nonlinear Coupling ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Long Wavelength ◽  
Coupled Mode ◽  
Limiting Case ◽  
Uniform Plasma

This paper considers nonlinear interaction between three monochromatic waves in a hot non-uniform electron plasma. With the aid of coupled mode theory the interaction of three longitudinal waves is studied and a specific case of the interaction of two longitudinal waves and one perpendicular wave is derived for the limiting case of long wavelength. Furthermore, the non-uniformity involves generalization of the theory of the interaction of two transverse waves and one longitudinal wave of a previous contribution.

Nonlinear Instabilities, Negative Energy Modes and Generalized Cherry Oscillators

1990 ◽  
Vol 45 (7) ◽  
pp. 839-846 ◽  
Author(s):  
D. Pfirsch
Keyword(s):  
Initial Conditions ◽  
Complete Solution ◽  
Continuum Theory ◽  
Wave Interaction ◽  
Negative Energy ◽  
Solution Set ◽  
Maxwell Theory ◽  
Resonant Oscillators ◽  
Simple Physical Interpretation ◽  
Two Parameter

AbstractIn 1925 Cherry [1] discussed two oscillators of positive and negative energy that are nonlinearly coupled in a special way, and presented a class of exact solutions of the nonlinear equations showing explosive instability independent of the strength of the nonlinearity and the initial amplitudes. In this paper Cherry's Hamiltonian is transformed into a form which allows a simple physical interpretation. The new Hamiltonian is generalized to three nonlinearly coupled oscillators; it corresponds to three-wave interaction in a continuum theory, like the Vlasov-Maxwell theory, if there exist linear negative energy waves [2-4, 5, 6], Cherry was able to present a two-parameter solution set for his example which would, however, allow a four-parameter solution set, and, as a first result, an analogous three-parameter solution set for the resonant three-oscillator case is obtained here which, however, would allow a six-parameter solution set. Nonlinear instability is therefore proven so far only for a very small part of the phase space of the oscillators. This paper gives in addition the complete solution for the three-oscillator case and shows that, except for a singular case, all initial conditions, especially those with arbitrarily small amplitudes, lead to explosive behaviour. This is true of the resonant case. The non-resonant oscillators can sometimes also become explosively unstable, but the initial amplitudes must not be infinitesimally small. A few examples are presented for illustration.

Numerical simulation of internal defect imaging with the longitudinal wave generated by laser induced ultrasonic array

2020 ◽  
pp. 2150103
Author(s):  
Hao Sui ◽  
Kesi Li ◽  
Zhenyu Zhu ◽  
Le Cheng ◽  
Xiaorong Gao ◽  
...  
Keyword(s):  
Longitudinal Wave ◽  
Phased Arrays ◽  
Synthetic Aperture ◽  
Wave Component ◽  
The Finite Element Method ◽  
Internal Defect ◽  
Longitudinal Waves ◽  
Synthetic Aperture Focusing ◽  
Synthetic Aperture Focusing Technique ◽  
Defect Imaging

To verify the performance of longitudinal waves induced by laser phased arrays (LPA) for detection and quantitative evaluation in internal defects, the finite element method (FEM) is utilized to establish the models of LPA scanning processing. The interaction of longitudinal wave and internal defect is analyzed. Besides, the two components of the reflected longitudinal waves (the longitudinal wave component [Formula: see text] and the shear wave component [Formula: see text] are focused on the imaging of defects with the synthetic aperture focusing technique (SAFT) and total focusing method (TFM) algorithms. It shows that the imaging of internal sub-millimeter defect is obtained using the LPA. The defect size and location are simultaneously calculated, with the relative error being 6.7% and 2.9%, respectively. The proposed longitudinal wave-based LPA is a promising method for the imaging and evaluation of internal micro defects.

scholarly journals A Study on Fatigue State Evaluation of Rail by the Use of Ultrasonic Nonlinearity

Materials ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 2698
Author(s):  
Bo Zhu ◽  
Jaesun Lee
Keyword(s):  
Longitudinal Wave ◽  
Second Harmonic ◽  
Early Stage ◽  
Wave Mixing ◽  
Third Harmonic ◽  
Longitudinal Waves ◽  
Testing Method ◽  
State Evaluation ◽  
Stress Fatigue ◽  
Train Safety

Nonlinear ultrasonic testing has been accepted as a promising manner for evaluating material integrity in an early stage. Stress fatigue is the main threats to train safety, railways examinations for stress fatigue are more significant and necessary. A series of ultrasonic nonlinear wave experiments are conducted for rail specimens extracted from railhead with different degree of fatigue produced by three-point bent loading condition. The nonlinear parameter is the indicator of nonlinear waves for expressing the degree the fatigue. The experimental results show that the sensitivity of a third harmonic longitudinal wave is higher than second harmonic longitudinal wave testing. As the same time, collinear wave mixing shows strong relative with fatigue damages than a second longitudinal wave nondestructive testing (NDT) method and provides more reliable results than third harmonic longitudinal waves nonlinear testing method.

scholarly journals Propagation of Plane Waves in a Thermally Conducting Mixture

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Baljeet Singh
Keyword(s):  
Free Surface ◽  
Longitudinal Wave ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Solid ◽  
Reflection Coefficients ◽  
Governing Equations ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Thermally Conducting

The governing equations for generalized thermoelasticity of a mixture of an elastic solid and a Newtonian fluid are formulated in the context of Lord-Shulman and Green-Lindsay theories of generalized thermoelasticity. These equations are solved to show the existence of three coupled longitudinal waves and two coupled transverse waves, which are dispersive in nature. Reflection from a thermally insulated stress-free surface is considered for incidence of coupled longitudinal wave. The speeds and reflection coefficients of plane waves are computed numerically for a particular model.

Nonlinear interaction between longitudinal waves in a magnetized plasma

1978 ◽  
Vol 19 (3) ◽  
pp. 405-410 ◽  
Author(s):  
A. A. Selim
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Quantum Field Theory ◽  
Nonlinear Interaction ◽  
Uniform Magnetic Field ◽  
Magnetized Plasma ◽  
Quantum Field ◽  
Arbitrary Angle ◽  
Longitudinal Waves ◽  
Coupled Mode

Quantum field theory is used to investigate the resonant nonlinear interaction between three longitudinal waves propagating at any arbitrary angle to a uniform magnetic field in a plasma. The coupled mode equations, coupling coefficient and a formula for the growth rates are derived.

Sensitivity Analysis and Inverse Problems in Microscale Heat Transfer

2015 ◽  
Vol 362 ◽  
pp. 209-223 ◽  
Author(s):  
Ewa Majchrzak ◽  
Jolanta Dziatkiewicz ◽  
Łukasz Turchan
Keyword(s):  
Heat Transfer ◽  
Sensitivity Analysis ◽  
Inverse Problems ◽  
Initial Conditions ◽  
Short Pulse ◽  
Relaxation Times ◽  
Coupling Factor ◽  
Hyperbolic Model ◽  
Short Pulse Laser ◽  
Microscale Heat Transfer

In the paper the selected problems related to the modeling of microscale heat transfer are presented. In particular, thermal processes occurring in thin metal films exposed to short-pulse laser are described by two-temperature hyperbolic model supplemented by appropriate boundary and initial conditions. Sensitivity analysis of electrons and phonons temperatures with respect to the microscopic parameters is discussed and also the inverse problems connected with the identification of relaxation times and coupling factor are presented. In the final part of the paper the examples of computations are shown.

scholarly journals A Study on Fatigue State Evaluation of Rail by the Use of Ultrasonic Nonlinearity

2019 ◽  
Author(s):  
Bo Zhu ◽  
Jaesun Lee
Keyword(s):  
Longitudinal Wave ◽  
Second Harmonic ◽  
Early Stage ◽  
Wave Mixing ◽  
Third Harmonic ◽  
Longitudinal Waves ◽  
Testing Method ◽  
State Evaluation ◽  
Stress Fatigue ◽  
Train Safety

Nonlinear ultrasonic testing has been accepted as a promising manner for evaluating material integrity in an early stage. Stress fatigue is the main threats to train safety, railways examinations for stress fatigue are more significant and necessary. A series of ultrasonic nonlinear wave experiments are conducted for rail specimens extracted from railhead with different degree of fatigue produced by three-point bent loading condition. The nonlinear parameter is the indicator of nonlinear waves for expressing the degree the fatigue. The experimental results show that the sensitivity of a third harmonic longitudinal wave is higher than second harmonic longitudinal wave testing. As the same time, collinear wave mixing shows strong relative with fatigue damages than a second longitudinal wave NDT method and provides more reliable results than third harmonic longitudinal waves nonlinear testing method.

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