Stability of strong electromagnetic waves in overdense plasmas against long-wavelength perturbations

1985 ◽  
Vol 33 (2) ◽  
pp. 285-301 ◽  
Author(s):  
F. J. Romeiras ◽  
G. Rowlands
Keyword(s):  
Dispersion Relation ◽  
Nonlinear Waves ◽  
Electromagnetic Waves ◽  
Modulation Depth ◽  
Longitudinal Direction ◽  
Transverse Component ◽  
Ion Density ◽  
Long Wavelength ◽  
The Stability ◽  
Two Parameters

We consider the stability against long-wavelength small parallel perturbations of a class of exact standing wave solutions of the equations that describe an unmagnetized relativistic overdense cold electron plasma. The main feature of these nonlinear waves is a circularly polarized transverse component of the electric field periodically modulated in the longitudinal direction. Using an analytical method developed by Rowlands we obtain a dispersion relation valid for long-wavelength perturbations. This dispersion relation is a biquadratic equation in the phase velocity of the perturbations whose coefficients are very complicated functions of the two parameters used to define the nonlinear waves: the normalized ion density and a quantity related to the modulation depth. This dispersion relation is discussed for the whole range of the two parameters revealing, in particular, the existence of a region in parameter space where the nonlinear waves are stable.

Stability of strong electromagnetic waves in overdense plasmas

1982 ◽  
Vol 27 (2) ◽  
pp. 239-259 ◽  
Author(s):  
F. J. Romeiras
Keyword(s):  
Nonlinear Waves ◽  
Electromagnetic Waves ◽  
Longitudinal Direction ◽  
Electron Plasma ◽  
Cold Electron ◽  
Small Perturbations ◽  
Circularly Polarized ◽  
Instability Growth ◽  
Linear Differential ◽  
The Stability

We consider the stability against small perturbations of a class of exact wave solutions of the equations that describe an unmagnetized relativistic cold electron plasma. The main feature of these nonlinear waves is a transverse circularly polarized electric field with periodic amplitude modulation in the longitudinal direction. Floquet's theory of linear differential equations with periodic coefficients is used to solve the perturbation equations and obtain the instability growth rates.

scholarly journals Symmetry breaking of azimuthal thermo-acoustic modes in annular cavities: a theoretical study

2014 ◽  
Vol 760 ◽  
pp. 431-465 ◽  
Author(s):  
M. Bauerheim ◽  
P. Salas ◽  
F. Nicoud ◽  
T. Poinsot
Keyword(s):  
Symmetry Breaking ◽  
Electromagnetic Waves ◽  
Seismic Waves ◽  
Theoretical Study ◽  
Stable Configuration ◽  
Splitting Strength ◽  
The Difference ◽  
Acoustic Instabilities ◽  
The Stability ◽  
Two Parameters

AbstractMany physical problems containing rotating symmetry exhibit azimuthal waves, from electromagnetic waves in nanophotonic crystals to seismic waves in giant stars. When this symmetry is broken, clockwise (CW) and counter-clockwise (CCW) waves are split into two distinct modes which can become unstable. This paper focuses on a theoretical study of symmetry breaking in annular cavities containing a number $N$ of flames prone to azimuthal thermo-acoustic instabilities. A general dispersion relation for non-perfectly-axisymmetric cavities is obtained and analytically solved to provide an explicit expression for the frequencies and growth rates of all azimuthal modes of the configuration. This analytical study unveils two parameters affecting the stability of the mode: (i) a coupling strength corresponding to the cumulative effects of the $N$ flames and (ii) a splitting strength due to the symmetry breaking when the flames are different. This theory has been validated using a 3D Helmholtz solver and good agreement is found. When only two types of flames are introduced into the annular cavity, the splitting strength is found to depend on two parameters: the difference between the two burner types and the pattern used to distribute the flames along the azimuthal direction. To first order, this theory suggests that the most stable configuration is obtained for a perfectly axisymmetric configuration. Therefore, breaking the symmetry by mixing different flames cannot improve the stability of an annular combustor independently of the flame distribution pattern.

A comparative study of the instabilities of two classes of nonlinear waves in cold plasmas

1986 ◽  
Vol 35 (3) ◽  
pp. 529-539 ◽  
Author(s):  
F. J. Romeiras ◽  
G. Rowlands
Keyword(s):  
Nonlinear Waves ◽  
Transverse Electric ◽  
Longitudinal Direction ◽  
Dispersion Relations ◽  
Cold Electron ◽  
Circularly Polarized ◽  
Electron Plasmas ◽  
Cold Plasmas ◽  
Set Up ◽  
The Stability

Results are presented of the stability analysis against small parallel perturbations of two classes of nonlinear waves in cold unmagnetized electron plasmas emphasizing similarities and differences. The first class is a stationary longitudinal wave set up by two counter-streaming cold electron beams; the second class is a mixed transverse-longitudinal standing wave in a relativistic plasma with a circularly polarized transverse electric field whose amplitude is periodically modulated in the longitudinal direction. The perturbation dispersion relations are discussed for all perturbation wavenumbers and all nonlinear wave amplitudes. Particular attention is given to the appearance of gaps in those dispersion relations.

scholarly journals On Minimum-B Stabilization of Electrostatic Drift Instabilities

1966 ◽  
Vol 21 (11) ◽  
pp. 1953-1959 ◽  
Author(s):  
R. Saison ◽  
H. K. Wimmel
Keyword(s):  
Dispersion Relation ◽  
Particle Distribution ◽  
Inhomogeneous Plasma ◽  
Distribution Functions ◽  
Loss Cone ◽  
First Order ◽  
Stabilization Theorem ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Limiting Case

A check is made of a stabilization theorem of ROSENBLUTH and KRALL (Phys. Fluids 8, 1004 [1965]) according to which an inhomogeneous plasma in a minimum-B field (β ≪ 1) should be stable with respect to electrostatic drift instabilities when the particle distribution functions satisfy a condition given by TAYLOR, i. e. when f0 = f(W, μ) and ∂f/∂W < 0 Although the dispersion relation of ROSENBLUTH and KRALL is confirmed to first order in the gyroradii and in ε ≡ d ln B/dx z the stabilization theorem is refuted, as also is the validity of the stability criterion used by ROSEN-BLUTH and KRALL, ⟨j·E⟩ ≧ 0 for all real ω. In the case ωpi ≫ | Ωi | equilibria are given which satisfy the condition of TAYLOR and are nevertheless unstable. For instability it is necessary to have a non-monotonic ν ⊥ distribution; the instabilities involved are thus loss-cone unstable drift waves. In the spatially homogeneous limiting case the instability persists as a pure loss cone instability with Re[ω] =0. A necessary and sufficient condition for stability is D (ω =∞, k,…) ≦ k2 for all k, the dispersion relation being written in the form D (ω, k, K,...) = k2+K2. In the case ωpi ≪ | Ωi | adherence to the condition given by TAYLOR guarantees stability.

Bifurcation and stability analysis of stagnation points for an asymmetric peristaltic transport

2020 ◽  
Vol 98 (2) ◽  
pp. 172-182 ◽  
Author(s):  
Kaleem Ullah ◽  
Nasir Ali
Keyword(s):  
Flow Field ◽  
Amplitude Ratio ◽  
Nonlinear Differential Equations ◽  
Global Bifurcation ◽  
Flow Region ◽  
Peristaltic Transport ◽  
Trapping Region ◽  
Long Wavelength ◽  
Stagnation Points ◽  
The Stability

This paper investigates the streamline topologies and stability of stagnation points and their bifurcations for an asymmetric peristaltic flow. The asymmetry of channel is due to the propagation of peristaltic waves with different phases and amplitudes on the flexible channel walls. An exact analytic solution of the flow problem subject to the constraints of low Reynolds number and long wavelength is obtained in wave frame of reference moving with wave velocity. A system of nonlinear differential equations is established to locate and classify the stagnation points in the flow domain. Different flow situations, manifested in the flow field, are categorized as: backward flow, trapping, and augmented flow. The transition from one situation to the other corresponds to bifurcation, which is explored graphically through local and global bifurcation diagrams. This analysis discloses the stability status of stagnation points and ranges of involved parameters in which various flow conditions appear in the flow field. It is concluded that the trapping in an asymmetric peristaltic transport can be reduced by increasing the phase difference of the channel walls. It is also found that the augmented flow region shrinks and the trapping region expands by increasing the amplitude ratio of the channel walls.

Magnetic Superlattice: Localized Magnetostatic Waves and Magnetic Polaritons

2003 ◽  
Vol 17 (15) ◽  
pp. 829-839
Author(s):  
R. T. Tagiyeva ◽  
M. Saglam
Keyword(s):  
Magnetic Material ◽  
Electromagnetic Wave ◽  
Dispersion Relation ◽  
Wave Theory ◽  
Frequency Region ◽  
Long Wavelength ◽  
Magnetostatic Waves ◽  
General Dispersion ◽  
Magnetic Polaritons ◽  
Magnetic Superlattice

Localized magnetostatic waves and magnetic polaritons at the junction of the magnetic material and magnetic superlattice composed of the alternating ferromagnetic or ferromagnetic and nonmagnetic layers are investigated in the framework of the electromagnetic wave theory in Voigt geometry. The general dispersion relation for localized magnetic polaritons and magnetostatic waves (MW) are derived in the long-wavelength limit. The dispersion curves and frequency region of the exsistence of the localized MW and magnetic polaritons are calculated numerically.

scholarly journals Persistent Liquidity Effects and Long-Run Money Demand

2014 ◽  
Vol 6 (2) ◽  
pp. 71-107 ◽  
Author(s):  
Fernando Alvarez ◽  
Francesco Lippi
Keyword(s):  
Interest Rates ◽  
Money Demand ◽  
Asset Markets ◽  
Propagation Mechanism ◽  
Monetary Model ◽  
Long Run ◽  
Short Run ◽  
The Stability ◽  
Two Parameters

We present a monetary model with segmented asset markets that implies a persistent fall in interest rates after a once-and-for-all increase in liquidity. The gradual propagation mechanism produced by our model is novel in the literature. We provide an analytical characterization of this mechanism, showing that the magnitude of the liquidity effect on impact, and its persistence, depend on the ratio of two parameters: the long-run interest rate elasticity of money demand and the intertemporal substitution elasticity. The model simultaneously explains the short-run “instability” of money demand estimates as well as the stability of long-run interest-elastic money demand. (JEL E13, E31, E41, E43, E52, E62)

scholarly journals Rayleigh-Taylor instability of two superposed magnetized viscous fluids with suspended dust particles

2010 ◽  
Vol 14 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Praveen Sharma ◽  
Ram Prajapati ◽  
Rajendra Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Dust Particles ◽  
Stable Configuration ◽  
Rayleigh Taylor Instability ◽  
Suspended Dust ◽  
The Stability

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

scholarly journals Modified Kawahara equation within a fractional derivative with non-singular kernel

2018 ◽  
Vol 22 (2) ◽  
pp. 789-796 ◽  
Author(s):  
Devendra Kumar ◽  
Jagdev Singh ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Derivative ◽  
Numerical Solution ◽  
Water Waves ◽  
Iterative Scheme ◽  
Singular Kernel ◽  
Kawahara Equation ◽  
Long Wavelength ◽  
Exponential Kernel ◽  
The Stability ◽  
Linear Water Waves

The article addresses a time-fractional modified Kawahara equation through a fractional derivative with exponential kernel. The Kawahara equation describes the generation of non-linear water-waves in the long-wavelength regime. The numerical solution of the fractional model of modified version of Kawahara equation is derived with the help of iterative scheme and the stability of applied technique is established. In order to demonstrate the usability and effectiveness of the new fractional derivative to describe water-waves in the long-wavelength regime, numerical results are presented graphically.

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