scholarly journals Brillouin-shifted third-harmonic backscattering of laser in a magnetized plasma

2015 ◽  
Vol 33 (1) ◽  
pp. 97-102 ◽  
Author(s):  
Alireza Paknezhad
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Static Magnetic Field ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Magnetized Plasma ◽  
Third Harmonic ◽  
Coupled Equations ◽  
Relativistic Mass ◽  
Weakly Coupled

AbstractThird-harmonic Brillouin backscattering (3HBBS) instability is investigated in the interaction of a picosecond extraordinary laser pulse with a homogeneous transversely magnetized underdense plasma. Nonlinear coupled equations that describe the instability are derived and solved for a weakly coupled regime to find the maximum growth rate. The nonlinearity arises through the combined effect of relativistic mass increase, static magnetic field, and ponderomotive acceleration of plasma electrons. The growth rate is found to decrease as the static magnetic field increases. It also increases by increasing both plasma density and laser intensity. It is also established that the growth rate of 3HBBS instability in a magnetized plasma is lower than that of fundamental Brillouin backscattering instability.

scholarly journals Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 1. Stability of solitary waves

2007 ◽  
Vol 73 (2) ◽  
pp. 215-229 ◽  
Author(s):  
M.A. ALLEN ◽  
S. PHIBANCHON ◽  
G. ROWLANDS
Keyword(s):  
Growth Rate ◽  
Solitary Waves ◽  
Nonlinear Waves ◽  
Electron Distribution ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Magnetized Plasma ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Waves ◽  
Stability Of Solitary Waves

Abstract.Weakly nonlinear waves in strongly magnetized plasma with slightly non-isothermal electrons are governed by a modified Zakharov–Kuznetsov (ZK) equation, containing both quadratic and half-order nonlinear terms, which we refer to as the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation. We present a method to obtain an approximation for the growth rate, γ, of sinusoidal perpendicular perturbations of wavenumber, k, to SKdVZK solitary waves over the entire range of instability. Unlike for (modified) ZK equations with one nonlinear term, in this method there is no analytical expression for kc, the cut-off wavenumber (at which the growth rate is zero) or its corresponding eigenfunction. We therefore obtain approximate expressions for these using an expansion parameter, a, related to the ratio of the nonlinear terms. The expressions are then used to find γ for k near kc as a function of a. The approximant derived from combining these analytical results with the ones for small k agrees very well with the values of γ obtained numerically. It is found that both kc and the maximum growth rate decrease as the electron distribution becomes progressively less peaked than the Maxwellian. We also present new algebraic and rarefactive solitary wave solutions to the equation.

Longitudinal waves in a perpendicular collisionless plasma shock: I. Cold ions

1970 ◽  
Vol 4 (4) ◽  
pp. 739-751 ◽  
Author(s):  
S. Peter Gary ◽  
J. J. Sanderson
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Collisionless Plasma ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Wave Number ◽  
Zero Magnetic Field ◽  
Linear Dispersion ◽  
Electrostatic Waves ◽  
Cold Ions

This paper considers electrostatic waves in a Vlasov plasma of unmagnetized ions and magnetized, Maxwellian electrons. The linear dispersion relation is derived for waves in a perpendicular shock such that the most important sources of instability are the E × B and ∇B electron drifts. For the case of cold ions, propagation perpendicular to the applied magnetic field, and the E × B drift alone, a numerical analysis of frequency vs. wave-number is presented. The effects of the ∇B drift are also considered, and it is shown that the maximum growth rate can be larger than the maximum growth rate for the zero magnetic field ion acoustic instabifity under comparable conditions.

scholarly journals Excitation of lower hybrid wave by an ion beam in magnetized plasma

2013 ◽  
Vol 31 (4) ◽  
pp. 747-752 ◽  
Author(s):  
Ved Prakash ◽  
Ruby Gupta ◽  
Suresh C. Sharma ◽  
Vijayshri
Keyword(s):  
Growth Rate ◽  
Ion Beam ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Magnetized Plasma ◽  
Unstable Wave ◽  
Lower Hybrid ◽  
Hybrid Wave ◽  
Lower Hybrid Wave ◽  
Beam Density

AbstractLower hybrid wave excitation in magnetized plasma by an ion beam via Cerenkov interaction is studied. The lower hybrid modes showed maximum growth rate of the instability when phase velocity of the lower hybrid mode along the magnetic field is comparable to the electron thermal velocity. We have derived the expression for the maximum growth rate and found that the growth rate of the instability increases with beam density. Moreover, the maximum growth rate of the instability scales as the one-third power of the beam density. The real part of the frequency of the unstable wave increases as almost the square root of the beam energy.

scholarly journals Fourth-order nonlinear evolution equations for surface gravity waves in the presence of a thin thermocline

1997 ◽  
Vol 39 (2) ◽  
pp. 214-229 ◽  
Author(s):  
Sudebi Bhattacharyya ◽  
K. P. Das
Keyword(s):  
Growth Rate ◽  
Fourth Order ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Maximum Growth ◽  
Single Equation ◽  
Maximum Growth Rate ◽  
Nonlinear Evolution Equations ◽  
Wave Number ◽  
Coupled Equations

AbstractTwo coupled nonlinear evolution equations correct to fourth order in wave steepness are derived for a three-dimensional wave packet in the presence of a thin thermocline. These two coupled equations are reduced to a single equation on the assumption that the space variation of the amplitudes takes place along a line making an arbitrary fixed angle with the direction of propagation of the wave. This single equation is used to study the stability of a uniform wave train. Expressions for maximum growth rate of instability and wave number at marginal stability are obtained. Some of the results are shown graphically. It is found that a thin thermocline has a stabilizing influence and the maximum growth rate of instability decreases with the increase of thermocline depth.

Kelvin–Helmholtz instability under horizontal rotation and magnetic fields

1998 ◽  
Vol 59 (2) ◽  
pp. 193-209
Author(s):  
L. A. DÁVALOS-OROZCO
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Fluid Layer ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Density Stratification ◽  
Velocity Shear ◽  
Sufficient Condition ◽  
Horizontal Shear ◽  
Helmholtz Instability

The author's previous work on the Rayleigh–Taylor instability is extended to the Kelvin–Helmholtz instability, and the maximum growth rate of a perturbation and an estimate of its upper bound is obtained for an infinite fluid layer under horizontal rotation where the density, horizontal velocity (shear) and magnetic field are continuously stratified in the direction of gravity. Conclusions are drawn about the possibility of stability for some directions of propagation of the perturbation, even in the case of unstably stratified density. It is also shown that the new terms that appear owing to the interaction of the horizontal shear flow, horizontal rotation and stratified magnetic field increase the range of values that contribute to the estimate of the maximum growth rate compared with previous work. Furthermore, a generalization of the sufficient condition for stability under horizontal rotation alone obtained by Johnson is calculated in the presence of density stratification. A new method is also given to obtain a sufficient condition for stability when a magnetic field is present in addition to rotation and density stratification.

scholarly journals Modulational Instability of Ion Acoustic Waves in a Magnetized Plasma Consisting of Isothermally Distributed Hot and Cold Electrons

2019 ◽  
pp. 1-13
Author(s):  
Sandip Dalui ◽  
Anup Bandyopadhyay
Keyword(s):  
Growth Rate ◽  
Acoustic Waves ◽  
Modulational Instability ◽  
Maximum Growth ◽  
Boltzmann Distribution ◽  
Maximum Growth Rate ◽  
Magnetized Plasma ◽  
Ion Acoustic Waves ◽  
Plasma System ◽  
Cold Electrons

Using the standard Reductive Perturbation Method a nonlinear Schr¨odinger equation is derived to study the modulational instability of small amplitude ion acoustic waves in a collisionless magnetized plasma composed of adiabatic warm ions, Maxwell-Boltzmann distribution of hot electrons as well as Maxwell-Boltzmann distribution of cold electrons, and the plasma system immersed in an external uniform static magnetic field (B0 = B0ˆz) propagating along the z-axis.The instability condition and the maximum growth rate of instability have been investigated analytically as well as numerically. We have studied the effect of each parameter of the present plasma system on the maximum growth rate of instability. In particular, it is found that the maximum growth rate of instability decreases with the increasing value of the ion cyclotron frequency with some set of values of the parameters associated with the present plasma system. Again, we have seen that the instability region decreases with the increasing value of the ion cyclotron frequency.

Filamentation of a laser beam in a strongly ionized magnetoplasma

1978 ◽  
Vol 19 (1) ◽  
pp. 55-61 ◽  
Author(s):  
L. A. Pitale
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Laser Beam ◽  
Spatial Scale ◽  
Large Scale ◽  
Maximum Growth ◽  
Mean Free Path ◽  
Maximum Growth Rate ◽  
Main Beam ◽  
Small Scale

On a time-scale of the order of the energy relaxation time, a high power laser beam, propagating in a strongly ionized magnetoplasma is shown to be unstable for small scale fluctuations. In the domain r0 < [mi/m]½ λm. v2/[ω2c + v2] (r0, λm, v, ωc, and m being respectively the spatial scale of the perturbation, electron mean free path, collision frequency, cyclotron frequency and mass and mi being the ion mass) the main loss of excess electron energy is due to thermal conduction; in the other limit collisional loss dominates. It is shown that for small scale fluctuations the growth rate increases with (i) increasing magnetic field and (ii) increasing r0. For large scale fluctuations the magnetic field does not show any effect; the growth rate, however, diminishes with increasing spatial scale. A maximum growth rate is obtained both for some optimum value of scale length and for intensity of the main beam.

scholarly journals α-Stability Analysis of Hydromagnetic Instabilities in Stars with Toroidal Magnetic Fields

1980 ◽  
Vol 58 ◽  
pp. 667-672
Author(s):  
M. Goossens ◽  
D. Biront
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Stability Analysis ◽  
Magnetic Fields ◽  
Sufficient Conditions ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Toroidal Magnetic Field ◽  
Displacement Fields ◽  
Necessary And Sufficient

Abstractα-stability analysis is used to investigate the adiabatic stability of a star containing an axisymmetric toroidal magnetic field. Necessary and sufficient conditions for α-stability are derived. Special attention is devoted to the typical hydromagnetic instabilities that can be introduced by a weak toroidal magnetic field in a star that is stably stratified in the absence of any magnetic field. An expression for the maximum growth rate of instability is derived and the basic properties of the displacement fields associated with the instabilities are indicated.

A note on growth curves of rabbit lines selected on growth rate or litter size

1993 ◽  
Vol 57 (2) ◽  
pp. 332-334 ◽  
Author(s):  
A. Blasco ◽  
E. Gómez
Keyword(s):  
Growth Rate ◽  
Litter Size ◽  
Growth Curves ◽  
Live Weight ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Standard Errors ◽  
Adult Weight ◽  
Weight Growth ◽  
Using Data

Two synthetic lines of rabbits were used in the experiment. Line V, selected on litter size, and line R, selected on growth rate. Ninety-six animals were randomly collected from 48 litters, taking a male and a female each time. Richards and Gompertz growth curves were fitted. Sexual dimorphism appeared in the line V but not in the R. Values for b and k were similar in all curves. Maximum growth rate took place in weeks 7 to 8. A break due to weaning could be observed in weeks 4 to 5. Although there is a remarkable similarity of the values of all the parameters using data from the first 20 weeks only, the higher standard errors on adult weight would make 30 weeks the preferable time to take data for live-weight growth curves.

Reassessment of Maximum Growth Rates for C3 and C4 Crops

1978 ◽  
Vol 14 (1) ◽  
pp. 1-5 ◽  
Author(s):  
J. L. Monteith
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Growing Season ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Crop Growth ◽  
Close Inspection ◽  
Similar Difference ◽  
Photosynthetic Efficiencies

SUMMARYFigures for maximum crop growth rates, reviewed by Gifford (1974), suggest that the productivity of C3 and C4 species is almost indistinguishable. However, close inspection of these figures at source and correspondence with several authors revealed a number of errors. When all unreliable figures were discarded, the maximum growth rate for C3 stands fell in the range 34–39 g m−2 d−1 compared with 50–54 g m−2 d−1 for C4 stands. Maximum growth rates averaged over the whole growing season showed a similar difference: 13 g m−2 d−1 for C3 and 22 g m−2 d−1 for C4. These figures correspond to photosynthetic efficiencies of approximately 1·4 and 2·0%.

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