Small Values Of Wave Number Research Articles

Effects of dust particles charged by inelastic collisions and by photoionization on Alfvén waves in a stellar wind

ABSTRACT Using a kinetic description of a homogeneous magnetized dusty plasma with Maxwellian distribution of electrons and protons and dust particles charged by inelastic collisions and by photoionization, we analyse the dispersion relation considering the case where waves and radiation propagate exactly parallel to the ambient magnetic field. The investigation emphasizes the changes that the photoionization process brings to the propagation and damping of the waves in a stellar wind environment, since Alfvén waves are believed to play a significant role in the heating and acceleration processes that take place in the wind. The results show that, in the presence of dust with negative equilibrium electrical charge, the Alfvén mode decouples into the whistler and ion cyclotron modes for all values of wavenumber, but when dust particles acquire neutral or positive values of electrical charge, these modes may couple for certain values of wavenumber. It is also seen that the whistler and ion cyclotron modes present null group velocity in an interval of small wavenumber, and that the maximum value of wavenumber for which the waves are non-propagating is reduced in the presence of the photoionization process. For very small values of wavenumber, the damping rates of the modes could change significantly from very small to very high values if the sign of the dust electrical charge is changed.

Longitudinal electric current generated by a transverse electromagnetic field in a collisional plasma

Kinetic Vlasov equation for collisional plasmas with BGK (Bhatnagar-Gross-Krook) collision integral is used. The case of arbitrary temperature (i.e. arbitrary degree of degeneration of electronic gas) is considered. From kinetic Vlasov equation the distribution function in square-law approximation on size of transversal electromagnetic field is received. The formula for calculation electric current is deduced. This formula contains one-dimension quadrature. It is shown, that the nonlinearity account leads to occurrence the longitudinal electric current directed along the wave vector. This longitudinal current is perpendicular to the known transversal classical current, received at the linear analysis. When frequency of collisions tends to zero, all received results for collisional plasma pass in known corresponding formulas for collisionless plasma. The case of small values of wave number is considered. It is shown, that the received quantity of longitudinal current at tendency of frequency of collisions to zero also passes in known corresponding expression of current for collisionless plasmas. Graphic research of dimensionless density of the current depending on wave number, frequency of oscillations of electromagnetic field and frequency of electron collisions with plasma particles is carried out.

Generation of longitudinal current by a transverse electromagnetic field in classical and quantum plasmas

From Vlasov kinetic equation for collisionless plasmas distribution function in square-law approximation on size of electromagnetic field is received. Formulas for calculation electric current at any temperature (any degree of degeneration of electronic gas) are deduced. The case of small values of the wave numbers is considered. It is shown, that the nonlinearity account leads to occurrence the longitudinal electric current directed along a wave vector. This longitudinal current orthogonal to known transversal classical current, received at the linear analysis. From the kinetic equation with Wigner integral for collisionless quantum plasma distribution function is received in square-law on vector potential approximation. Formulas for calculation electric current at any temperature are deduced. The case of small values of wave number is considered. It is shown, that size of a longitudinal current at small values of wave number and for classical plasma and for quantum plasma coincide. Graphic comparison of dimensionless size of a current quantum and classical plasma is made.

Electrohydrodynamic instability of a dielectric compressible liquid sheet streaming into an ambient stationary compressible gas

The effect of compressibility of fluids on the linear electrohydrodynamic instability of a dielectric liquid sheet issued from a nozzle into an ambient dielectric stationary gas in the presence of a horizontal electric field is investigated. It is found that increasing the Mach number from subsonic to transonic causes the maximum growth rate and the dominant wavenumber of the disturbances to increase, and the increase is higher in the presence of the electric field. Liquid compressibility has been found to have a minimal effect on instability. At constant wavenumber and electric field values, the growth rate of disturbances increases as the gas Mach number tends to 1, and then begins to decrease with further increase in the gas Mach number. At small values of wavenumber, antisymmetrical disturbances grow faster than symmetrical ones, while the growth rate of both types of disturbances approach each other at large wavenumbers, which increases by increasing the electric field values. At small Weber numbers, antisymmetrical disturbances exhibit a higher maximum growth rate and a lower dominant wavenumber than symmetrical disturbances. However, the maximum growth rate and dominant wavenumber of the two types of disturbances are almost identical when both Weber number and electric field values become large. An increase in the gas to liquid density ratio enhances the instability, and this effect is enhanced for high electric field values. Surface tension and electric fields always oppose and increase the development of instability, respectively; and they have opposite effects for long wavelengths and high Weber numbers.

Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions

The focus of the present work is to provide an analysis for the acoustic and thermal properties of the energy-conserving lattice Boltzmann models, and a solution to the numerical defects and instability associated with these models in two and three dimensions. We discover that a spurious algebraic coupling between the shear and energy modes of the linearized evolution operator is a defect universal to the energy-conserving Boltzmann models in two and three dimensions. This spurious mode coupling is highly anisotropic and may occur at small values of wave number k along certain directions, and it is a direct consequence of the following key features of the lattice Boltzmann equation: (1) its simple spatial-temporal dynamics, (2) the linearity of the relaxation modeling for collision operator, and (3) the energy-conservation constraint. To eliminate the spurious mode coupling, we propose a hybrid thermal lattice Boltzmann equation (HTLBE) in which the mass and momentum conservation equations are solved by using the multiple-relaxation-time model due to d'Humières, whereas the diffusion-advection equation for the temperature is solved separately by using finite-difference technique (or other means). Through the Chapman-Enskog analysis we show that the hydrodynamic equations derived from the proposed HTLBE model include the equivalent effect of gamma=C(P)/C(V) in both the speed and attenuation of sound. Appropriate coupling between the energy and velocity field is introduced to attain correct acoustics in the model. The numerical stability of the HTLBE scheme is analyzed by solving the dispersion equation of the linearized collision operator. We find that the numerical stability of the lattice Boltzmann scheme improves drastically once the spurious mode coupling is removed. It is shown that the HTLBE scheme is far superior to the existing thermal LBE schemes in terms of numerical stability, flexibility, and possible generalization for complex fluids. We also present the simulation results of the convective flow in a rectangular cavity with different temperatures on two opposite vertical walls and under the influence of gravity. Our numerical results agree well with the pseudospectral result.

Dielectric function and electrical dc conductivity of nonideal plasmas

Within generalized linear response theory, an expression for the dielectric function is derived that is consistent with standard approaches to the electrical dc conductivity. Explicit results are given for the first moment Born approximation. Some exact relations as well as the limiting behavior at small values of wave number and frequency are investigated.

EFFECTS OF COMPRESSIBILITY ON THE INSTABILITY OF LIQUID SHEETS

The effect of compressibility of fluids on the instability of a liquid sheet issued from a nozzle into an ambient gas is investigated by use of linear stability analysis. It is found that increasing the gas Mach number from subsonic to transonic causes the maximum growth rate, dominant wave number, and cut-off wave number of disturbances to increase. Liquid compressibility has a minimal effect on instability. At a constant wave number, the growth rate of disturbances increases as the gas Mach number tends to 1 and then begins to decline with further increase in the gas Mach number. Hence, liquid sheet breakup is due to surface disintegration not gross fracturing in agreement with experimental observations. At small values of wave number, antisymmetrical disturbances grow faster than symmetrical ones while the growth rate of both types of disturbances approach each other at large wave numbers. At small Weber number, antisymmetrical disturbances exhibit a higher maximum growth rate and a lower dominant wave number than symmetrical disturbances. However, the maximum growth rate and dominant wave number of the two types of disturbances are almost identical when Weber number becomes large. An increase in the gas-to-liquid density ratio enhances the instability. Surface tension always opposes the development of instability.

The Calculation of Current Correlations in Classical Fluids via Modeled Kinetic Equations

The transverse and longitudinal current correlations in a simple classical fluid were originally calculated from a modeled kinetic equation using an approximate solution valid for only small values of wave number $k$. These correlation functions have been recalculated using the exact solution of this kinetic equation for arbitrary values of $k$.

Stability of an Elastico-Viscous Liquid Film Flowing down an Inclined Plane

The stability of a layer of elastico-viscous liquid (Oldroyd's liquid B) flowing down an inclined plane under the action of gravity is investigated. An eigenvalue problem governing the stability of the flow against wave formation is formulated and solved for small values of wave number. It is found that the presence of elasticity in the liquid lowers the value of the critical Reynolds number.