The effect of an axial electric field on the nonlinear stability between two uniform stream flows of finitely conducting cylinders

2003 ◽  
Vol 81 (6) ◽  
pp. 805-821 ◽  
Author(s):  
Abdel Raouf F Elhefnawy ◽  
Galal M Moatimid ◽  
Abd Elmonem Khalil Elcoot
Keyword(s):  
Dispersion Relation ◽  
Electric Field ◽  
Circular Cross Section ◽  
Multiple Scale ◽  
Physical Parameters ◽  
Linear Dispersion ◽  
Order Problem ◽  
Nonlinear Schrödinger ◽  
Axial Electric Field ◽  
The Stability

Weakly nonlinear streaming instability of two conducting fluids with an interface is presented for cylinders of circular cross section. The two fluids are subjected to a uniform axial electric field. Gravitational effects are neglected. The method of multiple scale perturbation is used to obtain a dispersion relation for the first-order problem and two nonlinear Schrödinger equations for the higher orders. The nonlinear Schrödinger equation, generally, describes the competition between nonlinearity and a linear dispersion relation. One of these equations is used to determine the nonlinear cutoff electric field separating stable and unstable disturbances, while the other is used to analyze the stability of the system. The stability criterion is expressed theoretically in terms of various parameters of the problem. Stability diagrams are obtained for different sets of physical parameters. New instability regions in the parameter space, which appear due to nonlinear effects, are indicated. PACS Nos.: 47.20, 47.55.C, 47.65

Investigation of a Caesium Plasma Diode Using an Electron Beam Probing Technique 1, 2

1967 ◽  
Vol 22 (7) ◽  
pp. 1057-1067 ◽  
Author(s):  
Werner Ott
Keyword(s):  
Electron Beam ◽  
Electric Field ◽  
Charge Carriers ◽  
Axial Electric Field ◽  
Fluorescent Screen ◽  
Plasma Diode ◽  
The Stability ◽  
Ion Emission ◽  
Field Plots ◽  
Ribbon Beam

The plasma in a plane caesium diode with a hot emitter and a cold collector was investigated experimentally with a ribbon-shaped electron beam. The ribbon beam is projected through the diode at an angle of 45 degrees to its axis and allowed to strike a fluorescent screen. Variations in the axial electric field of the diode cause the ribbon beam to be distorted. The image of the distorted beam as seen on the fluorescent screen then constitutes a plot of the axial electric field along the axis of the diode.The field plots so obtained are compared with a theory in which the collisions of the charge carriers are neglected. By means of this comparison it is possible to evaluate the neutralization parameter, the plasma density, and an average drift energy of the charge carriers.The results show that the theory correctly describes the different modes of the potential distribution and especially the transitions between modes of operation as long as the diode is free of oscillations.The stability of the different possible static potential distributions was also investigated. It was found experimentally that the system is unstable if the electron emission is less than the ion emission and the collector potential is positive.

ON GRAVITATIONALLY AND ELECTRODYNAMICALLY BOUND NUCLEAR MATTER CORES OF STELLAR DIMENSIONS

2011 ◽  
Vol 20 (10) ◽  
pp. 1995-2002 ◽  
Author(s):  
MICHAEL ROTONDO ◽  
REMO RUFFINI ◽  
SHE-SHENG XUE ◽  
VLADIMIR POPOV
Keyword(s):  
Electric Field ◽  
Nuclear Matter ◽  
Analytic Solutions ◽  
Physical Parameters ◽  
Heavy Nuclei ◽  
Neutral Atoms ◽  
Charge Neutrality ◽  
Thomas Fermi ◽  
Surface Energies ◽  
The Stability

In a unified treatment we extrapolate results for neutral atoms with heavy nuclei to nuclear matter cores of stellar dimensions with mass numbers A ≈ (m Planck /mn)3 ~ 1057. We give explicit analytic solutions for the relativistic Thomas–Fermi equation of Nn neutrons, Np protons and Ne electrons in beta equilibrium, fulfilling global charge neutrality, with Np = Ne. We give explicit expressions for the physical parameters including the Coulomb and the surface energies and we study as well the stability of such configurations. Analogous to heavy nuclei these macroscopic cores exhibit an overcritical electric field near their surface.

STUDY ON ELECTROHYDRODYNAMIC CAPILLARY INSTABILITY OF VISCOELASTIC FLUIDS WITH RADIAL ELECTRIC FIELD

2014 ◽  
Vol 06 (04) ◽  
pp. 1450037
Author(s):  
MUKESH KUMAR AWASTHI
Keyword(s):  
Dispersion Relation ◽  
Electric Field ◽  
Radial Electric Field ◽  
Critical Value ◽  
Linear Analysis ◽  
Wave Number ◽  
Dual Effect ◽  
Capillary Instability ◽  
Viscous Potential Flow ◽  
The Stability

We study the linear analysis of electrohydrodynamic capillary instability of the interface between a viscous fluid and viscoelastic fluid of Maxwell type, when the phases are enclosed between two horizontal cylindrical surfaces coaxial with the interface, and when fluids are subjected to the radial electric field. Here, we use an irrotational theory known as viscous potential flow (VPF) theory in which viscosity enters through normal stress balance but shearing stresses are assumed to be zero. A quadratic dispersion relation that accounts for the growth of axisymmetric waves is obtained and stability criterion is given in terms of a critical value of wave number as well as electric field. It is observed that the radial electric field has dual effect on the stability of the system.

scholarly journals Study on Electrohydrodynamic Rayleigh-Taylor Instability with Heat and Mass Transfer

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Mukesh Kumar Awasthi ◽  
Vineet K. Srivastava
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Electric Field ◽  
Heat And Mass Transfer ◽  
Taylor Instability ◽  
Wave Number ◽  
Physical Parameters ◽  
Tangential Electric Field ◽  
Rayleigh Taylor Instability ◽  
The Stability

The linear analysis of Rayleigh-Taylor instability of the interface between two viscous and dielectric fluids in the presence of a tangential electric field has been carried out when there is heat and mass transfer across the interface. In our earlier work, the viscous potential flow analysis of Rayleigh-Taylor instability in presence of tangential electric field was studied. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer coefficient, and vapour fraction on the stability of the system. It has been observed that heat transfer and electric field both have stabilizing effect on the stability of the system.

scholarly journals The Instability of an Electrohydrodynamic Viscous Liquid Micro-Cylinder Buried in a Porous Medium: Effect of Thermosolutal Marangoni Convection

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Galal M. Moatimid ◽  
Mohamed A. Hassan
Keyword(s):  
Mass Transfer ◽  
Surface Tension ◽  
Free Surface ◽  
Dispersion Relation ◽  
Electric Field ◽  
Heat And Mass Transfer ◽  
Viscous Liquid ◽  
Marangoni Convection ◽  
Axial Electric Field ◽  
Stabilizing Effect

The electrohydrodynamic (EHD) thermosolutal Marangoni convection of viscous liquid, in the presence of an axial electric field through a micro cylindrical porous flow, is considered. It is assumed that the surface tension varies linearly with both temperature and concentration. The instability of the interface is investigated for the free surface of the fluid. The expression of the free surface function is derived taking into account the independence of the surface tension of the heat and mass transfer. The transcendental dispersion relation is obtained considering the dependence of the surface tension on the heat and mass transfer. Numerical estimations for the roots of the transcendental dispersion relation are obtained indicating the relation between the disturbance growth rate and the variation of the wave number. It is found that increasing both the temperature and concentration at the axial microcylinder has a destabilizing effect on the interface, according to the reduction of the surface tension. The existence of the porous structure restricts the flow and hence has a stabilizing effect. Also, the axial electric field has a stabilizing effect. Some of previous analytical and experimental results are recovered upon appropriate data choices.

scholarly journals Causality and stability in relativistic viscous non-resistive magneto-fluid dynamics

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Rajesh Biswas ◽  
Ashutosh Dash ◽  
Najmul Haque ◽  
Shi Pu ◽  
Victor Roy
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Order Theory ◽  
Causality Condition ◽  
Hydrodynamic Modes ◽  
Linear Dispersion ◽  
Is Theory ◽  
The Stability ◽  
Viscous Pressure ◽  
The Magnetic Field

Abstract We investigate the causality and the stability of the relativistic viscous non-resistive magneto-hydrodynamics in the framework of the Israel-Stewart (IS) second-order theory, and also within a modified IS theory which incorporates the effect of magnetic fields in the relaxation equations of the viscous stress. We compute the dispersion relation by perturbing the fluid variables around their equilibrium values. In the ideal magnetohydrodynamics limit, the linear dispersion relation yields the well-known propagating modes: the Alfvén and the magneto-sonic modes. In the presence of bulk viscous pressure, the causality bound is found to be independent of the magnitude of the magnetic field. The same bound also remains true, when we take the full non-linear form of the equation using the method of characteristics. In the presence of shear viscous pressure, the causality bound is independent of the magnitude of the magnetic field for the two magneto-sonic modes. The causality bound for the shear-Alfvén modes, however, depends both on the magnitude and the direction of the propagation. For modified IS theory in the presence of shear viscosity, new non-hydrodynamic modes emerge but the asymptotic causality condition is the same as that of IS. In summary, although the magnetic field does influence the wave propagation in the fluid, the study of the stability and asymptotic causality conditions in the fluid rest frame shows that the fluid remains stable and causal given that they obey certain asymptotic causality condition.

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