Viscous Plasma Research Articles

Numerical study of double tearing mode instability in viscous plasma

The scalings of double tearing mode (DTM) with various values of resistivity and viscosity have been investigated numerically by using a magneto hydrodynamic model in slab geometry. It is found that the growth rate changes from γ∝η3/5ν0 to γ∝η5/6ν-1/6 when the distance between two rational surfaces 2xs is sufficiently large. On the other hand, when the distance between two rational surfaces 2xs is very small, the scaling of γ and η and ν changes from γ∝η1/3ν0 to γ∝η2/3ν-1/3 as the viscosity increases. Moreover, the nonlinear evolution of symmetrical DTM is investigated in this paper. The study shows that the symmetrical DTM transforms to unsymmetrical DTM in the final phase.

Investigation of diffusivity and viscosity in solar plasma

For diffusive and viscous plasma, the dispersion relation ω2 = k 2 [v 2 − iω(ν + η)] + νηk 4 is applied for the North Polar Coronal Hole, where we have assumed the angular frequency ω to be a real quantity and the wave number k as a complex quantity. For ω = 2π/τ, we have chosen three values 10−2, 10−3 and 10−4 s for τ. For each value of τ, we have considered three situations: (i) where ν = 0 (no viscosity), (ii) where η = 0 (no magnetic diffusivity) and (iii) where both the diffusivity η and viscosity ν are present. For the cases (i) and (ii), we have obtained two solutions, ±(k r + i k i ). But, for the case (iii), we have obtained two pairs of solutions, ±(k r1 + i k i1) and ±(k r2 + i k i2). These two pairs correspond to the fast-mode and slow-mode waves.

Effect of Radiative Heat-Loss Function and Finite Larmor Radius Corrections on Jeans Instability of Viscous Thermally Conducting Self-Gravitating Astrophysical Plasma

The effect of radiative heat-loss function and finite ion Larmor radius (FLR) corrections on the self-gravitational instability of infinite homogeneous viscous plasma has been investigated incorporating the effects of thermal conductivity and finite electrical resistivity for the formation of a star in astrophysical plasma. The general dispersion relation is derived using the normal mode analysis method with the help of relevant linearized perturbation equations of the problem. Furthermore the wave propagation along and perpendicular to the direction of external magnetic field has been discussed. Stability of the medium is discussed by applying Routh Hurwitz’s criterion. We find that the presence of radiative heat-loss function and thermal conductivity modify the fundamental Jeans criterion of gravitational instability into radiative instability criterion. From the curves we see that temperature dependent heat-loss function, FLR corrections and viscosity have stabilizing effect, while density dependent heat-loss function has destabilizing effect on the growth rate of self-gravitational instability. Our result shows that the FLR corrections and radiative heat-loss functions affect the star formation.

Magnetorotational instability in viscous dusty plasmas with three-component model

The magnetorotational instability (MRI) in axisymmetric rotating dusty plasmas with viscous effects is investigated by means of a three-component model MRI with a vertical weak magnetic field. Starting from the three-fluid equations and Maxwell’s equations, I derive the general linear dispersion relation governing local MRI. The dust rotational flow is assumed to have the same angular velocity as ions and electrons. The dispersion relation of two special cases, without viscosity and dust effects respectively, is discussed in detail by taking into account the high-frequency approximation in order to make the perturbation frequency larger than the ion cyclotron frequency. The numerical results demonstrate that both the viscosity and dust effects can prevent the MRI growth, and the dust-induced effects are shown to be especially significant.

Seminal Plasma Components in Camelids and Comparisons with Other Species

Camelid semen is characterized by a highly viscous, low-volume ejaculate with a low concentration of spermatozoa that exhibit low progressive motility. The viscous seminal plasma is currently the major impediment to the development of assisted reproductive technologies (ARTs) in camelids. To advance ARTs such as sperm cryopreservation and artificial insemination in camelids, it is necessary to identify the cause of the viscosity and gain an understanding of the role of seminal plasma components on sperm function and fertility. Numerous compounds and proteins have been identified as mediators of sperm function and predictors of fertility in other livestock species, and understanding the importance of specific proteins has progressed the success of ARTs in these species. Current knowledge on the components of camelid seminal plasma is outlined, together with the implications of these components for the development of ARTs in camelids. The cause of semen viscosity, as well as proteins that are present in camelid seminal plasma, is described for the first time. Seminal plasma components are compared with those of other species to hypothesize their role in sperm function and fertility.

Analysis of Oscillations and Defect Measures for the Quasineutral Limit in Plasma Physics

We perform a rigorous analysis of the quasineutral limit for a hydrodynamical model of a viscous plasma represented by the Navier–Stokes–Poisson system in three dimensions. We show that as λ → 0 the velocity field u λ strongly converges towards an incompressible velocity vector field u and the density fluctuation ρ λ −1 weakly converges to zero. In general, the limit velocity field cannot be expected to satisfy the incompressible Navier–Stokes equation; indeed, the presence of high frequency oscillations strongly affects the quadratic nonlinearities and we have to take care of self-interacting wave packets. We provide a detailed mathematical description of the convergence process by using microlocal defect measures and by developing an explicit correctors analysis. Moreover, we were able to identify an explicit pseudo-parabolic PDE satisfied by the leading correctors terms. Our results include all the previous results in the literature; in particular, we show that the formal limit holds rigorously in the case of well prepared data.

Gravitational instability of radiative plasma with finite larmor radius corrections

The effect of radiative heat-loss function and finite ion Larmor radius (FLR) corrections on the gravitational instability of infinite homogeneous viscous plasma has been investigated incorporating the effects of thermal conductivity and finite electrical resistivity. We find that radiative heat-loss function and thermal conductivity modify the Jeans criterion into radiative instability criterion. Numerical calculations have been performed to show the effect of various parameters on the growth of the gravitational instability.

Quark polarization in a viscous quark-gluon plasma

Quarks produced in the early stage of noncentral heavy-ion collisions could develop a global spin polarization along the opposite direction of the reaction plane due to the spin-orbital coupling via parton interaction in a medium that has finite longitudinal flow shear along the direction of the impact parameter. We study how such polarization evolves via multiple scattering in a viscous quark-gluon plasma with an initial laminar flow. The final polarization is found to be sensitive to the viscosity and the initial shear of local longitudinal flow.

Viscous effects in time-dependent planar reconnection

Context. Viscous dissipation is expected to play a significant part in energy release in solar flares, yet the role of viscosity in a weakly resistive plasma of the solar corona remains unclear. Aims. We attempt to clarify the role of viscous effects in magnetic reconnection by performing simulations of reconnection in planar periodic geometry in an incompressible viscous resistive plasma. Methods. We consider magnetic reconnection, driven by large-scale vortical flows. We use both the classical shear viscosity and the Braginskii form for the ion parallel viscosity in a magnetised plasma. We determine the scalings of the current sheet parameters and the global rates of resistive and viscous dissipation. We use steady-state exact solutions and scaling arguments to interpret the numerical results. Results. We show that, regardless of the form of viscosity, the resistive non-viscous analytical solutions for flux pile-up merging provide a very good approximation of the numerical results in the reconnecting current sheet. We find no evidence for a viscoresistive scale. Numerical results for a highly sheared magnetic field, however, appear to deviate from the analytical predictions in the case of the Braginskii viscosity.

Rayleigh-Taylor instability in quantum magnetized viscous plasma

Quantum effects on Rayleigh-Taylor instability of stratified viscous plasmas layer under the influence of vertical magnetic field are investigated. By linearly solving the viscous QMHD equations into normal mode, a forth-order ordinary differential equation is obtained to describe the velocity perturbation. Then the growth rate is derived for the case where a plasma with exponential density distribution is confined between two rigid planes. The results show that, the presence of vertical magnetic field beside the quantum effect will bring about more stability on the growth rate of unstable configuration for viscous plasma, which is greater than that of inviscous plasma.

Two-dimensional lattice Boltzmann study of red blood cell motion through microvascular bifurcation: cell deformability and suspending viscosity effects

Red blood cell (RBC) motion and trajectories in bifurcated microvessels are simulated using a two-dimensional immersed boundary-lattice Boltzmann method (IB-LBM). A RBC is modeled as a capsule with viscous interior fluid enclosed by a flexible membrane. For the symmetric bifurcation model employed, the critical offset position in the mother branch, which separates the RBC flux toward the two branches, has been calculated. The RBC flux and the hematocrit partitioning between the two daughter branches have also been studied. Effects of the flow-rate ratio, cell deformability and suspending viscosity have been examined. Simulation results indicate that increased cell rigidity and suspending viscosity have counter effects on cell trajectory through a bifurcation: the cell trajectory shifts toward the low flow-rate branch for less deformable cells, and toward the high flow-rate branch for more viscous plasma. These results imply that a higher cell rigidity would reduce the regular phase separation of hematocrit and plasma skimming processes in microcirculation, while an increased viscosity has the opposite effect. This has implications for relevant studies in fundamental biology and biomedical applications.

Shock pattern solutions for viscous-collisional plasma ion acoustic waves in view of the linear theory of the non-equilibrium thermodynamics

In the framework of irreversible thermodynamics, we study nonlinear ion-acoustic waves (IAWs) in viscous and collisional plasmas. Electrons, which form the background, are assumed to be nonthermal. On account of ion viscosity and ion-electron collisions, we investigate using ion fluid equations. We study the effects of the nonthermally distributed electrons β and the temperature ratio σ (= Ti/Te) on the stability, where the stability for Burger’s equation is analyzed by two methods: the phase portrait method and irreversible thermodynamics relations at different values of σ and β. We usa a reductive perturbation technique, where the nonlinear evolution of an IAW is governed by the driven Burger equation. This equation is solved exactly by using two methods: the tanh-function method and the Cole–Hopf transformation. Both methods produce shock wave solutions, their results compared, and good agreement exists in most predictions. The analytical calculations show that an IAW propagates as a shock wave with subsonic speed. The flow velocity, pressure, number density, electrostatic potential, and thermodynamic characteristics are estimated and illustrated as functions of time t and the distance x. It is found via the tanh-function method that the amplitudes of the sought-for functions of the system are suppressed and move towards an equilibrium state at the highest value of β. The tanh-function method reveals an advantage over the Cole–Hopf method in the viscous and collisional cases of IAWs, where it satisfies the stability conditions at the highest value of β with the chosen σ values when applied to evaluate the Onsager relation.

Direct photon production from viscous quark-gluon plasma

We simulate direct photon production in the evolution of viscous quark-gluon plasma medium. Photons from Compton and annihilation processes are considered. The viscous effect on photon production is very strong and reliable simulation is possible only in a limited ${p}_{T}$ range. For minimally viscous fluid ($\ensuremath{\eta}/s=0.08$), direct photons can be reliably computed only up to ${p}_{T}\ensuremath{\leqslant}1.3$ GeV. With reduced viscosity ($\ensuremath{\eta}/s=0.04$), the limit increases to ${p}_{T}\ensuremath{\leqslant}2$ GeV.

ENERGY LOSSES BY ANISOTROPIC VISCOUS DISSIPATION IN TRANSIENT MAGNETIC RECONNECTION

Global energy losses associated with transient magnetic reconnection in a viscous resistive plasma are examined. The Braginskii stress tensor is used to model the plasma viscosity for conditions typical of the solar corona. Analytic arguments are used to show that the large-scale advective flows associated with magnetic merging are likely to generate significant viscous losses. It is pointed out that the development of a visco-resistive reconnection scale, predicted for the classical shear viscosity, is not expected in the more realistic case of the Braginskii viscosity. Numerical simulations of planar coalescence merging show that viscous losses should easily dominate resistive losses for physically plausible parameters in flaring regions. Our computations imply that flare-like rates exceeding 1029 erg s–1 can be achieved under plausible coronal conditions.

Hubble parameter in QCD Universe for finite bulk viscosity

AbstractWe consider the influence of the perturbative bulk viscosity on the evolution of the Hubble parameter in the QCD era of the early Universe. For the geometry of the Universe we assume the homogeneous and isotropic Friedmann‐Lemaitre‐Robertson‐Walker metric, while the background matter is assumed to be characterized by barotropic equations of state, obtained from recent lattice QCD simulations, and heavy‐ion collisions, respectively. Taking into account a perturbative form for the bulk viscosity coefficient, we obtain the evolution of the Hubble parameter, and we compare it with its evolution for an ideal (non‐viscous) cosmological matter. A numerical solution for the viscous QCD plasma in the framework of the causal Israel‐Stewart thermodynamics is also obtained. Both the perturbative approach and the numerical solution qualitatively agree in reproducing the viscous corrections to the Hubble parameter, which in the viscous case turns out to be slightly different as compared to the non‐viscous case. Our results are strictly limited within a very narrow temperature‐ or time‐interval in the QCD era, where the quark‐gluon plasma is likely dominant.

Effect of Hall current on the Jeans instability of magnetized viscous quantum plasma

The effect of Hall current on the Jeans instability of an infinitely conducting, homogeneous, viscous quantum plasma is investigated. The basic equations of the problem are constructed and linearized by using the quantum magnetohydrodynamic model. The contributions of Hall current and viscosity of the medium are incorporated into the present analysis because of their astrophysical importance. The general dispersion relation is obtained using the normal mode analysis technique, which is reduced for both the transverse and the longitudinal mode of propagation. The longitudinal mode is found to be modified by Hall current, while the transverse mode is unaffected by the presence of the Hall parameter. The Jeans criterion of instability is obtained, which is modified by Alfven velocity and quantum corrections but is unaffected by the presence of the Hall parameter and viscosity. The longitudinal mode is found to be modified by Alfven speed and the Hall parameter and is independent of quantum corrections. Viscosity, magnetic field and quantum corrections all have a stabilizing influence on the growth rate of the Jeans instability.

Nonlinear electron oscillations in a viscous and resistive plasma

Nonlinear, spatially periodic, long-wavelength electrostatic modes of an electron fluid oscillating against a motionless ion fluid (Langmuir waves) are given, with viscous and resistive effects included. The cold plasma approximation is adopted, which requires the wavelength to be sufficiently large. The pertinent requirement valid for large amplitude waves is determined. The general nonlinear solution of the continuity and momentum transfer equations for the electron fluid along with Poisson's equation is obtained in simple parametric form. It is shown that in all typical hydrogen plasmas, the influence of plasma resistivity on the modes in question is negligible. Within the limitations of the solution found, the nonlinear time evolution of any (periodic) initial electron number density profile ne(x,t=0) can be determined (examples). For the modes in question, an idealized model of a strictly cold and collisionless plasma is shown to be applicable to any real plasma, provided that the wavelength λ>>λmin(n(0),Te) , where n(0)=const and Te are the equilibrium values of the electron number density and electron temperature. Within this idealized model, the minimum of the initial electron density n(e)(xmin,t=0) must be larger than half its equilibrium value, n(0)/2 . Otherwise, the corresponding maximum n(e)(xmax,t=τ(p)/2) , obtained after half a period of the plasma oscillation blows up. Relaxation of this restriction on n(e)(x,t=0) as one decreases λ , due to the increase of the electron viscosity effects, is examined in detail. Strong plasma viscosity is shown to change considerably the density profile during the time evolution, e.g., by splitting the largest maximum in two.

Quasi-Neutral Limit for a Model of Viscous Plasma

We perform a rigorous analysis of the quasi-neutral limit for a model of viscous plasma represented by the Navier–Stokes–Poisson system of equations. It is shown that the limit problem is the Navier–Stokes system describing a barotropic fluid flow, with the pressure augmented by a component related to the nonlinearity in the original Poisson equation.

Forced oscillations of a viscous incompressible plasma with allowance for the electron inertia in a circular tube

The forced oscillations of a plasma column resulting from harmonic oscillations of the total current at a frequency ω are investigated analytically and numerically. The column plasma is assumed to be quasi-neutral two-component viscous and electroconducting, the electron inertia and the displacement current being completely taken into account. The electrons and ions are considered to be incompressible interpenetrating fluids. It is shown that the oscillations of the total current lead to the appearance of colliding plasma flows in the column, and, as the oscillation frequency ω increases, a skin layer with respect to main plasma parameters (current density, electromagnetic field, and hydrodynamic electron and ion velocities) develops on the boundary of the column. A comparison with the MHD theory is carried out and the role of the electron inertia and the displacement current in the generation of forced oscillations is investigated. The results obtained are used to analyze the plasma compression in apparatuses such as z-pinch and plasma focus.

Elemental transport coefficients in viscous plasma flows near local thermodynamic equilibrium

We propose a convenient formulation of elemental transport coefficients in chemically reacting and plasma flows locally approaching thermodynamic equilibrium. A set of transport coefficients for elemental diffusion velocities, heat flux, and electric current is introduced. These coefficients relate the transport fluxes with the electric field and with the spatial gradients of elemental fractions, pressure, and temperature. The proposed formalism based on chemical elements and fully symmetric with the classical transport theory based on chemical species, is particularly suitable to model mixing and demixing phenomena due to diffusion of chemical elements. The aim of this work is threefold: to define a simple and rigorous framework suitable for numerical implementation, to allow order of magnitude estimations and qualitative predictions of elemental transport phenomena, and to gain a deeper insight into the physics of chemically reacting flows near local equilibrium.