Anisotropic Pressure Tensor Research Articles

Nanotube diameter dependency of anisotropic pressure of an ionic liquid confined in a carbon nanotube: A molecular dynamics study for [emim][PF6] case

We have presented molecular dynamics (MD) simulations of 1-ethyl-3-methylimidazolium hexafluorophosphate [emim][PF6] inside carbon nanotubes (CNTs) with different diameters. By considering the anisotropic pressure tensor for the ionic liquid inside the CNTs, the parameters of an equation of state (EoS) for the radial and axial directions have been derived. The nanotube diameter dependency of the EoS parameters has been also investigated.

A new interhemispheric 16‐moment model of the plasmasphere‐ionosphere system: IPIM

AbstractWe present a new interhemispheric numerical model: the IRAP plasmasphere‐ionosphere model (IPIM). This model describes the transport of the multispecies ionospheric plasma from one hemisphere to the other along convecting and corotating magnetic field lines, taking into account source processes at low altitude such as photoproduction, chemistry, and energization through the coupling with a kinetic code solving the transport of suprathermal electron along the field line. Among the new developments, a 16‐moment‐based approach is used for the transport equations in order to allow development of strong temperature anisotropy at high altitude and we consider important but often neglected effects, such as inertial acceleration (centrifugal and Coriolis). In this paper, after presenting in detail the principle of the model, we focus on preliminary results showing the original contribution of this new model. For these first runs, we simulate the convection and corotation transport of closed flux tubes in the plasmasphere for tilted/eccentric dipolar magnetic field configuration in solstice and equinox conditions. We follow different flux tubes between 1.2 and 6 Earth Radii (RE) and demonstrate the capability of the model to describe a wide range of density (above 15 orders of magnitude). The relevance of the mathematical approach used is highlighted, as anisotropies can develop above 3000 km in the plasmasphere as a result of the mirroring effect related to the anisotropic pressure tensor. Moreover, we show that the addition of inertial acceleration may become critical to describe plasma interhemispheric transport above 4RE. The ability of the model to describe the external plasmasphere is demonstrated, and innovative studies are foreseen, regarding the dynamics of the plasma along the magnetic field lines (in particular interhemispheric exchanges and “opening”/“closure” of a flux tube).

Gravitational instability on propagation of MHD waves in astrophysical plasma

AbstractWe determine the general dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in astrophysical plasma by considering the effect of gravitational instability and viscosity with anisotropic pressure tensor and heat-conducting plasma. Basic MHD equations have been derived and linearized by the method of perturbation to develop the general form of dispersion relation equation. Our result indicates that the transverse propagation of waves in such a plasma is affected by the inclusion of heat conduction. For wave propagation, parallel to the magnetic field direction, we find that the fairhose mode is unaffected, whereas the mode corresponding to the gravitational instability is modified in astrophysical plasma with anisotropic pressure tensor being stable in the presence of viscosity and strong magnetic field at considerable wavelength.

Effect of viscosity on propagation of MHD waves in astrophysical plasma

AbstractWe determine the general dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in an astrophysical plasma by considering the effect of viscosity with an anisotropic pressure tensor. Basic MHD equations have been derived and linearized by the method of perturbation to develop the general form of the dispersion relation equation. Our result indicates that an astrophysical plasma with an anisotropic pressure tensor is stable in the presence of viscosity and a strong magnetic field at considerable wavelength.

Toward an Equation of State for Water inside Carbon Nanotubes

Water inside carbon nanotubes as an example of nanoconfined water has gained noticeable attention, in both theoretical and applied aspects. Molecular simulation has played a major role in the studies in this field. Yet, there is a need for systematic study of simulation results and compilation of scientifically reliable predictive relations. Here we present Monte Carlo simulations of water inside carbon nanotubes with different radii. An equation of state which was derived on the basis of the extended Lennard-Jones (12,6,3) as the effective pair potential is chosen for the system of water inside the carbon nanotubes. The equation of state is modified to take the effects of anisotropic pressure tensor into account. Using the simulation results, the applicability of this equation of state for water inside the carbon nanotubes is studied and the parameters of the equation of state for this system are obtained.

On viscous flow and azimuthal anisotropy of the quark–gluon plasma in a strong magnetic field

We calculate the viscous pressure tensor of the quark–gluon plasma in a strong magnetic field. It is azimuthally anisotropic and is characterized by five shear viscosity coefficients, four of which vanish when the field strength eB is much larger than the plasma temperature squared. We argue that the azimuthally anisotropic viscous pressure tensor generates the asymmetric transverse flow. As an illustration, we consider non-relativistic plasma flow in a very strong constant magnetic field; azimuthal asymmetry in this case is as large as 1/3, even not taking into account the collision geometry. This result suggests that the magnitude of the shear viscosity extracted from the experimental data ignoring the magnetic field must be underestimated, although a more quantitative estimate warrants further numerical investigation.

Type I Planetary Migration in a Self‐Gravitating Disk

We investigate the tidal interaction between a low-mass planet and a self-gravitating protoplanetary disk, by means of two-dimensional hydrodynamic simulations. We first show that considering a planet freely migrating in a disk without self-gravity leads to a significant overestimate of the migration rate. The overestimate can reach a factor of two for a disk having three times the surface density of the minimum mass solar nebula. Unbiased drift rates may be obtained only by considering a planet and a disk orbiting within the same gravitational potential. In a second part, the disk self-gravity is taken into account. We confirm that the disk gravity enhances the differential Lindblad torque with respect to the situation where neither the planet nor the disk feels the disk gravity. This enhancement only depends on the Toomre parameter at the planet location. It is typically one order of magnitude smaller than the spurious one induced by assuming a planet migrating in a disk without self-gravity. We confirm that the torque enhancement due to the disk gravity can be entirely accounted for by a shift of Lindblad resonances, and can be reproduced by the use of an anisotropic pressure tensor. We do not find any significant impact of the disk gravity on the corotation torque.

Szekeres-type mappings of Kasner and Petrov type I(M+) purely magnetic spacetimes

We show that Szekeres-type mappings of Kasner spacetime generate a 2-variable Haddow magnetic spacetime of Petrov type I(M∞) and of Segré type . It is then shown that this spacetime is unique for the generating functions of 3- or 4-variable generalizations. Moreover, sufficient conditions on the variable dependence of the metric coefficients distinguishing types I(M∞) and I(M+) are established for diagonal purely magnetic spacetimes. These results are then combined by embedding the 2-variable Haddow magnetic spacetime within a diagonal spacetime such that the resulting spacetime is of Petrov type I(M+), in general. In turn, this leads to a family of non-vacuum purely magnetic spacetimes of Petrov type I(M+). It is then shown that either the anisotropic pressure tensor or heat-flux vector can be set to zero. Notably, the former class contains a sub-class of Haddow magnetic spacetimes also of Petrov type I(M+). Finally, the possibility of conformally relating the general family of non-vacuum purely magnetic spacetimes to vacuum is shown not to be possible.

Shearing Box Simulations of the MRI in a Collisionless Plasma

We describe local shearing box simulations of turbulence driven by the magnetorotational instability (MRI) in a collisionless plasma. Collisionless effects may be important in radiatively inefficient accretion flows, such as near the black hole in the Galactic center. The MHD version of ZEUS is modified to evolve an anisotropic pressure tensor. A fluid closure approximation is used to calculate heat conduction along magnetic field lines. The anisotropic pressure tensor provides a qualitatively new mechanism for transporting angular momentum in accretion flows (in addition to the Maxwell and Reynolds stresses). We estimate limits on the pressure anisotropy due to pitch angle scattering by kinetic instabilities. Such instabilities provide an effective collision rate in a collisionless plasma and lead to more MHD-like dynamics. We find that the MRI leads to efficient growth of the magnetic field in a collisionless plasma, with saturation amplitudes comparable to those in MHD. In the saturated state, the anisotropic stress is comparable to the Maxwell stress, implying that the rate of angular momentum transport may be moderately enhanced in a collisionless plasma.

Wave modes in a magnetoplasma with anisotropic perturbation pressure–fluid and kinetic calculations

The fluid quintic dispersion equation and the full kinetic Boltzmann–Vlasov equation have been programmed for a one-species magnetoplasma in a form permitting direct comparison between them. The quintic equation yields five wave-modes, two electromagnetic, a Langmuir or Bernstein mode and two transversely polarized acoustic modes driven by the trace-free part of the anisotropic pressure tensor. The slower acoustic mode is found in the kinetic analysis to be evanescent, the other suffers appreciable Landau damping except in the first gyroharmonic band when its phase velocity approaches and even exceeds that of the Langmuir mode, with a resultant mixing of modal properties. The Langmuir or Bernstein mode refractive index surfaces found in the fluid and kinetic analyses are generally in good agreement, but gyroharmonic wave–particle interactions seen in the Bernstein modes are missed in the fluid analysis, such as resonant effects very close to the gyroharmonic frequencies and strong damping at all propagation angles when the wave frequency lies in a forbidden Bernstein region. In all cases the fluid analysis provides additional information on wave polarization and generalized energy fluxes–electromagnetic and acoustic–permitting easy identification of modes.

Geometric Equations of State in Friedmann-Lemaître Universes Admitting Matter and Ricci Collineations

As a rule in General Relativity the spacetime metric fixes the Einstein tensor and through the Field Equations (FE) the energy-momentum tensor. However one cannot write the FE explicitly until a class of observers has been considered. Every class of observers defines a decomposition of the energy-momentum tensor in terms of the dynamical variables energy density ($\mu$), the isotropic pressure ($p$), the heat flux $q^a$ and the traceless anisotropic pressure tensor $\pi_{ab}$. The solution of the FE requires additional assumptions among the dynamical variables known with the generic name equations of state. These imply that the properties of the matter for a given class of observers depends not only on the energy-momentum tensor but on extra a priori assumptions which are relevant to that particular class of observers. This makes difficult the comparison of the Physics observed by different classes of observers for the {\it same} spacetime metric. One way to overcome this unsatisfactory situation is to define the extra condition required among the dynamical variables by a geometric condition, which will be based on the metric and not to the observers. Among the possible and multiple conditions one could use the consideration of collineations. We examine this possibility for the Friedmann-Lema\^{i}tre-Robertson-Walker models admitting matter and Ricci collineations and determine the equations of state for the comoving observers. We find linear and non-linear equations of state, which lead to solutions satisfying the energy conditions, therefore describing physically viable cosmological models.

Anisotropic magnetohydrostatic equilibria with arbitrary magnetic fields

For any arbitrarily given magnetic field, an anisotropic pressure tensor of the form appearing in guiding center theories and drift theories exists such that the magnetohydrostatic pressure balance is met.

Wave modes in a magnetoplasma with anisotropic perturbation pressure

The momentum balance equation and the balance equation for the pressure tensor of a collision-free one-species magnetoplasma are linearized and Fourier-transformed, together with Maxwell's curl equations. They are combined in an algebraic dispersion system for the average perturbation velocity of the plasma particles. To do this a set of five fourth-order projectors is introduced, constructed with the aid of a commutative ‘ring product’ of two second-order projectors. It is shown that the trace-free part of the anisotropic perturbation pressure tensor, usually ignored for the sake of simplicity in such analyses, is of the same order of magnitude as the trace of this tensor. The vanishing determinant of the dispersion system is the dispersion equation of fifth degree in the square of the refractive index.

Exact Bianchi type V imperfect fluid solutions

It is shown that it is sufficient to solve a single first order differential equation to determine exact Bianchi type V imperfect fluid solutions of Einstein's field equations. Two exact solutions are presented in this paper. One of these two solutions corresponds to the case when the anisotropic pressure tensor is proportional to the shear tensor. This proportionality, it is shown, is a necessary but not a sufficient condition for the absence of heat flow in a Bianchi type V universe. It is also observed that the presence of heat flow necessarily introduces anisotropy in a Bianchi type V universe.

Wiggler-free FEL with an intense helical beam

We describe a new theoretical and numerical framework for magnetohydrodynamic (MHD) simulations with an incorporated anisotropic pressure tensor, which can play an important role in collisionless plasmas. The classical approach to handle the anisotropy is based on application of the double adiabatic approximation, assuming that the pressure tensor is well described only by those components that are oriented parallel and perpendicular to the local magnetic field. This gyrotropic assumption, however, fails around magnetically neutral regions, where the cyclotron period may become comparable to or even longer than the system's dynamical time, which causes a singularity in the mathematical expression. In this paper, we demonstrate that this singularity can be completely removed by direct use of the 2nd-moment of the Vlasov equation, combined with an ingenious gyrotropization model. Numerical tests are used to verify that our model properly reduces to the standard MHD results or the double adiabatic formulation in an asymptotic manner under the limit of fast isotropization and fast gyrotropization, respectively.

Linear hydromagnetic waves in an ultrarelativistic, collisionless plasma with a pressure anisotropy.

Magnetohydrodynamic (MHD) waves in a strongly magnetized collionless plasma are considered. Consideration is carried on for the plasma with an anisotropic pressure tensor. We have derived a closed set of MHD equations describing linear hydromagnetic waves, and found the corresponding dispersion relation. We found the general solution of the dispersion equation, and considered various special cases corresponding to various standard types of MHD waves and the firehouse instability. Alternative solutions are found by means of the equations of state derived earlier for a medium with such properties and an ultrarelativistic temperature in Tsikarishvili et al. [Phys. Rev. A 46, 1078 (1992)].

Hydrodynamics of collisionless relativistic plasma with pressure anisotropy

The closed set of relativistic hydrodynamical equations describing strongly magnetized collisionless plasma with an anisotropic pressure tensor is offered. This model is the generalization of Chew–Goldberger–Low [Proc. R. Soc. London Ser. A 236, 112 (1956)] theory for the relativistic case. It is shown that at high temperatures the equation of state differs significantly from the ones used earlier.

General-relativistic hydrodynamics of a collisionless plasma in a strong magnetic field.

The closed set of general-relativistic hydrodynamical equations describing a strongly magnetized collisionless plasma with an anisotropic pressure tensor is derived. Consideration is based on the ``3+1'' formulation of magnetohydrodynamics and the orthonormal tetrad technique. The model is the further generalization of the theory of Chew, Goldberger, and Low [Proc. R. Soc. London Ser. A 236, 1204 (1954)] for the general-relativistic case. In ultrarelativistic limit the equations of state are obtained, which differ noticeably from those known previously.

Birkeland currents in an anisotropic, magnetostatic plasma

An expression for the parallel current density is derived for a plasma characterized by negligible bulk flow (magnetostatic) velocity and a two‐component (anisotropic) pressure tensor by expanding the equilibrium Vlasov equation for each species in the adiabatic parameter until such point as a nonvanishing moment j∥ = ∫ d³ υυ∥ ƒ is identified. The result is a nonlocal one: it relates j∥ at one point s along a field line to j∥ at another (reference) point s0 plus an integral function of the pressure and magnetic field between them. It is a generalization and elaboration of results obtained by Bostrom (1975), Heinemann (1990), and Heinemann and Pontius (1991). The expression could have been obtained by integrating the current continuity equation with −▽ · j⊥ as a source term and j⊥ given by perpendicular momentum balance. We explicitly show the equivalency. The widely used Vasyliunas (1970) equation follows when P⊥ is set equal to P∥ and s and s0 are taken to be at the ionosphere and the equator. An extended discussion of the relationship of results derived here to others in the literature is carried out in an effort to bring unity and perspective to this problem area.

Hydrodynamical constraints on cosmic-ray acceleration in relativistic shocks

A two-fluid hydrodynamical model governing the transport of cosmic rays in a relativistically moving background plasma is developed. The equations are used to discuss the time asymptotic structure of a relativistic, plane-parallel shock wave significantly modified by first-order Fermi acceleration of cosmic rays. The model allows for an anisotropic cosmic-ray pressure tensor with pressure components parallel and perpendicular to the shock normal. It is surmised that the well-known energy threshold problem for diffusive shock acceleration that downstream particles have a large enough velocity to overtake the shock and subsequently scatter in the upstream medium before returning to the downstream medium may be expressed hydrodynamically by the condition V less than V(cr), where V is the fluid velocity relative to the shock and V(cr) is the relativistic cosmic-ray sound speed. Astrophysical implications of the results are briefly discussed.