Anisotropic Thermal Pressure Research Articles

On the arbitrary amplitude ion-acoustic structures in an anisotropic non-Maxwellian electron–positron–ion magnetoplasma

This paper comprehensively investigates the oblique propagation of ion-acoustic solitary waves (IASWs) with arbitrary amplitude in a magnetoplasma consisting of inertialess non-Maxwellian (nonthermal) electrons, inertialess Maxwellian positrons, and inertial adiabatically heated ions. It is postulated that the positive ions demonstrate adiabatic behavior that is distinguished by anisotropic thermal pressure. The study utilizes Sagdeev's pseudopotential theory to analyze the fluid equations of the plasma model and reduce them to the energy equation. Different plasma configuration factors, such as nonthermal parameters, positron concentration, and parallel and perpendicular ion pressure, are being studied to see how they affect the properties of solitary waves with large amplitudes. The findings demonstrate the simultaneous coexistence of compressive and rarefactive IASWs, significantly influenced by positrons and nonthermal electron parameters. The study provides valuable insights into wave phenomena in magnetized plasmas and presents possible applications in both Space and laboratory plasma environments.

Oblique propagation of arbitrary amplitude ion acoustic solitary waves in anisotropic electron positron ion plasma

The oblique propagation of arbitrary ion acoustic solitary waves (IASWs) in magnetized electron-positron-ion plasmas is investigated by employing Sagdeev pseudopotential approach. Ions are assumed to be adiabatic having anisotropic thermal pressure. Electrons and positrons are considered to be isothermal, following Maxwellian distribution. In terms of electrostatic potential, Sagdeev potential function is obtained and analyzed numerically in the context of relevant plasma configuration parameters. The existence region of solitary pulses is defined accurately. It is investigated how several plasma configuration parameters, such as the positron concentration, parallel, and perpendicular ion pressure affect soliton characteristics.

Commentary on “Constraints on the Equations of State of stiff anisotropic minerals: rutile, and the implications for rutile elastic barometry” [Miner. Mag. 83 (2019) pp. 339–347

AbstractThe conclusion of Zaffiroet al.(2019; Constraints on the Equations of State of stiff anisotropic minerals: rutile, and the implications for rutile elastic barometry.Mineralogical Magazine,83, 339–347) that the Mie–Grüneisen–Debye (MGD) Equation of State (EoS) cannot fit the available data for rutile is shown to be incorrect, even though rutile exhibits significant anisotropic thermal pressure which invalidates the quasi-harmonic approximation used as the basis for the MGD EoS. The refined parameters for the MGD EoS of rutile are:KTR0= 205.05(25) GPa,$K_{TR0}^{\prime} $= 7.2(5), θD= 399(20) K, γ0= 1.40(2) andq= 1.5(7). This EoS predicts volumes, bulk moduli and volume thermal expansion coefficients for rutile at metamorphic conditions that are statistically indistinguishable from those predicted by the ‘isothermal’ type of EoS reported previously.

Limits to the Validity of Thermal-Pressure Equations of State

Thermal-pressure Equations of State (EoS) such as the Mie-Grüneisen-Debye (MGD) model depend on several assumptions, including the quasi-harmonic approximation (QHA) and a simplified phonon density of states. We show how the QHA is violated by materials exhibiting anisotropic thermal pressure. We also show that at pressures lower than those of the isochor of the reference volume, the static pressure may become sufficiently negative to make the compressional part of the EoS invalid. This limit is sensitive to the combined effects of the EoS parameters K’0, q and the Grüneisen parameter γ0. Large values of q, which correspond to a rapid decrease in phonon mode frequencies with increasing volume, can also lead to the bulk modulus becoming zero at high pressures and temperatures that are not particularly extreme for planetary geotherms. The MGD EoS therefore has an extremely limited P and T regime over which it is both valid and has physically-meaningful properties. Outside of this range, additional terms should be included in the thermal pressure that represents the physical properties of the solid. Or, alternatively, ‘isothermal’ EoS in which the temperature variation of the elastic properties is explicitly modeled without reference to a physical model can be used.

Constraints on the Equations of State of stiff anisotropic minerals: rutile, and the implications for rutile elastic barometry

AbstractWe present an assessment of the thermo-elastic behaviour of rutile based on X-ray diffraction data and direct elastic measurements available in the literature. The data confirms that the quasi-harmonic approximation is not valid for rutile because rutile exhibits substantial anisotropic thermal pressure, meaning that the unit-cell parameters change significantly along isochors. Simultaneous fitting of both the diffraction and elasticity data yields parameters ofKTR0= 205.14(15) GPa,KSR0= 207.30(14) GPa,$K_{TR0}^{\prime} $= 6.9(4) in a 3rd-order Birch-Murnaghan Equation of State for compression, αV0= 2.526(16) × 10–5K–1, Einstein temperature θE= 328(12) K, Anderson-Grüneisen parameter δT= 7.6(6), with a fixed thermal Grüneisen parameter γ = 1.4 to describe the thermal expansion and variation of bulk modulus with temperature at room pressure. This Equation of State fits all of the available data up to 7.3 GPa at room temperature, and up to 1100 K at room pressure within its uncertainties. We also present a series of formulations and a simple protocol to obtain thermodynamically consistent Equations of State for the volume and the unit-cell parameters for stiff materials, such as rutile. In combination with published data for garnets, the Equation of State for rutile indicates that rutile inclusions trapped inside garnets in metamorphic rocks should exhibit negative residual pressures when measured at room conditions.

Ion acoustic cnoidal waves in a magnetized plasma in the presence of ion pressure anisotropy

An investigation of the ion acoustic nonlinear periodic (cnoidal) waves in a magnetized plasma with positive ions having anisotropic thermal pressure and Maxwellian electrons is carried out. The Korteweg-de Vries equation for the wave potential is derived via a reductive perturbation technique and its cnoidal wave solution is obtained. The effect of various relevant plasma parameters like ion pressure anisotropy and obliqueness of field on the characteristics of ion acoustic nonlinear periodic wave structures is investigated in detail. The present investigation could be useful in space and astrophysical plasma systems having ion pressure anisotropy, particularly, in the magnetosphere and near Earth magnetosheath.

CoMg olivine: cation partitioning, thermal expansion and structural variation studied by in situ neutron and synchrotron powder diffraction

The crystal structure of CoMg olivine has been investigated by in situ neutron and synchrotron X-ray powder diffraction at temperatures between 23°C and 1050°C. The olivine sample was prepared at 1450°C by solid-state reaction. During quench, the structure acquired a partially anti-ordered Co,Mg site occupancy, X Co M 1 > X Co M 2 , which upon ensuing heating persisted up to 550°C due to slow exchange kinetics. Above 600°C, internal equilibrium was readily obtained. The temperature variation of the Co,Mg site occupancies was modelled by R T ln( K D )= − 12080 ( ±620 ) −160 ( ±0.58 ) T [ J mol − 1 ]. The pronounced negative exchange enthalpy strongly favours the anti-ordered state, as does the positive exchange entropy so that CoMg olivine will remain in this state up to the melting point. The anisotropy of thermal expansion was analysed using an isothermal equation-of-state (EoS) (Kumar, 1995) coupled with the thermal Mie-Gruneisen EoS. This coupling allowed for relating the anisotropic expansivity to an anisotropic thermal pressure. Both properties are linked to the temperature-dependent rotations of the M1 and M2 octahedra in the [001] plane. The rotations increase from Mg via CoMg to Fe olivine. The Kumar and Birch-Murnaghan EoS’s gave virtually indistinguishable results upon modelling thermal expansion. The increase of the mean bond distances and with temperature changes at ~550°C when the redistribution of Co and Mg begins. In terms of a distortion parameter defined as a normalized standard deviation, the bond length distortion of the M2 octahedron is larger than that of M1. Conversely, M1 is more distorted than M2, if the distortion is defined by the variation of the octahedral faces as well as by the variation of the O-M-O angles subtended at the M sites. The former distortion relates to the exchange entropy.

Multidimensional Hall magnetohydrodynamics with isotropic or anisotropic thermal pressure: Numerical scheme and its validation using solitary waves

We present a numerical solver for plasma dynamics simulations in Hall magnetohydrodynamic (HMHD) approximation in one, two and three dimensions. We consider both isotropic and anisotropic thermal pressure cases, where a general gyrotropic approximation is used. Both explicit energy conservation equation and general polytropic state equations are considered. The numerical scheme incorporates second-order Runge–Kutta advancing in time and Kurganov–Tadmor scheme with van Leer flux limiter for the approximation of fluxes. A flux-interpolated constrained-transport approach is used to preserve solenoidal magnetic field in the simulations. The implemented code is validated using several test problems previously described in the literature. Additionally, we propose a new validation method for HMHD codes based on solitary waves that provides a possibility of quantitative rigorous testing in nonlinear (large amplitude) regime as an extension to standard tests using small-amplitude whistler waves. Quantitative tests of accuracy and performance of the implemented code show the fidelity of the proposed approach.

Effect of Anisotropic Ion Pressure on Solitary Waves in Magnetized Dusty Plasmas

AbstractThe propagation of linear and nonlinear dust ion acoustic waves (DIAWs) are studied in a collisionless magnetized plasma which consists of warm ions having anisotropic thermal pressure, nonthermal (energetic) electrons and static dust particles of positive and negative charge polarity. The anisotropic ion pressure is defined using double adiabatic Chew‐Golberger‐Low (CGL) theory. In the linear regime, the propagation properties of the two possible modes are investigated via ion pressure anisotropy, dust particle polarity and nonthermality of electrons. Using reductive method Zakharov‐Kuznetsov (ZK) equation is derived for the propagation of two dimensional electrostatic dust ion acoustic solitary waves in dusty plasmas. It is found that both compressive and rarefactive solitons are formed in presence of nonthermal electrons using Cairn's distribution [R.A. Cairns, A.A. Mamun, R. Bingham, R.O. Dendy, R. Bostrom, C.M.C. Nairn and P.K. Shukla, Geophys.Res. Lett. 22, 2709 (1995)] in the system. The ion pressure anisotropy, nonthermality of electrons and charge polarity of the dust particles have significant effects on the amplitude and width of the dust ion acoustic solitary waves in such anisotropic nonthermal magnetized dusty plasmas. The numerical results are also presented for illustration. Our finding is applicable to space dusty plasma regimes having anisotropic ion pressure and nonthermal electrons. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A two-fluid model describing the finite-collisionality, stationary Alfvén wave in anisotropic plasma

Abstract. The stationary inertial Alfvén (StIA) wave (Knudsen, 1996) was predicted for cold, collisionless plasma. The model was generalized (Finnegan et al., 2008) to include nonzero values of electron and ion collisional resistivity and thermal pressure. Here, the two-fluid model is further generalized to include anisotropic thermal pressure. A bounded range of values of parallel electron drift velocity is found that excludes periodic stationary Alfvén wave solutions. This exclusion region depends on the value of the local Alfvén speed VA, plasma beta perpendicular to the magnetic field β⊥ and electron temperature anisotropy.

Evolution of magnetic fields in the IGM: kinetic MHD turbulence

AbstractIn this work, we present 3D MHD simulations of non-helical, forced turbulence, with an anisotropic thermal pressure with respect to the orientation of the local magnetic field. Such anisotropy arises when the plasma is weakly collisional, i.e., when the Larmor frequency is much greater than the ion-ion collision frequency. In this Kinetic MHD regime (KMHD), there are instabilities that give rise to fast growing magnetic fluctuations in the smallest scales. The plasma that fills the intergalactic and intracluster media has small density (n ~ 10−3cm−3), hence the effects of these instabilities could be important in the turbulent amplification of the magnetic fields there. In order to study the KMHD turbulence, we have performed 3D numerical simulations employing a godunov-MHD code (e.g., Kowal, Lazarian & Beresnyak 2007; Falceta-Gonçalves, Lazarian & Kowal 2008). The power spectrum of the velocity and magnetic fields were calculated for two cases: when there is a pre-existing mean magnetic field, and when there is only an initial weak magnetic field.

Compressible streaming instabilities of warm multicomponent collisional magnetized astrophysical disks

A general theory for instabilities of multicomponent warm magnetized accretion disks is developed using Maxwell’s equations and the equations of motion and continuity for each disk component. The compressibility, anisotropic thermal pressure, and collisions of the charged species with neutrals are taken into account. The thermal effects are involved without any simplifications. An equilibrium state is discussed. The dispersion relation is derived in the most general form for an arbitrary direction of the wave vector of perturbations and for an arbitrary strength of the thermal effects. The solutions of the dispersion relation are found in some specific case appropriated for the weakly ionized plasma in the regions of the protostellar and protoplanetary disks, where the electrons can be considered as thermal and magnetized and the ions and dust grains as cold and unmagnetized. These solutions describe new axisymmetric and nonaxisymmetric electromagnetic disk instabilities due to collisions and the difference between the stationary azimuthal velocities of different charged species.

Weakly nonlinear transport in warm multicomponent dusty magnetoplasmas

A general nonlinear theory for low-frequency electromagnetic field generation due to the action of non-uniform and non-stationary high-frequency electromagnetic radiation (ponderomotive force) in uniform multicomponent dusty magnetoplasmas is developed. The anisotropic thermal pressure of all species in slow and fast oscillations is taken into account. This theory permits us to consider the nonlinear action of all waves that can exist in such plasmas. As an example, the equations for dust particle velocities arising due to nonlinear electric fields induced by electromagnetic cyclotron waves travelling along an external magnetic field are obtained. The dust grains are considered to be magnetized as well as unmagnetized. Various regimes of dust grain dynamics depending on the spatio-temporal variation of a fast wave amplitude are discussed. It is shown that induced nonlinear electric fields can have both an electrostatic and an electromagnetic nature. In some cases these fields across the background magnetic field in warm plasmas are considerably larger than those in cold plasmas. The longitudinal nonlinear electric field remains the same in warm and cold plasmas in its order of magnitude. Regimes are found for which the transverse acceleration of dust grains is much larger than the longitudinal one.

Compressible hydromagnetic shear flows with anisotropic thermal pressure: Nonmodal study of waves and instabilities

The evolution of linear magnetohydrodynamic waves and plasma instabilities (firehose and mirror) in a compressible, magnetized plane Couette flow with anisotropic thermal pressure is investigated. In the present study we revealed that the pressure anisotropy brings significant novelty to the effect of coupling and linear reciprocal transformation of the wave modes originally discovered [Chagelishvili, Rogava, and Tsiklauri, Phys. Rev. E 53, 6028 (1996)]. It is found that behavior of the firehose and mirror instabilities is drastically changed due to the presence of shear in the flow. These novel effects are caused by the non-normality of linear dynamics in shear flows and they have been revealed through use of the nonmodal approach.

On the conical refraction of hydromagnetic waves in plasma with anisotropic thermal pressure: General consideration

A phenomenon analogous to the conical refraction well known in crystalo-optics and crystaloacoustics is considered for the magnetohydrodynamical waves in a collisionless plasma with anisotropic thermal pressure. Imposing the most general condition for the existence of the phenomenon, the angle of the conical refraction is calculated, which appeared to be dependent on the ratio of the Alfvén velocity and sound speed measured in the perpendicular direction with respect to the external magnetic field. Feasible ways to experimentally demonstrate the phenomenon are discussed and a novelty brought about by the general consideration is outlined.

On the conical refraction of hydromagnetic waves in plasma with anisotropic thermal pressure

A phenomenon analogous to the conical refraction widely known in crystalo-optics and crystalo-acoustics is discovered for the magnetohydrodynamical waves in a collisionless plasma with anisotropic thermal pressure. Angle of the conical refraction is calculated for the medium under study which is predicted to be 18°26′. Possible experimental corroboration of the discovered phenomenon is discussed.