Search

The star rotation will undoubtedly affect the star's characteristics described by the hydrostatic equilibrium equation. The centrifugal force distorts the star's shape and modifies its equilibrium structure. The choice of the gravity model such as Eddington inspired Born Infeld theory of gravity will also affect the geometry properties of stars. In this case, it will change the corresponding Poisson's equations. So it is desirable to see the modification of hydrostatic equation of states of the non-relativistic rotating stellar object within Eddington inspired Born Infeld theory of gravity. Lane-Emden equations have been used to describe the mass-density distribution in the stars of polytropic equation state of the stars with and without rotation [4]. In this paper, we would like to derive analytically and numerically the modified Lame-Emden equations for rotating non-relativistic stars within Eddington inspired Born Infeld theory of gravity. In this study Eddington inspired Born Infeld theory of gravity will give contribution to make the differences in the geometry and mass of the star.

The initial states and pressure of detonation products in a bubble have a great impact on bubble pulsation in underwater explosions; particularly, the initial accelerated expansion of a bubble can determine the energy distribution. The energy output and distribution of explosives were obtained on the basis of the underwater explosion experiment in this paper. To study the process of bubble pulsation and energy output, we proposed a gas equation of state (EOS) combining the pvk form, Jones–Wilkins–Lee (JWL) EOS, and the initial states of a bubble to take the effects of the initial bubble pressure and detonation products state transformation into account; furthermore, the bubble radius, velocity, and acceleration vs time were obtained through the Rayleigh–Plesset equation under our experimental condition. The differences of bubble behaviors were compared by adopting the JWL EOS and a polytropic EOS with k = 3. The results showed that the initial bubble pressure and detonation products state transformation influence the accelerating expansion and the subsequent bubble oscillation, respectively. Subsequently, comparisons of the energy output and distribution for different gas EOSs showed that the initial shock wave energy for the JWL EOS was underestimated in accelerating expansion, and the bubble energy was overestimated using the polytropic EOS for k = 3; the obtained energy output and distribution had a better agreement with experimental data when adopting the improved gas EOS. In addition, the energy distribution was determined before the detonation products turned to the explosion gas state in initial expansion based on the relationship of the accelerating expansion characteristics and the initial shock wave energy generation. The research has a great significance to reveal the mechanism of bubble pulsation in underwater explosions.

Exact solutions for quasineutral plasma acceleration of magnetized plasma in the paraxial magnetic nozzle are obtained. It is shown that the non-monotonic magnetic field with a local maximum of the magnetic field is a necessary condition for the formation of the quasineutral accelerating potential structure. A global nature of the accelerating potential that occurs as a result of the constraint due to the regularity condition at the sonic point is emphasized and properties of such solutions are discussed for the case of general polytropic equation of state for electrons.

This work presents a numerical design of a micro solar gas turbine for the rural areas of Sahel. Thermodynamic analysis, Mean Line Method, Ansys Blade Gen, Ansys CFX Turbo Grid and Ansys CFX solver were used to do the conceptual study and numerical analysis. The Mean line design results of solar micro gas turbine give a rotation speed of 115,000 rpm, a pressure ratio of 4, an expansion power equal to 40.28 kW and a compression power equal to 29.97 kW for an air flow of 0.14 kg.s−1 and a turbine inlet temperature equal to 850°C. Total to total turbine efficiency is 80% while compressor polytropic efficiency is 79%. The turbine rotor has 13 blades while that of the compressor consists of 18 main and secondary blades.

This paper studies sufficient conditions for deriving the kappa distribution in polytropic plasmas by an improved method compared with the previous work [R. Guo, Phys. Plasmas \textbf{27}, 122104 (2020)]. We find that the polytropic equation of state can lead to the kappa distribution without any other assumptions in one dimension. In higher dimensions, an extra assumption that the global distribution must only depend on the energy is still needed. In addition, the self-consistence of the electrostatic potential is investigated in such plasmas. The study implies that in single-component plasmas, the potential is constrained by the Lane-Emden equation. However, in two-component plasmas, any arbitrary potential could exist with a suitable background ion density. Finally, we discuss the connections between the kappa distribution and the polytrope.

This paper presents an overview of waves and instabilities in relativistic degenerate plasma using magnetohydrodynamic double polytropic laws. The model equations are closed by the double polytropic laws. The general dispersion relation has been derived using the normal mode analysis, which consists of two interesting modes, i.e., shear Alfven mode and modified magnetosonic modes (both slow and fast). The shear Alfven mode is significantly modified by anisotropic pressure and relativistic effects and remains unaffected from quantum effects. The shear Alfven mode develops the firehose instability, which is free from the relativistic factor. The obtained slow and fast magnetosonic modes are further discussed in parallel, perpendicular, and oblique modes of propagation. The Alfven and sound waves propagate in parallel mode, while only the magnetosonic mode propagates in perpendicular mode. The sound wave and magnetosonic wave modes are found to be modified by relativistic and quantum effects. The oblique wave propagation provides fast and slow modes, which propagate with the combined force of anisotropic pressure, Bohm force, magnetic field, and exchange potential. The applicability of the results obtained from the dispersion relation in the relativistic degenerate anisotropic magnetohydrodynamic model can be to the pulsar magnetosphere environment.

Ideal gas dynamics can develop shock-like singularities with discontinuous density. Viscosity typically regularizes such singularities and leads to a shock structure. On the other hand, in 1d, singularities in the Hopf equation can be non-dissipatively smoothed via KdV dispersion. Here, we develop a minimal conservative regularization of 3d ideal adiabatic flow of a gas with polytropic exponent $\gamma$. It is achieved by augmenting the Hamiltonian by a capillarity energy $\beta(\rho) (\nabla \rho)^2$. The simplest capillarity coefficient leading to local conservation laws for mass, momentum, energy and entropy using the standard Poisson brackets is $\beta(\rho) = \beta_*/\rho$ for constant $\beta_*$. This leads to a Korteweg-like stress and nonlinear terms in the momentum equation with third derivatives of $\rho$, which are related to the Bohm potential and Gross quantum pressure. Just like KdV, our equations admit sound waves with a leading cubic dispersion relation, solitary and periodic traveling waves. As with KdV, there are no steady continuous shock-like solutions satisfying the Rankine-Hugoniot conditions. Nevertheless, in 1d, for $\gamma = 2$, numerical solutions show that the gradient catastrophe is averted through the formation of pairs of solitary waves which can display approximate phase-shift scattering. Numerics also indicate recurrent behavior in periodic domains. These observations are related to an equivalence between our regularized equations (in the special case of constant specific entropy potential flow in any dimension) and the defocussing nonlinear Schrodinger equation (cubically nonlinear for $\gamma = 2$), with $\beta_*$ playing the role of $\hbar^2$. Thus, our regularization of gas dynamics may be viewed as a generalization of both the single field KdV & NLS equations to include the adiabatic dynamics of density, velocity, pressure & entropy in any dimension., Comment: 19 pages, 20 figure files

A commonly used approach to simulate ion thruster plumes is a hybrid particle-in-cell (PIC) with the Boltzmann relation to model electrons. The limitations of such an approach are investigated by benchmarking hybrid PIC against fully kinetic PIC simulations using the real Xe+ to electron mass ratio (mi/me = 241073). The results show that both full PIC and hybrid PIC lead to similar plume density structures but very different plume potentials. If one could ignore the ion beam neutralization region near the thruster exit, the main physics missing from a hybrid PIC plume model is that from the anisotropic electron characteristics. Including the beam neutralization region leads to further changes in electron temperature and plume potential. Compared to full PIC simulations, the hybrid PIC model results in an overestimation of the plume potential by about 30%–40% in the transverse direction for the simulations considered. Since the electrons in the plume are nonequilibrium and anisotropic, simply replacing the Boltzmann relation with the more general polytropic thermodynamic relation for electrons in a hybrid PIC plume model will not lead to a significant improvement in accuracy.

The paper shows the surprising result of the universality of the mean-free-path formulation for plasmas described by kappa distributions. In particular, the ratio of the mean-free-path over the Debye length depends only on the Debye number – the number of particles within the Debye length scale. The derived formula appears to be identical for the cases of Maxwell-Boltzmann and kappa distributed plasmas; thus, it is not explicitly depended on kappa – the parameter that labels and governs the kappa distributions. The key aspect of these results is the specific functional dependence of the mean-free-path on the polytropic index; this is inextricably linked to the dependence of the Debye length on the polytropic index. The importance of the dependence of the mean-free-path on the polytropic index is demonstrated with applications in the solar wind plasma.

It is shown that the Debye length formulation, for plasmas described by kappa distributions, depends on the polytropic index, rather than the parameter that labels and governs these distributions, the kappa index—in contrast to what it was previously derived. As a consequence, the ratio of the Debye length over the plasma oscillation period gives exactly the sound speed, instead of being proportional to the thermal speed; this ratio is generalized to the fast magnetosonic speed when the magnetic Debye length is considered, leading also to the development of the vector Debye length. Finally, as an application, we derive the Debye length values for the solar wind plasma near 1 AU, exhibiting clear distinction between slow and fast wind modes, while we provide insights into the connection between plasma and polytropic processes.

This paper is concerned with three-dimensional compressible viscous and heat-conducting micropolar fluid in the domain to the subset of R3 bounded with two coaxial cylinders that present the solid thermoinsulated walls, being in a perfect and polytropic thermodynamical sense. We prove that cylindrically symmetric solutions decay to a constant exponentially as time goes to infinity based on the assumptions that the initial total energy is sufficiently small and initial data are sufficiently smooth cylindrically symmetric functions.

A commonly used assumption for modeling electrons in the collisionless plasma expansion into a wake is that the electrons are an ideal gas following a thermodynamic process governed by the polytropic law. The validity and accuracy of this assumption are assessed through a direct comparison between hybrid particle-in-cell (PIC) and fully kinetic PIC simulations. The electron thermal energy transfer along with the expansion process is analyzed. It is shown that a collisionless plasma wake can be divided into a fluid-like expansion region and a kinetic expansion region based on the local equilibrium degree of the electrons. In the fluid-like expansion region, the electrons are near equilibrium and almost isothermal, and the accuracy of hybrid PIC in that region can be improved by properly tuning the polytropic coefficient. In the kinetic expansion region, the electrons are strongly nonequilibrium, and the accuracy of hybrid PIC is always poor. Consequently, a fluid model with a polytropic thermodynamic law for electrons is meaningless in that region.A commonly used assumption for modeling electrons in the collisionless plasma expansion into a wake is that the electrons are an ideal gas following a thermodynamic process governed by the polytropic law. The validity and accuracy of this assumption are assessed through a direct comparison between hybrid particle-in-cell (PIC) and fully kinetic PIC simulations. The electron thermal energy transfer along with the expansion process is analyzed. It is shown that a collisionless plasma wake can be divided into a fluid-like expansion region and a kinetic expansion region based on the local equilibrium degree of the electrons. In the fluid-like expansion region, the electrons are near equilibrium and almost isothermal, and the accuracy of hybrid PIC in that region can be improved by properly tuning the polytropic coefficient. In the kinetic expansion region, the electrons are strongly nonequilibrium, and the accuracy of hybrid PIC is always poor. Consequently, a fluid model with a polytropic thermodynamic law f...

The nonlinear evolutionary dynamics of gravitational instability in a complex self-gravitating viscoelastic nonthermal polytropic astrofluid is semi-analytically investigated on the Jeansian scales of space and time. The key effects out of fluid buoyancy, thermal fluctuations, and volumetric expansions are concurrently considered and carefully included. A nonlinear normal mode (local) analysis yields a Korteweg-de Vries (KdV) equation with a unique set of multi-parametric coefficients. We provide a numerical platform to demonstrate how the KdV dynamics excites an interesting spectral class of compressive solitary chain patterns as the evolutionary eigenmodes having atypical dynamical behaviour. Their diversified characteristic features are explained elaborately alongside phase-plane analysis. Various stabilizing (destabilizing) and accelerating (decelerating) factors of the instability are illustratively explored together with a validated reliability checkup. The relevancy of our investigated results in the context of super-dense compact astro-objects and their circumvent viscoelastic atmospheres is summarily outlined.

The propagation of arbitrary amplitude ion-acoustic solitons is investigated in a plasma containing cool adiabatic positive ions and hot electrons or negative ions. The latter can be described by polytropic pressure-density relations, both with or without the retention of inertial effects. For analytical tractability, the resulting Sagdeev pseudopotential needs to be expressed in terms of the hot negative species density, rather than the electrostatic potential. The inclusion of inertia is found to have no qualitative effect, but yields quantitative differences that vary monotonically with the mass ratio and the polytropic index. This result contrasts with results for analogous problems involving three species, where it was found that inertia could yield significant qualitative differences. Attention is also drawn to the fact that in the literature there are numerous papers in which species are assumed to behave adiabatically, where the isothermal assumption would be more appropriate. Such an assumption l...

The nonlinear characteristics of dust acoustic (DA) waves in an unmagnetized collisionless complex plasma containing adiabatic electrons and ions and negatively charged dust grains (including the effects of modified polarization force) are investigated. Employing the reductive perturbation technique, a Korteweg–de Vries–Burgers (KdVB) equation is derived. The analytical solution for the KdVB equation is discussed. Also, the bifurcation and phase portrait analyses are presented to recognize different types of possible solutions. The dependence of the properties of nonlinear DA waves on the system parameters is investigated. It has been shown that an increase in the value of the modified polarization parameter leads to a fast decay and diminishes the oscillation amplitude of the DA damped cnoidal wave. The relevance of our findings and their possible applications to laboratory and space plasma situations is discussed.

Weakly nonlinear magnetoacoustic waves in thin magnetic flux tubes are investigated in rarefied plasmas when an anisotropic kinetic pressure is taken into account. The parallel and perpendicular pressures are defined by two polytropic pressure laws. This model can be considered as a natural extension of the magnetohydrodynamics approximation when the plasma is rarefied. The dispersion relation for slow surface sausage waves propagating in magnetically embedded flux tubes in the presence of pressure anisotropy is used to derive the extended Leibovich–Roberts equation in rarefied and anisotropic plasmas. The properties and limitations of this equation are discussed.

Small-amplitude magnetohydrodynamic waves are studied in a dilute collisionless plasma with an anisotropic plasma pressure. The parallel and perpendicular pressure components are defined by two polytropic pressure laws. Previous results obtained within the framework of the Chew–Goldberger–Low double-adiabatic and double-isothermal models are recovered for specific values of the polytropic indices. The double-polytropic model can be considered as an extension of its single-polytropic counterpart model. Dispersion relations for the linear waves are derived and analyzed in the presence of pressure anisotropy. Particular cases of linear and nonlinear waves in a magnetic slab with double-polytropic plasma are investigated. The presence of the effective parallel and perpendicular sound speeds in the slab gives rise to a complicated interplay between kink and sausage modes supported by the slab. The behavior of weakly nonlinear waves in the slab are governed by the Benjamin–Ono equation. The soliton-like solutio...

We solve a radial theoretical model that describes the ion sheath around a cylindrical Langmuir probe with finite non-zero ion temperature in which singularity in an a priori unknown point prevents direct integration. The singularity appears naturally in fluid models when the velocity of the ions reaches the local ion speed of sound. The solutions are smooth and continuous and are valid from the plasma to the probe with no need for asymptotic matching. The solutions that we present are valid for any value of the positive ion to electron temperature ratio and for any constant polytropic coefficient. The model is numerically solved to obtain the electric potential and the ion population density profiles for any given positive ion current collected by the probe. The ion-current to probe-voltage characteristic curves and the Sonin plot are calculated in order to use the results of the model in plasma diagnosis. The proposed methodology is adaptable to other geometries and in the presence of other presheath me...

The small amplitude quantum magnetohydrodynamic (QMHD) waves and linear firehose and mirror instabilities in uniformly rotating dense quantum plasma have been investigated using generalized polytropic pressure laws. The QMHD model and Chew–Goldberger–Low (CGL) set of equations are used to formulate the basic equations of the problem. The general dispersion relation is derived using normal mode analysis which is discussed in parallel, transverse, and oblique wave propagations. The fast, slow, and intermediate QMHD wave modes and linear firehose and mirror instabilities are analyzed for isotropic MHD and CGL quantum fluid plasmas. The firehose instability remains unaffected while the mirror instability is modified by polytropic exponents and quantum diffraction parameter. The graphical illustrations show that quantum corrections have a stabilizing influence on the mirror instability. The presence of uniform rotation stabilizes while quantum corrections destabilize the growth rate of the system. It is also o...

The linear convective instability of imploding gaseous masses is investigated with a self-similar solution, which takes radiation heat conduction into account. The solution shows that the implosion process continuously transits from the initial adiabatic regime to the consequent nonadiabatic regime, where the mechanical compression work and the radiation loss balance such that the Peclet number of the system is kept constant. The transition accompanies the decrease in the polytropic index, Γ≡d(log p)/d(log ρ) where p and ρ are, respectively, the pressure and density, with the adiabatic index γ (⩾ Γ) as its initial value. As a result of the radiative cooling, the fluid becomes unstable to convective modes, when the criterion for instability, d(p/ρΓ)/dr

In this work, a generalized expression of the photoacoustic (PA) effect in a multilayer material is derived. This expression takes thermal and optical properties and geometry of a multilayer structure, as well as the thermal contact resistances between layers into consideration. In addition, a composite piston model consisting of a thermal piston and a mechanical piston of the PA effect is developed and interpreted from the viewpoint of thermodynamics. Mistakes occurring in the thermal piston model and in the composite piston model developed before are pointed out and corrected. It is also shown that the PA effect has an isochoric character for the thermal piston and a polytropic character with a polytropic factor of (2−1/γ) for the mechanical piston. The theory developed in this work is in good agreement with the experimental results, and is applicable to a wide range of photoacoustic problems.

The Kelvin–Helmholtz (K-H) instability of two fluids of a plasma, streaming in opposite directions with the same velocity and in the presence of an external magnetic field, is investigated. The external magnetic field in both fluids are in different directions. The usual magnetohydrodynamic (MHD) equations with anisotropic pressures are considered. The generalized pressure relation is used and two equations of state for two pressures are taken up in the problem. The equations are linearized and initially two different flow velocities are taken for the system. The problem is solved and a dispersion relation is obtained. It is found that the instability condition for the static configuration depends on the polytropic index of the pressure relations. The condition of instability is further obtained for MHD and Chew–Goldberger–Low (CGL) systems. For the nonstatic streaming configuration it is also found that growth rate of K-H instability depends on various polytropic indices and magnetic field.

Stationary one-dimensional nonlinear waves in two-fluid hydrodynamics are studied analytically in the assumption of polytropic pressure and massless electrons. Particular attention is paid to the presence of soliton solutions, which exist when the asymptotic plasma velocity is in the range v+2

The influences of thermal radiation on the state equation of shock waves, derived in the previous paper [L. N. Tsintsadze, Phys. Plasmas 2, 4462 (1995)], are studied and a series of relations of thermodynamic quantities that hold for shock waves are derived. It is shown that the presence of radiation can strongly change the compressibility of the plasma. It is well known that for polytropic gases the compressibility cannot change more than four times the initial value in the case of nonrelativistic temperatures. The numerical calculations show that there are no such restrictions, when the radiation energy exceeds the kinetic energy of the plasma. The ultrarelativistic temperature range is also covered in our numerical calculations. Also studied are the influences of the radiation on the PT and the TV diagrams. A significant modification due to radiation is found in every case studied.

Given the importance of linear mode properties (e.g., characteristic speeds) in identification/classification of discontinuities, a detailed comparison between the mode properties in fluid theory and kinetic theory in high β plasmas is carried out. It is found that conventional fluid theories of linear modes in both isotropic and anisotropic plasmas do not yield the correct mode properties, even in the long‐wavelength limit. In particular, fluid phase velocities are very sensitive to the model and parameters (polytropic indices) employed. Because of this, fluid theory loses its predictive power. In linear kinetic theory, modes cannot be ordered according to their phase velocities. For instance, at small and moderate propagation angles, the slow/sound (S/SO) mode can have the fastest phase velocity. In such cases, a (quasiparallel) fast shock would be associated with the S/SO mode rather than the usual fast/magnetosonic (F/MS) mode. This has important implications for fast shocks. Since it is the F/MS rath...

Direct numerical simulation (DNS) is used to examine scalar correlation in low Mach number, polytropic, homogeneous, two‐dimensional turbulence (Ms≤0.7) for which the initial conditions, Reynolds, and Mach numbers have been chosen to produce three types of flow suggested by theory: (a) nearly incompressible flow dominated by vorticity, (b) nearly pure acoustic turbulence dominated by compression, and (c) nearly statistical equipartition of vorticity and compressions. Turbulent flows typical of each of these cases have been generated and a passive scalar field imbedded in them. The results show that a finite‐difference based computer program is capable of producing results that are in reasonable agreement with pseudospectral calculations. Scalar correlations have been calculated from the DNS results and the relative magnitudes of terms in low‐order scalar moment equations determined. It is shown that the scalar equation terms with explicit compressibility are negligible on a long time‐averaged basis. A phy...

The stability analysis with respect to ‘‘small’’ radial adiabatic perturbations of spherically symmetric stellar equilibrium models which are polytropic with a constant adiabatic index only near the center and the boundary of the star leads to the consideration of a class of singular minimal Sturm–Liouville operators. It is shown that the physical boundary conditions choose in a unique way the corresponding Friedrichs extensions. Moreover, all linear self‐adjoint extensions of the members of the class are determined and are shown to have a purely discrete spectrum.

The stability analysis for spherically symmetric stellar equilibrium models with respect to ‘‘small’’ adiabatic Lagrangian perturbations leads to the consideration of a class of densely defined, linear symmetric operators in Hilbert space, which are induced by certain singular vector–integro–partial differential operator. The extension properties of these operators as well as the spectral properties of the linear self‐adjoint extensions which are chosen by physical boundary conditions are investigated. For this, the equilibrium models are assumed to be polytropic, with a constant adiabatic index only near the center and near the boundary of the star. Among others it is shown that the operators of the class having a polytropic index near the boundary which is ≥1 are in particular essentially self‐adjoint and have a closure with a pure point spectrum.

The fluid approach has been widely used to study plasma sheath dynamics. For a sheath containing hot ions whose temperature is greater than the electron's, how to truncate the fluid hierarchy chain equations while retaining to the fullest extent of the kinetic effects is always a difficult problem. In this paper, a one-dimensional, collisionless sheath containing hot ions is studied via particle-in-cell simulations. By analyzing the ion energy equation and taking the kinetic effects into account, we have shown that the ion polytropic coefficient in the vicinity of the sheath edge is approximately constant so that the state equation with the modified polytropic coefficient can be used to close the hierarchy chain of the ion fluid equations. The value of the polytropic coefficient strongly depends on the hot ion temperature and its concentration in the plasma. The semi-analytical model is given to interpret the simulation results. As an application, the kinetic effects on the ion saturation current density ...

Methods of differential geometry and Bernoulli’s equation, written as B=0, are used to develop a new approach for constructing an exact solution for axial flow in a classical, two‐dimensional, ZND detonation wave in a polytropic explosive with an arbitrary rate of decomposition. This geometric approach is fundamentally different from the traditional approaches to this axial flow problem formulated by Wood and Kirkwood (WK) and Fickett and Davis (FD), and gives equations for the axial particle velocity (u), the sound speed (c), the pressure (p), and the density (ρ), that are expressed in terms of the detonation velocity (D), the extent of decomposition (λ), the polytropic index (K), and two nonideal parameters e3 and e1, and reduce to the equations for steady‐state, one‐dimensional detonation as e3 and e1 approach zero. In contrast to the FD approach, the equations for u and c are obtained from first integrals of a tangent vector A on (u,c,λ) space, and the invariant condition, AB=aB=0, bypasses the FD e...

The concepts of generalized polytropic processes and polytropic refrigeration cycles, which consist of two isothermal processes and two generalized polytropic processes of paramagnetic salt, are introduced. It is shown that such a class of general magnetic refrigeration cycles, which includes the Carnot, Stirling, and other useful magnetic refrigeration cycles, possesses the conditions of perfect regeneration and can have the same coefficient of performance as the Carnot cycle for the same temperature range. Thus, they have many applications in the research and manufacture of magnetic refrigerators.

The conditions for a unit vector field to be the velocity of a relativistic barotropic perfect fluid are given. These conditions induce an eightfold classification of such fluids; for every class, the admissible barotropic variables are found. Some special cases, in particular polytropic fluids, are analyzed separately.

Recent decades have seen research into the conditions necessary for the formation of the monotonic potential shape in the sheath, appearing at the plasma boundaries like walls, in fluid, and kinetic approximations separately. Although either of these approaches yields a formulation commonly known as the much-acclaimed Bohm criterion (BC), the respective results involve essentially different physical quantities that describe the ion gas behavior. In the fluid approach, such a quantity is clearly identified as the ion directional velocity. In the kinetic approach, the ion behavior is formulated via a quantity (the squared inverse velocity averaged by the ion distribution function) without any clear physical significance, which is, moreover, impractical. In the present paper, we try to explain this difference by deriving a condition called here the Unified Bohm Criterion, which combines an advanced fluid model with an upgraded explicit kinetic formula in a new form of the BC. By introducing a generalized polytropic coefficient function, the unified BC can be interpreted in a form that holds, irrespective of whether the ions are described kinetically or in the fluid approximation.

Time-resolved temperature and density conditions in the core of shock-ignition implosions have been determined for the first time. The diagnostic method relies on the observation, with a streaked crystal spectrometer, of the signature of an Ar tracer added to the deuterium gas fill. The data analysis confirms the importance of the shell attenuation effect previously noted on time-integrated spectroscopic measurements of thick-wall targets [R. Florido et al., Phys. Rev. E 83, 066408 (2011)]. This effect must be taken into account in order to obtain reliable results. The extracted temperature and density time-histories are representative of the state of the core during the implosion deceleration and burning phases. As a consequence of the ignitor shock launched by the sharp intensity spike at the end of the laser pulse, observed average core electron temperature and mass density reach T ∼ 1100 eV and ρ ∼ 2 g/cm3; then temperature drops to T ∼ 920 eV while density rises to ρ ∼ 3.4 g/cm3 about the time of peak compression. Compared to 1D hydrodynamic simulations, the experiment shows similar maximum temperatures and smaller densities. Simulations do not reproduce all observations. Differences are noted in the heating dynamics driven by the ignitor shock and the optical depth time-history of the compressed shell. Time-histories of core conditions extracted from spectroscopy show that the implosion can be interpreted as a two-stage polytropic process. Furthermore, an energy balance analysis of implosion core suggests an increase in total energy greater than what 1D hydrodynamic simulations predict. This new methodology can be implemented in other ICF experiments to look into implosion dynamics and help to understand the underlying physics.

Electrons streaming in a background electron and ion plasma may lead to the formation of electrostatic solitary wave (ESW) and hole structure which have been observed in various space plasma environments. Past studies on the formation of ESW are mostly based on the particle simulations due to the necessity of incorporating particle's trapping effects. In this study, the fluid aspects and thermodynamics of streaming instabilities in electron-ion plasmas including bi-streaming and bump-on-tail instabilities are addressed based on the comparison between fluid theory and the results from particle-in-cell simulations. The energy closure adopted in the fluid model is the polytropic law of d(pρ−γ)/dt=0 with γ being a free parameter. Two unstable modes are identified for the bump-on-tail instability and the growth rates as well as the dispersion relation of the streaming instabilities derived from the linear theory are found to be in good agreement with the particle simulations for both bi-streaming and bump-on-t...

We performed experiments at the Omega Laser Facility to characterize the initial, laser-driven state of a radiative shock experiment. These experiments aimed to measure the shock breakout time from a thin, laser-irradiated Be disk. The data are then used to inform a range of valid model parameters, such as electron flux limiter and polytropic γ, used when simulating radiative shock experiments using radiation hydrodynamics codes. The characterization experiment and the radiative shock experiment use a laser irradiance of ∼7 × 1014 W cm−2 to launch a shock in the Be disk. A velocity interferometer and a streaked optical pyrometer were used to infer the amount of time for the shock to move through the Be disk. The experimental results were compared with simulation results from the Hyades code, which can be used to model the initial conditions of a radiative shock system using the CRASH code.

This work extends the one-dimensional radiation-hydrodynamic imploding spherical argon plasma liner simulations of T. J. Awe et al. [Phys. Plasmas 18, 072705 (2011)] by using a detailed tabular equation-of-state (EOS) model, whereas Awe et al. used a polytropic EOS model. Results using the tabular EOS model give lower stagnation pressures by a factor of 3.9-8.6 and lower peak ion temperatures compared to the polytropic EOS results. Both local thermodynamic equilibrium (LTE) and non-LTE EOS models were used in this work, giving similar results on stagnation pressure. The lower stagnation pressures using a tabular EOS model are attributed to a reduction in the liner's ability to compress arising from the energy sink introduced by ionization and electron excitation, which are not accounted for in a polytropic EOS model. Variation of the plasma liner species for the same initial liner geometry, mass density, and velocity was also explored using the LTE tabular EOS model, showing that the highest stagnation pressure is achieved with the highest atomic mass species for the constraints imposed., Comment: 21 pages, 3 tables, 7 figures, accepted for publication by Phys. Plasmas (9/24/2012)

Adiabatic multi-ions species containing positive and negative ions in the presence of nonthermal electrons are considered. The properties of small, but finite, ion acoustic waves are investigated taking into account the pressure effect of positive/negative ions in the fluid equations with a polytropic (γ) coefficient ranging from 1 to 3. The reductive perturbation method has been employed to derive the Korteweg-de Vries equation for small amplitude ion-acoustic waves. The effect of ion pressure is found important, particularly for higher values of γ. The results of the present investigation may be applicable to some plasma environments, such as the Earth’s ionosphere region.

A theory of shocks dominated by radiation energy flux in optically mixed thin-upstream thick-downstream systems, in which the temperature immediately ahead and some short distance behind the shock front are equilibrated by radiation transport, is presented. This theory is applied to determine properties of the normal and oblique radiative shock, followed by applications to interactions when radiative and polytropic shocks are present in the same system. Comparison with experimental data is presented.

In this paper, a supersymmetric extension of the polytropic gas dynamics equations is constructed through the use of a superspace involving two independent fermionic variables and two bosonic superfields. A superalgebra of symmetries of the proposed extended model is determined and a systematic classification of the one-dimensional subalgebras of this superalgebra is performed. Through the use of the symmetry reduction method, a number of invariant solutions of the supersymmetric polytropic gas dynamics equations are found. Several types of solutions are obtained, including algebraic-type solutions and propagation waves (simple and double waves). Many of the obtained solutions involve arbitrary functions of one or two bosonic or fermionic variables. In the case where the arbitrary functions involve only the independent fermionic variables, the solutions are expressed in terms of Taylor expansions., Comment: 26 pages

The paper investigates the role of relative motion between the fluid components of a plasma model, which is simulated by concatenation of two anisotropic magnetohydrodynamic (MHD) fluids, on the propagation of low-frequency waves and instabilities. The gyrotropic pressure of both the MHD components is given by generalized polytropic laws that allow the system to reduce to a variety of states. The linearized analysis is carried out and dispersion relation is derived using the normal mode technique. The dispersion relation, which gives numerous earlier results as special cases, is discussed both analytically as well as numerically for parameters appropriate for the space plasma. It is found that the relative motion between the two components, besides modifying the condition for fire-hose instability, causes the concatenated system to exhibit different kinds of relative ordering of the magnitudes of phase speeds of the various MHD modes in the directions parallel and antiparallel to the magnetic field. The relative motion between the components also influences the phase relationship between density and magnetic field fluctuations for the various compressive modes in the background ambient plasma.

Lie point symmetries and nonlocal symmetries of partial differential equation (PDE) systems are widely used for construction of exact invariant solutions. In this paper we describe an extended algorithmic procedure that, for a given nonlocal (potential) symmetry, can yield additional exact solutions, which cannot be found using the usual algorithm. In particular, such additional solutions are exact solutions of the given PDE system, but are not invariant solutions of the corresponding potential system. As an example, we consider a tree of nonlocally related PDE systems for Lagrange planar gas dynamics equations and classify its nonlocal symmetries for an ideal polytropic gas. For two different nonlocal symmetries of the Lagrange system, we demonstrate that the extended method yields wider classes of exact solutions than the usual method.

Many electrically and heat conducting fluid flows cannot be described within the framework of incompressible medium or by compressible magnetohydrodynamic equations on the assumption of polytropic (or adiabatic) process. Therefore, we consider a heat conducting compressible fluid with the use of an energy equation. Application of large eddy simulation approach to heat conducting compressible magnetohydrodynamics is considered. The system of the filtered magnetohydrodynamic equations with the total energy equation using the mass-weighted filtering procedure has been obtained. It is shown that novel subgrid-scale terms arise in the Favre-filtered equations due to the presence of a magnetic field in the total energy equation. Parametrizations of these extra terms are developed. In order to derive these subgrid-scale terms, we use an approach based on generalized central moments. Computations at various Mach numbers are made for decaying compressible magnetohydrodynamic turbulence. The obtained numerical larg...

The effects of uniform rotation, finite electrical resistivity, electron inertia, and Hall current on the self-gravitational instability of anisotropic pressure plasma with generalized polytrope laws have been studied. A general dispersion relation is obtained with the help of the relevant linearized perturbed magnetohydrodynamic (MHD) equations incorporating the relevant contributions of various effects of the problem using the method of normal mode analysis. The general dispersion relation is further reduced for the special cases of rotation; i.e., parallel and perpendicular to the direction of the magnetic field. The longitudinal and transverse modes of propagation are discussed separately for investigation of condition of instability. The effects of rotation, Hall current, finite electron inertia, and polytropic indices are discussed on the gravitational, “firehose,” and “mirror” instabilities. The numerical calculations have been performed to obtain the dependence of the growth rate of the gravitatio...

This paper discusses the existence of ion-acoustic solitons in a plasma consisting of hot and cool ions, and hot electrons, where the words “hot” and “cool” reflect the ratio of thermal effects to inertial effects. For the hot species general polytropic pressure relations are considered, as well as the isothermal limit, γ=1 (Boltzmann distribution). It is shown that negative potential solitons are not supported. Existence domains in parameter space (effective soliton Mach number and fractional cool ion density) for positive potential solitons are found, the limits being imposed by physical effects such as vanishing densities. Numerical results are given for a typical value of γ>1 and for γ=1, for three representative values of the hot ion to electron temperature ratio.

In a recent paper by Kuhn et al. [Phys. Plasmas 13, 013503 (2006)], it has been demonstrated that in a plasma, the polytropic coefficient γ is a spatially varying quantity rather than a global constant as usually assumed in fluid theory. Assuming cold ion sources and using the asymptotic two-scale approximation (in which the ratio of the Debye length over the characteristic presheath length, e, is set to zero), it was found that the γ profile exhibits a sharp peak (with values roughly between 6 and 8) at the plasma-sheath boundary. In the present paper, it is shown that in a finite e approach, this sharp peak is smoothed to a regular maximum, which for increasing e (e.g., decreasing plasma density) decreases and finally disappears. In any case, assumptions like γ=1 and/or γ=3, which are customarily encountered in the context of fluid approaches, are disproved. Although the present results were obtained for collisionless plasmas, it is reasonable to assume that the behavior uncovered holds qualitatively fo...

We investigate the Hamiltonian as well as Lax formulations of the polytropic gas dynamics which can be characterized by the polytropic exponent γ=1+h. We show that when h=1∕m with ∣m∣∊N⩾2, the resonant phenomena occur in bi-Hamiltonian formulation and logarithmic-type conserved charges emerge naturally. We provide a logarithmic Lax representation for conserved charges and the whole hierarchy flows, which coincides with the bi-Hamiltonian formulation constructed from a two-dimensional Frobenius manifold associated with the polytropic gas dynamics.

In view of applications to electron-positron and fullerene pair plasmas, a thorough discussion is given of the dispersion of linear electrostatic waves, before finding the parameter ranges in which stationary nonlinear electrostatic modes can exist, when there is a thermodynamic asymmetry between both constituents. Arguments for such an asymmetry can be found in the observed dispersion in fullerene pair plasma experiments, but point to small asymmetries. The existence of solitary modes is first discussed in general terms for various polytropic pressure-density relations, showing that the solitons are always compressive in both pair components. For large thermal asymmetries, there is at most a doubling of the densities, but small asymmetries lead to weakly nonlinear amplitudes, described by familiar Korteweg-de Vries solitons. Observations of an intermediate wave in the theoretical gap between the acoustic and Langmuir branches of the linear dispersion diagram might be accounted for, at least partially, by a train of weak solitons, as the difference between weak solitary modes and linear harmonic waves is rather difficult to ascertain experimentally.

In this paper the general problem of linking fluid and kinetic plasma parameters, with special attention devoted to the plasma boundaries where, due to strong deviations from thermodynamic equilibrium, there are intrinsic difficulties regarding the closure of the hydrodynamic equations, is considered. This problem is demonstrated by means of two examples for which the solutions of the kinetic equations are known. These examples are the collision-free Tonks-Langmuir model [Phys. Rev. 34, 876 (1929)] and Riemann’s presheath model [Phys. Fluids 24, 2163 (1981)] dominated by charge-exchange collisions. It is found that in the vicinity of the sheath edge the “polytropic” coefficient γ(x) shows an unexpected behavior that contradicts the commonly used hydrodynamic approaches assuming γ=const. In spite of all differences, the two models investigated exhibit quite similar behavior of the hydrodynamic quantities and of the polytropic coefficient in the presheath and sheath regions. This rises to hopes that the res...

The propagation of a pressure wave in an initially quiescent bubbly liquid of relatively high void fraction contained in a two-dimensional (2D) or three-dimensional (3D) rectangular domain is investigated by direct numerical simulations of the Navier-Stokes equations using a front-tracking/finite-volume method. The gas pressure inside the bubbles is either set equal to a constant or varied by the polytropic relation. Results obtained for 2D and 3D domains show mean shock speeds in agreement with those of one-dimensional homogeneous bubbly liquid theory.