Set Of Fluid Equations Research Articles

Numerical treatment of a magnetized electron fluid model in a 3D simulator of plasma thruster plumes

Simulations of energetic plumes from plasma thrusters are of great interest for estimating performances and interactions with the spacecraft. Both in fully fluid and hybrid (particle/fluid) models, the electron population is described by a set of fluid equations whose resolution by different numerical schemes can be strongly affected by convergence and accuracy issues. The case of magnetized plumes is more critical. Here, the numerical discretization of the electron fluid model of a 3D hybrid simulator of plasma plumes was upgraded from a finite-differences (FD) formulation in a collocated grid to a finite-volumes (FV) approach in a staggered grid. Both approaches make use of structured meshes of different resolutions and are compared in two scenarios of interest: 1) an unmagnetized plasma plume around a spacecraft and 2) a magnetized plume expansion in free space. In both physical scenarios, the FD scheme exhibits a global continuity error related to truncation errors that can be reduced only by refining the mesh. The origin of this error is further investigated and explained here. The FV scheme instead can save much computational time using coarser meshes since it is unaffected by these errors due to the conservativeness of its formulation. The physical advantage of the FV scheme over the FD approach is more evident for magnetized plumes with high Hall parameters since it allows us to reach higher anisotropy conditions, here assessed in order to gain insights into the plume magnetization effects, finding that the already foreseen saturation of circulating electric current occurs for Hall parameters of several hundreds.

Forbidden dark matter annihilation into leptons with full collision terms

The standard approach of calculating the relic density of thermally produced dark matter based on the assumption of kinetic equilibrium is known to fail for forbidden dark matter models since only the high momentum tail of the dark matter phase space distribution function contributes significantly to dark matter annihilations. Furthermore, it is known that the computationally less expensive Fokker-Planck approximation for the collision term describing elastic scattering processes between non-relativistic dark matter particles and the Standard Model thermal bath breaks down if both scattering partners are close in mass. This, however, is the defining feature of the forbidden dark matter paradigm. In this paper, we therefore include the full elastic collision term in the full momentum-dependent Boltzmann equation as well as in a set of fluid equations that couple the evolution of the number density and dark matter temperature for a simplified model featuring forbidden dark matter annihilations into muon or tau leptons through a scalar mediator. On the technical side, we perform all angular integrals in the full collision term analytically and take into account the effect of dark matter self-interactions on the relic density. The overall phenomenological outcome is that the updated relic density calculation results in a significant reduction of the experimentally allowed parameter space compared to the traditional approach, which solves only for the abundance. In addition, almost the entire currently viable parameter space can be probed with CMB-S4, next-generation beam-dump experiments or at a future high-luminosity electron-position collider, except for the resonant region where the mediator corresponds to approximately twice the muon or tau mass.

Influence of quantum particles on self-gravitational magnetic dust acoustic double layers

The impact of Fermi–Dirac distributed electrons and ions on the features of dust acoustic double layers in a four-component magnetized dusty plasma was investigated. In this model, the plasma consists of Fermi–Dirac distributed electrons and ions and negative and positive dust particles. The plasma species experience electrical, magnetical, and self-gravitational forces as well as the degeneracy pressure force that is caused by the Pauli exclusion law and the quantum tunneling force due to Bohm force. Employing a reductive perturbation method, the quantum extended Korteweg-de Vries equation was extracted from the set of fluid equations. The results show that the energy of generated dust acoustic double layers is extremely smaller than that in similar classical plasmas. The ratio of the Fermi temperature of ions to electrons is an effective parameter in the structure of double layers. With the variation of this parameter, the structure of double layers changes from compressive to rarefactive, and its polarity switches from negative to positive.

Evolution of ion-acoustic soliton waves in Venus’s ionosphere permeated by the solar wind

Abstract Wave observations are as yet an important technique to resolve fine structures in the plasma that cannot be identified by different instruments. In this way, we proposed the generation of electrostatic solitary waves during the interaction between the solar wind particles and Venus’s atmosphere at high altitude. The plasma system is treated as a multicomponent unmagnetized plasma consists of background electrons, positive ions (H+ and O+), and streaming solar wind electrons and protons. The dispersion relation is derived for linear waves and the stability/instability of electrostatic wavepackets is investigated. The dependence of the instability growth rate on the ion beam speed has been analyzed. Stability analysis reveals the occurrence of an imaginary frequency part in three regions. Using the reductive perturbation theory, the set of fluid equations is reduced to the Korteweg-de Vries (KdV) equation to describe the evolution of small but finite amplitude soliton waves. The model predicts the propagation of electrostatic soliton waves with an electric field of 1.2 mV/m and a time duration of 0.4 ms. The output of the fast Fourier transform of the electric field pulse is a broadband in the frequency range of ~ 3.2 to 199.5 kHz. It is proposed that the model can be a decent possibility for clarifying the observation of a wide variety of plasma oscillations by Galileo flyby of Venus.

Polytropic Coefficient Function for Tonks-Langmuir-Type Bounded Plasmas with Kappa-Distributed Electrons and Cold Ion Source

In the fluid description of the classical Tonks-Langmuir (TL) model [Tonks and Langmuir, Phys Rev., 34: 876, 1929], arises the “closure problem.” The continuity and the momentum equations need, in addition, a closure equation. Usually, this closure equation assumes zero ion pressure (pi = 0), or a constant ion polytropic coefficient (γi). These simplified assumptions are likely to produce incorrect results, because (i) the ions have a non-zero temperature, even if the ion source is assumed to be cold, and (ii) the polytropic coefficient is, in fact, a function of space (or potential), and is far from constant (Kuhn et al., AIP Conference Proceedings, 1306: 216, 2010). Here, the concept of polytropic coefficient function (PCF) is applied to a TL-type discharge with a Kappa-distributed ion source. The ion density and temperature are calculated numerically, for different values of the spectral index κ. The polytropic coefficient function is then calculated using the relation γ = 1 + (n/T) (dT/dn). Striking deviation from results of the classical case are observed. It is shown here that, for Kappa-distributed ion sources, the ion PCF is not a constant, but is a function of the potential. Moreover, the sheath-edge potential differs significantly from the classical case. It is concluded that in order to close the set of fluid equations in an appropriate manner, better approximations to the PCF are needed.

Nonlinear ion-acoustic solitary waves in an electron-positron-ion plasma with relativistic positron beam

The propagation characteristics of nonlinear ion–acoustic (IA) solitary waves (SWs) are studied in thermal electron–positron–ion plasma considering the effect of relativistic positron beam. Starting from a set of fluid equations and using the reductive perturbation technique, we derive a Korteweg–de Vries (KdV) equation which governs the evolution of weakly nonlinear IA SWs in relativistic beam driven plasmas. The properties of the IA soliton are studied, and it is shown that the presence of relativistic positron beam significantly modifies the characteristics of IA solitons.

Pseudo-Newtonian Equations for Evolution of Particles and Fluids in Stationary Space-times

Abstract Pseudo-Newtonian potentials are a tool often used in theoretical astrophysics to capture some key features of a black hole space-time in a Newtonian framework. As a result, one can use Newtonian numerical codes, and Newtonian formalism, in general, in an effective description of important astrophysical processes such as accretion onto black holes. In this paper, we develop a general pseudo-Newtonian formalism, which pertains to the motion of particles, light, and fluids in stationary space-times. In return, we are able to assess the applicability of the pseudo-Newtonian scheme. The simplest and most elegant formulas are obtained in space-times without gravitomagnetic effects, such as the Schwarzschild rather than the Kerr space-time; the quantitative errors are smallest for motion with low binding energy. Included is a ready-to-use set of fluid equations in Schwarzschild space-time in Cartesian and radial coordinates.

New characteristics of double layers in two-temperature Lorentzian plasmas

Double layers (DLs) structures in a collisionless Lorentzian plasma consisting of warm ions and two-temperature superthermal electrons are studied by using the reductive perturbation method. The basic set of fluid equations is reduced to extended Korteweg-de Vries (EK-dV) equation. It is shown that in temperatures lower than critical value for densities around first critical concentrations of cold electrons (\(d \to d_{c_{1}}\)) DL structures coexist. The effects of cold to hot electron density ratio d, cold to hot electrons temperature ratio σ, spectral index of cold and hot electrons κc and κh, ion temperature δ on DLs structure are also, discussed.

Nonlinear fluid equations for fully toroidal electromagnetic waves for the core tokamak plasma

AbstractThe rather general set of fluid equations with full curvature effects (Shukla and Weiland, Phys. Rev. A 40, 341 (1989)) has been modified to apply to the core and generalized to include also microtearing modes.

Dust-acoustic solitary waves of the modified KdV equation in a warm dusty plasma with cold and hot nonthermal ions

A theoretical investigation has been made for the propagation of small, but finite, nonlinear dustacoustic waves (DAW) in a collisionless, unmagnetized dust plasma that contains hot negativelycharged dust particles, cold nonthermal ions, hot nonthermal ions and Maxwellian-distributed electrons. The reductive perturbation method is employed to reduce the basic set of fluid equations to the modified Korteweg-de Vried (KdV) equation. How the amplitudes and the widths of the dust-acoustic waves vary with the plasma parameters is studied by using numerical simulations. Results show that not only the fast ion but also the number densities and the temperatures of the dust, the cold ions, the hot ions and the electrons all can play significant roles in determining the features of the amplitude and the width.

Propagation of Solitary Waves in Warm Magnetized Plasma with Two Temperature Electrons

Nonlinear wave structure of ion acoustic disturbances is investigated in magnetized plasma consisting of warm ions and two electron components, namely hot and cold. The basic set of fluid equations for the flow variables is reduced to a single equation known as Sagdeev Potential (SP) equation using non perturbative approach. The properties of solitary wave structures are studied by pseudo potential method, which is valid for arbitrary amplitude. The amplitude of the solitary waves and the depth of the potential well are found to decrease with the increase of the direction-cosine of the wave propagation. The ranges of temperature ratios (ion to electrons) for the existence of solitary waves and their effects on the plasma medium are studied in detail and presented graphically fordifferent sets of plasma parameters.

Boundary Condition on Electron Temperature for Antiforce Current Bearing Waves

In our investigation of breakdown waves, we apply a one-dimensional, three-component, steady-state fluid model. The wave is considered to be shock fronted and the electrons are assumed to be the main element in propagation of the wave. In our fluid model, the electron gas temperature is assumed to be large enough to sustain the wave motion. Our set of fluid equations is composed of the equations of conservation of mass, momentum and energy plus the Poisson’s equation. This investigation involves breakdown waves for which a large current exist in the vicinity of the wave front. Existence of current behind the wave front alters the equation of conservation of energy and also the Poisson’s equation. Therefore, the boundary conditions at the shock front will change as well. For current bearing breakdown waves we will derive the appropriate boundary condition for electron temperature, and using the new boundary condition, we will integrate the fluid dynamical equations through the dynamical transition region of the wave

The structure of the breakdown front

An analytic treatment of the breakdown front is given, using a simplified set of fluid equations, and assuming the existence of a steady-state reference frame. Key quantities are derived, such as the densities at the peak and far from the peak, and the scale lengths for the main variables close to the front. These results should permit testing of computational models, which should employ a more accurate set of fluid equations, and may be useful in deriving macroscopic models which do not resolve the length scales identified.

Continuous phase transition in the region of the vacuum arc cathode spot

A model for the near-cathode region of electric arcs is presented to investigate the liquid-plasma phase transition in the cathode spot region. Due to the high values of pressure and temperature after spot ignition, a “continuous phase transition” occurs in the liquid-vapor interface. A set of fluid equations with suitable boundary conditions have been solved to obtain diagrams of the spot plasma in the temperature-density plane during the spot evolution for a typical spot. To evaluate the model, the magnitude of some essential quantities such as the mean ion charge state of plasma and current density have been calculated, which are in accordance with experimental results.

Spin solitons in magnetized pair plasmas

A set of fluid equations, taking into account the spin properties of the electrons and positrons in a magnetoplasma, are derived. The magnetohydrodynamic limit of the pair plasma is investigated. It is shown that the microscopic spin properties of the electrons and positrons can lead to interesting macroscopic and collective effects in strongly magnetized plasmas. In particular, it is found that new Alfvénic solitary structures, governed by a modified Korteweg–de Vries equation, are allowed in such plasmas. These solitary structures vanish if the quantum spin effects are neglected. Our results should be of relevance for astrophysical plasmas, e.g., in pulsar magnetospheres, as well as for low-temperature laboratory plasmas.

Spin magnetohydrodynamics

Starting from the non-relativistic Pauli description of spin- particles, a set of fluid equations, governing the dynamics of such particles interacting with external fields and other particles, is derived. The equations describe electrons, positrons, holes and similar conglomerates. In the case of electrons, the magnetohydrodynamic limit of an electron–ion plasma is investigated. The results should be of interest and relevance both to laboratory and astrophysical plasmas.

Simulation of geometrical effects on surface wave discharges

Surface wave discharges (SWDs) are sustained by electromagnetic waves propagating along the plasma surface. We present results of a two-dimensional model, based on the self-consistent numerical solution of Maxwell's equations for the surface wave fields and a set of fluid equations for the plasma, that explain observed effects of the SWD geometry.

Dynamics of Radiation due to Vacuum Nonlinearities

In quantum electrodynamics, photon–photon scattering can be the result of the exchange of virtual electron–positron pairs. This gives rise to a non-trivial dispersion relation for a single photon moving on a background of electromagnetic fields. Knowledge of the dispersion relation can be transferred, using standard methods, into new insights in the dynamical equations for the photons. Effectively, those equations will contain different types of self-interaction terms, depending on whether the photons are coherent or not. It is shown that coherent photons are governed by a nonlinear Schrödinger type equation, such that the self-interaction terms vanish in the limit of parallel propagating waves. For incoherent photons, a set of fluid equations can determine the evolution of the corresponding radiation gas. In the case of a self-interacting radiation fluid, it is shown that Landau damping can occur.

Propagation of Partially Coherent Photons in an Ultra-Intense Radiation Gas

The scattering of photons off photons at the one-loop level is investigated. We give a short review of the weak field limit, as given by the first order term in the series expansion of the Heisenberg–Euler Lagrangian. The dispersion relation for a photon in a radiation gas is presented. Based on this, a wave kinetic equation and a set of fluid equations is formulated. These equations describe the interaction between a partially coherent electromagnetic pulse and an intense radiation gas. The implications of the results are discussed.

Structure of a source-driven magnetized oblique presheath.

A source-driven magnetized presheath is analyzed in an obliquely incident magnetic field. The conventional fluid treatments of the collisionless and collisional magnetized presheath use standard fluid equations to recover the velocity profiles that satisfy the Bohm sheath criterion at the electrostatic sheath edge. In a purely source-driven collisionless presheath, however, there is no mechanism to redistribute the change in parallel energy in the perpendicular direction and therefore the boundary values of flow velocities are strong functions of angle of incidence. In the present treatment, numerical solutions are obtained for a set of fluid equations derived from the moment description of a generalized gyrokinetic equation. The density, velocity, and temperature profiles in a source-driven presheath are computed, which show a dependence on the angle of incidence of the magnetic field on a perfectly absorbing solid surface.