Collisional Cases Research Articles

Circular orbits and collisions of particles with magnetic dipole moment near magnetized Kerr black holes in modified gravity

Throughout this work, we explored the dynamics of test particles with magnetic dipole moment around magnetized rotating Kerr black holes in scalar–vector–tensor gravity theory (STVG), known as modified gravity theory (MOG). We assume that the black hole is immersed in external asymptotically uniform magnetic fields. We derive effective potential for circular orbits of the magnetized particles, taking into account both the magnetic and STVG interactions. We study profiles of the position of the innermost stable circular orbits (ISCOs) of the magnetized particles. We show that the MOG interaction is essentially, and the magnetic interaction enhances its effects on the ISCO radius and the angular momentum at ISCO. Also, we consider collisional cases of magnetized particles and the maximum and minimum limits of angular momentum that ensure the particle colliding near the horizon. Finally, we analyze the center-of-mass energy of colliding magnetized particles near the black hole horizon.

Kinetic interpretation of the classical Rayleigh-Taylor instability.

Rayleigh-Taylor (RT) instabilities are prevalent in many physical regimes ranging from astrophysical to laboratory plasmas and have primarily been studied using fluid models, the majority of which have been ideal fluid models. This work presents a five-dimensional (two spatial dimensions, three velocity space dimensions) simulation using the continuum-kinetic model to study the effect of the collisional mean free path and transport on the instability growth. The continuum-kinetic model provides noise-free access to the full particle distribution function permitting a detailed investigation of the role of kinetic physics in hydrodynamic phenomena such as the RT instability. For long mean free path, there is no RT instability growth, but as collisionality increases, particles relax towards the Maxwellian velocity distribution, and the kinetic simulations reproduce the fluid simulation results. An important and novel contribution of this work is in the intermediate collisional cases that are not accessible with traditional fluid models and require kinetic modeling. Simulations of intermediate collisional cases show that the RT instability evolution is significantly altered compared to the highly collisional fluidlike cases. Specifically, the growth rate of the intermediate collisionality RT instability is lower than the high collisionality case while also producing a significantly more diffused interface. The higher moments of the distribution function play a more significant role relative to inertial terms for intermediate collisionality during the evolution of the RT instability interface. Particle energy flux is calculated from moments of the distribution and shows that transport is significantly altered in the intermediate collisional case and deviates much more so from the high collisionality limit of the fluid regime.

FLUID ANALYSIS OF MAGNETIZED PLASMA SHEATH IN A CYLINDRICAL GEOMETRY

Plasma sheath formed in front of a material wall plays an important role in overall plasma properties. Magnetized plasma sheath for both collisional and collisionless cases in a cylindrical co-ordinate system was studied using a fluid model. The fluid equations were compiled for the considered geometry and were solved numerically, using the fourth-order Runge-Kutta method for prescribed boundary and initial conditions. The ion velocity along the axis of the cylinder and the ion density profiles were studied for collisionless and collisional cases and at different obliqueness of the magnetic field. The ion velocities acquired its maximum value at the wall with monotonic increment in collisionless cases, whereas the ion density profile was not monotonic in collisionless case as well as when the obliqueness of the magnetic field starts increasing. In such cases, the ion density increases close to the entrance and then decreases monotonically towards the wall. The study provides insight to plasma properties in cylindrical plasmas which are common in discharge tubes, light sources and plasma jets.

Space charge formation and Bohm’s criterion in the edge of thermal electronegative plasma

The collisional electronegative plasma space charge is investigated in the presence of the thermal positive ions. The Boltzmann distribution is assumed for electrons and negative ions and fluid equations are used to treat the accelerated positive ion through the sheath region. The influence of the positive ion temperature on the profile of the space charge is obtained for different negative ion concentration and negative ion temperature for collisionless and collisional cases. It is shown that the position of the space charge peak is independent of positive ion temperature while its amplitude depends on the positive ion temperature. The presence of the negative ion leads to damping of the space charge amplitude. In addition the thermal effect of the positive ion on the kinetic energy of the ion extracted from an ion source is studied in difference of collisionality and electronegativity. It is shown that, in the presence of thermal positive ion, the influence of the negative ion temperature on the sheath characteristics disappears. It is observed that in the presence of the hot positive ion, the twofold feature of the space charge starts at higher values of negative ion temperature which is more pronounced in collisional case. Finally, the influences of the positive and negative ion temperature, as well as the electronegativity and collisionality on the net electric current are studied.

Double layers and other phenomena in low-pressure plasma columns generated by ultra-violet light

Low-pressure steady-state plasmas are analysed by means of a two-fluid model in both plane and cylindrical geometries. The charged particles are generated by UV illumination. Both a Gaussian and a one-step profile of the ionization are taken into account. Numerical results reveal various types of solutions depending on the ionization profile and the collisionality. The first state arises if the ionization spreads from the centre over a great part of the plasma. It has an almost quasineutral plasma core and a positively charged boundary sheath. The curvature of the number density of the charge particles is negative, except the boundary sheath. The second state occurs if the ionization is mainly localized in the vicinity of the centre and the collisionality is below a threshold. A slightly positive plasma core is surrounded by a double layer there where the ionization falls off steeply. Between the double layer and the boundary sheath a broad zone can exist where the plasma is nearly quasi-neutral and the electric field is small. Within the double layer the ion drift speed attains the Bohm velocity in collisionless plasmas, it is smaller in collisional cases. In a broad domain, the curvature of the number density of the charged particles can be positive. This is a feature of the so-called contracted columns. The transition between both the states occurs abruptly under collisonless conditions and becomes smooth as the collisionality increases. The minimum of the space charge density can become positive in this case. Several layers are possible, as well. Using the Gaussian profile analytical criteria can be given for a few of the mentioned phenomena. Probably, ionization profiles prescribed by photons allow to understand the origin of the contracted column more completely than up to now.

Topological classifications and bifurcations of periodic orbits in the potential field of highly irregular-shaped celestial bodies

This paper studies the distribution of characteristic multipliers, the structure of submanifolds, the phase diagram, bifurcations and chaotic motions in the potential field of rotating highly irregular-shaped celestial bodies (hereafter called irregular bodies). The topological structure of the submanifolds for the orbits in the potential field of an irregular body is shown to be classified into 34 different cases, including 6 ordinary cases, 3 collisional cases, 3 degenerate real saddle cases, 7 periodic cases, 7 period-doubling cases, 1 periodic and collisional case, 1 periodic and degenerate real saddle case, 1 period-doubling and collisional case, 1 period-doubling and degenerate real saddle case, and 4 periodic and period-doubling cases. The different distribution of the characteristic multipliers has been shown to fix the structure of the submanifolds, the type of orbits, the dynamical behaviour and the phase diagram of the motion. Classifications and properties for each case are presented. Moreover, tangent bifurcations, period-doubling bifurcations, Neimark-Sacker bifurcations and the real saddle bifurcations of periodic orbits in the potential field of an irregular body are discovered. Submanifolds appear to be Mobius strips and Klein bottles when the period-doubling bifurcation occurs.

Transition in electron physics of magnetic reconnection in weakly collisional plasma

Using particle-in-cell (PIC) simulations with a Monte Carlo treatment of the Coulomb collision operator, we study the transition in electron dynamics of magnetic reconnection for various levels of collisionality. The weakly collisional cases considered all fall into the so-called Hall or kinetic regime. Nevertheless, collisions may still alter the electron kinetic physics characteristic of collisionless reconnection, where adiabatic trapping energizes the electrons and leads to strong anisotropy of the electron velocity distribution and pressure. This anisotropy can support extended current sheets, associated with secondary island formation and turbulent flux rope interactions in three dimensional systems. The collisional simulations demonstrate how weak collisions may modify or eliminate these electron structures in the kinetic regimes. While the reconnection rate is not sensitive to the collisionality in the range studied, we find that increasing collisionality reduces the level of electron energization near the reconnection site. Finally, the results provide guidance for new laboratory reconnection experiments that will access the weakly collisional regimes.

Leap frog integrator modifications in highly collisional particle-in-cell codes

Leap frog integration method is a standard, simple, fast, and accurate way to implement velocity and position integration in particle-in-cell codes. Due to the direct solution of kinetics of particles in phase space central to the particle-in-cell procedure, important information can be obtained on particle velocity distributions, and consequently on transport and heating processes. This approach is commonly associated with physical situations where collisional effects are weak, but can also be profitably applied in some highly collisional cases, such as occur in semiconductor devices and gaseous discharges at atmospheric pressure. In this paper, we show that the implementation of the leap frog integration method in these circumstances can violate some of the assumptions central to the accuracy of this scheme. Indeed, without adaptation, the method gives incorrect results. We show here how the method must be modified to deal correctly with highly collisional cases.

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

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

The effect of the electron sound speed on wave propagation in the ionospheric plasma

In this study, the effect of the electron sound speed on the extraordinary wave propagation is calculated without an approximation for either collisional or collisionless cases in the ionospheric plasma by using the real geometry of the Earth’s magnetic field for the Northern Hemisphere. It is observed that there is no remarkable effect on the propagation of the extraordinary wave, especially at reflection altitudes. But it is also observed that the magnitudes of k2 (the square of the wave number) have changed every season, and the phase velocity of wave in warm ionospheric plasma has increased.

MULTICOMPONENT THEORY OF BUOYANCY INSTABILITIES IN ASTROPHYSICAL PLASMA OBJECTS: THE CASE OF MAGNETIC FIELD PERPENDICULAR TO GRAVITY

We develop a general theory of buoyancy instabilities in the electron-ion plasma with the electron heat flux based not upon MHD equations, but using a multicomponent plasma approach in which the momentum equation is solved for each species. We investigate the geometry in which the background magnetic field is perpendicular to the gravity and stratification. General expressions for the perturbed velocities are given without any simplifications. Collisions between electrons and ions are taken into account in the momentum equations in a general form, permitting us to consider both weakly and strongly collisional objects. However, the electron heat flux is assumed to be directed along the magnetic field that implies a weakly collisional case. Using simplifications justified for an investigation of buoyancy instabilities with the electron thermal flux, we derive simple dispersion relations both for collisionless and collisional cases for arbitrary directions of the wave vector. The collisionless dispersion relation considerably differs from that obtained in the MHD framework and is similar to the Schwarzschild's criterion. This difference is connected with simplified assumptions used in the MHD analysis of buoyancy instabilities and with the role of the longitudinal electric field perturbation which is not captured by the ideal MHD equations. The results obtained can be applied to clusters of galaxies and other astrophysical objects.

Parameter space region in the collisional magnetized electronegative plasma

The influence of the elastic collisions on the structure of a magnetized electronegative discharge is investigated. For a constant magnetic field, the profiles of the velocities of positive ions, the density of species, and electric potential are obtained. Furthermore, the positive ion flux is obtained as a function of magnetic field strength for different values of the collision frequency. The results show that in the absence of collision in a constant magnetic field, the discharge structure is uniform while by taking the collision into account, the structure becomes multilayer stratified. By increasing the collision frequency the discharge leaves the multilayer structure, and related oscillations in the plasma potential and space charge vanish. The parameter space region is obtained for collisionless and collisional cases. In this paper it is shown that a combined effect of collision and magnetic field determines the presheath-sheath structure.

Collisional Effects on Absorption and Energy Transport in a Dense Solid-Carbon Thin Film Irradiated by Subpicosecond Lasers

The collisional effects on the kinetics of interactions between a high-power subpicosecond laser and a solidcarbon thin film in a fast-ignition scenario are investigated by one-dimensional particle-in-cell simulations. Collisions are found to play an essential role in energy absorption and transport, compared to collisionless cases. In the collisional cases, the absorption at the heating edge, heat transport inside the thin film, and hot electron production are reduced in the early transient process.

Propagation regimes for an electromagnetic beam in magnetized plasma

The propagation of a Gaussian electromagnetic beam along the direction of magnetic field in a plasma is investigated. The extraordinary (Ex+iEy) mode is explicitly considered in the analysis, although the results for the ordinary mode can be obtained upon replacing the electron cyclotron frequency ωc by −ωc. The propagating beam electric field is coupled to the surrounding plasma via the dielectric tensor, taking into account the existence of a stationary magnetic field. Both collisionless and collisional cases are considered, separately. Adopting an established methodological framework for beam propagation in unmagnetized plasmas, we extend to magnetized plasmas by considering the beam profile for points below the critical curve in the beam-power versus beam-width plane, and by employing a relationship among electron concentration and electron temperature, provided by kinetic theory (rather than phenomenology). It is shown that, for points lying above the critical curve in the beam-power versus beam-width plane, the beam experiences oscillatory convergence (self-focusing), while for points between the critical curve and divider curve, the beam undergoes oscillatory divergence and for points on and below the divider curve the beam suffers a steady divergence. For typical values of parameters, numerical results are presented and discussed.

Stability of the lower hybrid instability excited by longitudinal currents in a collisional, multi-ion plasma

We have investigated the stability of the lower hybrid wave in a collisional plasma containing hydrogen and positively and negatively charged oxygen ions. The collisions of all the species in the plasma have been considered. The electrons, streaming parallel to the magnetic field, can excite the instability if their drift velocity exceeds the parallel phase velocity of the wave. This is true for both the weakly as well as the strongly collisional cases. If the ion collisions are neglected, the growth/damping rate depends on the electron collision frequency and is modified by a factor dependent directly on the number densities and square of the charges on the oxygen ions and inversely on the masses of these ions. Ion collisions, however only damp the wave; this damping being dependent also on the ion collision frequencies, in addition to the above dependencies. We find that the dispersion relation in the low collisional limit can account for lower hybrid waves in the observed frequency range.

Stabilization of the lower hybrid instability excited by longitudinal currents in a multi-ion plasma

We have investigated the stability of the lower hybrid wave in a plasma containing hydrogen and positively and negatively charged oxygen ions. The electrons, streaming parallel to the magnetic field, can excite the instability provided their drift velocity exceeds the parallel phase velocity of the wave. This is true for both the collisionless and collisional cases. The growth/damping rate is modified by a factor dependent directly on the number densities and square of the charges on the oxygen ions and inversely on the masses of these ions. Thus oxygen ions, irrespective of the nature of the charge on them, tend to stabilize the wave; the higher the degree of ionization of the oxygen ions, the greater the stabilization for a given number density.

Bifurcation theory of the transition to collisionless ion-temperature-gradient-driven plasma turbulence

The collisionless limit of the transition to ion-temperature-gradient-driven plasma turbulence is considered with a dynamical-systems approach. The importance of systematic analysis for understanding the differences in the bifurcations and dynamics of linearly damped and undamped systems is emphasized. A model with ten degrees of freedom is studied as a concrete example. A four-dimensional center manifold (CM) is analyzed, and fixed points of its dynamics are identified and used to predict a “Dimits shift” of the threshold for turbulence due to the excitation of zonal flows. The exact value of that shift in terms of physical parameters is established for the model; the effects of higher-order truncations on the dynamics are noted. Multiple-scale analysis of the CM equations is used to discuss possible effects of modulational instability on scenarios for the transition to turbulence in both collisional and collisionless cases.

Plasmas with more than one species of positive ion and the Bohm Criterion

The fluid equations for an active plasma generated by electron impact containing more than one species of positive ion are examined in detail when the ionization frequencies are assumed to be spatially constant with a view to generalizing the Bohm Criterion. It is shown that in this specific situation the various ion spatial distributions and transverse ion speed distributions are geometrically similar and thus each species arrives at the sheath with its own Bohm speed, when the plasma is collisionless. The collisional situation is also examined with the conclusion that in that case as well, ion densities and ion speeds are again geometrically similar. The transition between the collisionless and collisional cases is discussed but not examined in detail.

Internal sheaths in electronegative discharges

In three component electronegative discharges a parameter regime can be found in which the positive ions reach the local ion sound velocity at a position where the negative ion density may be significant compared to the electron density. For this regime a quasineutral electronegative core breaks down and a space charge region forms. Solutions in the space charge region are obtained in collisionless and collisional cases, neglecting ionization and positive-negative ion recombination. The structure of the non-neutral region is shown to vary significantly with the ratio of the negative ion and electron densities at the core edge, the ratio of ion and electron temperatures, and the ratio of the electron Debye length to the ion mean free path. If the first ratio is not too large the non-neutral region displays potential oscillations on the electron Debye length spatial scale, which damp away on the scale of the ion–neutral mean free path. The non-neutral region then terminates within the plasma. The change in electric potential across this region is several times the negative ion temperature, which is sufficient to confine the negative ions to the core. The non-neutral region merges with a quasineutral halo containing essentially only positive ions and electrons. If the negative ion density is sufficiently high compared to the electron density the electropositive halo disappears and the non-neutral region extends from the ion sound velocity threshold to the wall. For intermediate values of the negative ion density, a space charge double layer forms between the electronegative and electropositive regions.

Onsager relaxation of toroidal plasmas

The slow relaxation of isolated toroidal plasmas towards their thermodynamical equilibrium is studied in an Onsager framework based on the entropy metric. The basic tool is a variational principle, equivalent to the kinetic equation, involving the profiles of density, temperature, electric potential and electric current. These profiles enter two functionals reflecting the entropy of the field plasma - plasma system and the entropy production rate. These functionals are symmetrical. By themselves, they would drive an Onsager evolution of the system. However, the variational principle also contains an antisymmetrical functional reflecting the trajectory effects. These effects are eliminated, so that the Onsager relaxation is automatically established, in situations of low collisionality where the trajectories are integrable and close to the magnetic surfaces (e.g. in axisymmetric tokamaks). In such situations the Onsager character of the slow relaxation is a mere consequence of the Hamiltonian nature of the field - plasma system. In the collisional or non-integrable cases, an Onsager evolution may be still derived from the variational principle, but the plasma layers around successive magnetic surfaces must be independent enough, in the sense that unconfined trapped particles are forbidden unless they are detrapped long before they depart significantly from the magnetic surfaces. New minimization procedures are proposed to obtain entropy and entropy production rate functionals expressed in terms of the profiles of density etc, which drive the Onsager relaxation of the profiles. Onsager relaxations are possible in the presence of a turbulent field, either in an integrable situation (e.g. well separated magnetic islands) or in a non-integrable case (overlapping islands). The variational principle then involves the characteristic frequencies of the turbulent field, on the same grounds as the profiles of density, etc.