Uniform density equilibrium model of self-gravitating stellar systems

A class of equilibrium solutions of the Vlasov equation for self-gravitating systems is discussed. The density and the potential are derived in form of Jacobi polynomials, which in a special case give rise to a model with uniform density.     

The Alfvén-Carlquist double-layer theory of solar flares

We use the Vlasov equations for ions and electrons to develop a theory of a double layer in which there are both free and trapped electrons and ions. We find the equations which replace the Langmuir condition and the Bohm conditions and by numerically solving the resultant differential equation we find for particular choices of distribution functions the potential distribution in the layer. We discuss the applicability of this theory to solar flares, and show that conditions in solar flares may be such that double layers can exist for which the free particles have a power-law energy distribution. These particles will be accelerated in a double layer and may in this way account for the production of high-energy particles during the impulsive phase of solar flares.     

Ion-cyclotron waves in solar coronal hole

We investigate the effect of the plume/interplume lane (PIPL) structure of the solar polar coronal hole (PCH) on the propagation characteristics of ion-cyclotron waves (ICW). The gradients of physical parameters determined by SOHO and TRACE satellites both parallel and perpendicular to the magnetic field are considered with the aim of determining how the efficiency of the ICR process varies along the PIPL structure of PCH. We construct a model based on the kinetic theory by using quasi-linear approximation. We solve the Vlasov equation for O VI ions and obtain the dispersion relation of ICW. The resonance process in the interplume lanes is much more effective than in the plumes, agreeing with the observations which show the source of fast solar wind is interplume lanes. The solution of the Vlasov equation in PIPL structure of PCH, the physical parameters of which display gradients along and perpendicular direction to the external magnetic field, is thus obtained in a more general form than the previous investigations.     

Exact statistical mechanics of a one-dimensional self-gravitating system

The statistical mechanics of an isolated self-gravitating system consisting ofN uniform mass sheets is considered using both canonical and microcanonical ensembles. The one-particle distribution function is found in closed form. The limit for large numbers of sheets with fixed total mass and energy is taken and is shown to yield the isothermal solution of the Vlasov equation. The order of magnitude of the approach to Vlasov theory is found to be 0(1/N). Numerical results for spatial density and velocity distributions are given.     

Existence and stability of strong potential double layers

An elementary integral equation technique is used to construct strong and weak stationary shock solutions from the one-dimensional Vlasov equation. It is shown that the plasma is Penrose stable in all points in space under certain conditions.This work was supported in part by the Atomic Energy Commission Grant No. AT(11-1)-2059, and NSF Grant GA-31676.supported by a CSIR bursary.     

Relativistic Langmuir solitons-applications to pulsars

The non-linear Schrödinger equation, describing the non-linear Langmuir waves in a relativistic Vlasov plasma in a strong magnetic field, is derived. In the relativistic limit,KT>mc ², this equation gives envelope solitons which are discussed from a point of view of their applications to pulsars.     

Kinetic description of the Langmuir solitons in ultra-relativistic electron-positron plasmas

The nonlinear interaction between the high frequency Langmuir wave and the low frequency density fluctuation in ultrarelativistic isothermal electron positron plasmas is investigated from kinetic Vlasov equation. One dimensional Langmuir solitons are obtained, the width of which is so large that it is not relevant to the coherent pulsar radio emission.     

Ion–Cyclotron Resonance Frequency Interval Dependence on the O VI Ion Number Density in the North Polar Coronal Hole 1.5R–3R Region

The frequency intervals in which O VI ions get in resonance with ion–cyclotron waves are calculated using the kinetic model, for the latest six values found in literature on O VI ion number densities in the 1.5R–3R region of the NPCH. It is found that the common resonance interval is 1.5 kHz to 3 kHz. The R-variations of wave numbers necessary for the above calculations are evaluated numerically, solving the cubic dispersion relation with the dielectric response derived from the quasi-linear Vlasov equation for the left-circularly polarized ion-cyclotron waves.     

空间尘埃等离子体Maser效应以及所导致的Langmuir辐射

本文从弱湍动等离子体理论出发,由Ｖｌａｓｏｖ方程导出了Ｍａｓｅｒ效应作用机制下共振波的演化规律;并且讨论了尘埃等离子体电子束入射情况下,共振Ｌａｎｇｍｕｉｒ波的增长率．研究结果表明,Ｍａｓｅｒ效应比其它不稳定性（如本文中论及的束流不稳定性等）能更好地解释空间中的反常Ｌａｎｇｍｕｉｒ辐射现象．     

Two-stream instability in a collisionless plasma

This paper discusses the development of two-stream instability in a collisionless plasma. The plasma is described by velocity moments of Vlasov equation where heat flow tensor has been neglected. A dispersion relation for arbitrary propagation is derived for a collisionless electron fluid. Special cases of propagation parallel and perpendicular to the field lines are discussed. Growth rate is computed for parameters representative of the shear layers of solar wind at one AU. It is found that the shear layers are likely to be overstable.     

Quantum treatment of kinetic Alfvén wave

Dispersion properties of kinetic Alfvén wave in quantum magnetoplasma are derived. The quantum contribution to the Landau damping of kinetic Alfvén wave is also derived by using linearized Vlasov equation which contains the Bohm quantum potential. Classical Landau damped kinetic Alfvén waves play an important role in turbulence of astrophysical plasmas. The quantum modification in Landau damping of kinetic Alfvén wave can also play a significant role in changing the scaling law of turbulent spectra as well as the formation of damped localized Alfvénic structures in dense astrophysical plasmas.     

Instability of the electromagnetic ordinary mode in counterstreaming plasmas

The instability of a linearly-polarised electromagnetic ordinary mode in a plasma and propagating perpendicular to a uniform magnetic field caused by a counterstreaming of electrons along the latter is studied using a Vlasov plasma model. The results show that (i) for weak magnetic fields, the thermal effects stabilise the ordinary mode; (ii) for strong magnetic fields, the thermal effects destabilise the ordinary mode.     

The relativistic quasilinear theory of particle acceleration by hydromagnetic turbulence

The quasilinear theory of acceleration of relativistic particles by hydromagnetic turbulence is treated in the adiabatic limit of small gyration radius. The theory is based on the relativistic Vlasov equation; however, a given pitch-angle scattering rate by microturbulence is postulated and is added to this equation. The resulting acceleration is found to be given by a diffusion coefficient in total momentum, which is proportional to the spectrum of turbulence with a rate coefficient . is a frequency that represents the efficiency of each wave component of the turbulence in producing acceleration. It is given as an integral over the solution of a differential equation in pitch angle. is evaluated in various limiting cases and is shown to lead to familiar forms of acceleration, such as Fermi acceleration and magnetic pumping. Thus, a comprehensive theory of these forms of heating is achieved.     

Three-dimensional numerical simulation of a nonstationary gravitating <Emphasis Type="Italic">N</Emphasis>-body system with gas

We developed a three-dimensional numerical model to investigate nonstationary processes in gravitating N-body systems with gas. We used efficient algorithms for solving the Vlasov and Poisson equations that included the evolutionary processes under consideration, which ensures rapid convergence at high accuracy. We give examples of the numerical solution of the problem on the growth of physical instability in the model of a flat rotating disk with a gaseous component and its three-dimensional dynamics under various initial conditions including a nonzero velocity dispersion along the rotation axis.     

Retrograde precession of stellar orbits and gravitational loss-cone instability in galactic centers

We consider disk and spherical subsystems of stars with nearly radial orbits under conditions when the well-known radial orbit instability is not possible. This requires that the precession of stellar orbits be retrograde, i.e., in the direction opposite to the orbital rotation of stars. We show that an instability that is an analogue of the loss-cone instability known in plasma physics can then develop in the presence of a “loss cone” in the angular momentum distribution of stars, which ensures a deficit or even absence of stars with low angular momenta. Examples of systems with a loss cone are the centers of galaxies or star clusters with massive black holes. The instability can produce a flux of stars onto the galactic center, i.e., it can serve as a mechanism of fueling the nuclear activity of galaxies. Mathematically, the problem is reduced to analyzing simple characteristic equations that describe small perturbations in a disk and a sphere of radially highly elongated stellar orbits. In turn, these characteristics equations are derived through a number of successive simplifications of the general linearized Vlasov equations (i.e., the system that includes the collisionless Boltzmann kinetic equation and the Poisson equation) in action—angle variables.     

Study of the planet-satellite system growth process as a result of the accumulation of dust cloud material

In our paper, we suggest a model allowing study of the growth process of the double system (planet-satellite) as a result of the accumulation of scattered material from the common dust condensation. The model consists of two components—a computer component and an analytic component. In the course of the numerical experiment, the computer model allows determination of the dependence of the ratio of particle number captured by each body on their mass ratio. From there, the obtained dependence is used to close the analytical model of the protoplanet growth that is reduced to the solving of a differential equation. It is shown that at any form of the dependence, the equation is integrated in quadratures, and its solution in a number of concrete cases is studied. As a result, possible scenarios of double-system growth are obtained.     

Evolution of double layers in magnetised plasmas contaminated with dust charge fluctuations

Coherent structures entailing the existence of double layers have been studied in magnetised plasma contaminated with dust charging fluctuations. It has been shown that the dust charging in magnetic plasma leads to complexity in the derivation of the Sagdeev wave equation, but under way new procedure enable one to study the nature of double layers showing the effective role of the constituents of the plasma. A parametric analysis is a subject of interest in laboratory and space plasmas, and it has been explained with the input of various typical plasma numerics. The proposed mathematical mechanism has shown the success to yield plasma acoustic modes in a dusty plasma which, in turn, has been solved convincingly for double layers. Observations have been evaluated in an appropriate model with a view to agree with the observations in astrophysical problems dealing with present new findings.     

Kinetic Alfven wave driven by density and magnetic field inhomogeneities in plasmas of finite β

On the basis of an analysis of the instability of drift caused by density and magnetic field inhomogeneities in plasmas with finite β, the effect of the instability on the excitation of kinetic Alfven wave (KAW) is probed. In the kinetic theory, which correctly treats the effect of the finite Larmor radius and the wave-particle resonant interaction, the motion of the ions is described with the Vlasov equation and the motion of electrons, with the kinetic drift equation. Comparing the effects by inhomogeneities in the density and in the magnetic field in plasmas with finite β, we found that the drift instability is more easily excited by the former, and in the instability so excited, the energy transfer is more intense. This energy transfer provides the physical basis for the excitation of KAW. As shown by numerical solutions, KAWs can be widely excited and produced in the magnetosphere, especially in the cusp of the magnetosphere, in the magnetopause and in the boundary layers of plasma sheets, where inhomogeneities are obvious. The results of the present work further illustrate that the KAW plays an important role in the energy transfer in magnetospheric regions.     

Gravitational loss-cone instability in stellar systems with retrograde orbit precession

We study spherical and disc clusters in a near-Keplerian potential of galactic centres or massive black holes. In such a potential orbit precession is commonly retrograde, that is, the direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly-radial orbits. We show that if there is a loss-cone at low angular momentum (e.g. due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics   l ≥ 3  . If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independent of azimuthal number m . The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum.
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems.