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1.
In his theory of violent relaxation, Lynden-Bell gave a rigorous derivation of the equilibrium distribution, but only a qualitative discussion of the manner in which equilibrium is attained Here we present a fully explicit dynamical theory of collisionless relaxation towards Lynden-Bel equilibrium.The analysis proceeds from the coarse-graining in phase space of the collisionless Boltzmann equation the mesh size being determined by the precision of the observational data. The theoretical developmen leads to a kinetic equation generalizing that obtained by Kadomtsev and Pogutse in the rather differen context of homogeneous plasma turbulence. The collision integral differs from the classical Fokker Planck type essentially by the appearance of products of three distribution functions. It drives th systems towards the Lynden-Bell equilibrium state, on a time-scale which is inversely proportional to th coarse-graining mesh and, in the non-degenerate limit, to the fine-grained phase density. Owing to th various approximations introduced, the theory does not, however, describe the violent relaxation proces itself, but rather its late quiescent phases. 相似文献
2.
We study spherically symmetrical equilibrium states of collisionless stellar systems confined to a spherical box. These equilibrium states correspond to the statistics introduced by Lynden-Bell in his theory of 'violent relaxation', and are described by a Fermi–Dirac distribution function. We compute the corresponding equilibrium diagram and show that a global entropy maximum exists for any accessible control parameter. This equilibrium state shows a pronounced separation between a degenerate core and a halo. We therefore check that degeneracy is able to stop the gravitational collapse (of a collisionless system), and we propose a simple model for the 'core–halo' structure. We also discuss the relevance of our study for real galaxies or other astrophysical systems such as massive neutrinos. 相似文献
3.
A thermodynamic approach to the construction of a phenomenological macroscopic model of developed turbulence in a compressible fluid is considered with regard for the formation of space–time dissipative structures. A set of random variables were introduced into the model as internal parameters of the turbulent–chaos subsystem. This allowed us to obtain, by methods of nonequilibrium thermodynamics, the kinetic Fokker–Planck equation in the configuration space. This equation serves to determine the temporary evolution of the conditional probability distribution function of structural parameters pertaining to the cascade process of fragmentation of large-scale eddies and temperature inhomogeneities and to analyze Markovian stochastic processes of transition from one nonequilibrium stationary turbulent-motion state to another as a result of successive loss of stability caused by a change in the governing parameters. An alternative method for investigating the mechanisms of such transitions, based on the stochastic Langevin-type equation intimately related to the derived kinetic equation, is also considered. Some postulates and physical and mathematical assumptions used in the thermodynamic model of structurized turbulence are discussed in detail. In particular, we considered, using the deterministic transport equation for conditional means, the cardinal problem of the developed approach—the possibility of the existence of asymptotically stable stationary states of the turbulent-chaos subsystem. Also proposed is the nonequilibrium thermodynamic potential for internal coordinates, which extends the well-known Boltzmann–Planck relationship for equilibrium states to the nonequilibrium stationary states of the representing ensemble. This potential is shown to be the Lyapunov function for such states. The relation is also explored between the internal intermittence in the inertial interval of scales and the fluctuations of the energy of dissipation. This study is aimed at constructing representative models of natural space environments. It develops a synergetic approach to modeling the structurized turbulence of astrophysical and geophysical systems, which was proposed by the author in previous papers (Kolesnichenko, 2002, 2003). 相似文献
4.
The structure of collisionless shocks propagating parallel to the magnetic field is discussed in the case of a large ratio of plasma pressure to magnetic pressure. The theory makes use of the basic ideas of Kennel and Sagdeev and it is shown that their shock model is to be interpreted in terms of relaxation shocks. The calculations are based on a purely macroscopic set of equations including finite Larmor radius effects. The resulting shock structure is determined both in a quasilinear WKB-type approximation and through a direct numerical integration of the basic non-linear equations. The results from both methods agree fairly well, although the level of the turbulence is high. It is argued that strong parallel shocks have a double structure, where the main transition is followed by a broad relaxation wave. It is suggested that the magnetosheath should be considered as the relaxation zone of the Earth's bow shock. 相似文献
5.
The present review concerns the relevance of collisionless reconnection in the astrophysical context. Emphasis is put on recent developments in theory obtained from collisionless numerical simulations in two and three dimensions. It is stressed that magnetic reconnection is a universal process of particular importance under collisionless conditions, when both collisional and anomalous dissipation are irrelevant. While collisional (resistive) reconnection is a slow, diffusive process, collisionless reconnection is spontaneous. On any astrophysical time scale, it is explosive. It sets on when electric current widths become comparable to the leptonic inertial length in the so-called lepton (electron/positron) “diffusion region”, where leptons de-magnetise. Here, the magnetic field contacts its oppositely directed partner and annihilates. Spontaneous reconnection breaks the original magnetic symmetry, violently releases the stored free energy of the electric current, and causes plasma heating and particle acceleration. Ultimately, the released energy is provided by mechanical motion of either the two colliding magnetised plasmas that generate the current sheet or the internal turbulence cascading down to lepton-scale current filaments. Spontaneous reconnection in such extended current sheets that separate two colliding plasmas results in the generation of many reconnection sites (tearing modes) distributed over the current surface, each consisting of lepton exhausts and jets which are separated by plasmoids. Volume-filling factors of reconnection sites are estimated to be as large as \({<}10^{-5}\) per current sheet. Lepton currents inside exhausts may be strong enough to excite Buneman and, for large thermal pressure anisotropy, also Weibel instabilities. They bifurcate and break off into many small-scale current filaments and magnetic flux ropes exhibiting turbulent magnetic power spectra of very flat power-law shape \(W_b\propto k^{-\alpha }\) in wavenumber k with power becoming as low as \(\alpha \approx 2\). Spontaneous reconnection generates small-scale turbulence. Imposed external turbulence tends to temporarily increase the reconnection rate. Reconnecting ultra-relativistic current sheets decay into large numbers of magnetic flux ropes composed of chains of plasmoids and lepton exhausts. They form highly structured current surfaces, “current carpets”. By including synchrotron radiation losses, one favours tearing-mode reconnection over the drift-kink deformation of the current sheet. Lepton acceleration occurs in the reconnection-electric field in multiple encounters with the exhausts and plasmoids. This is a Fermi-like process. It results in power-law tails on the lepton energy distribution. This effect becomes pronounced in ultra-relativistic reconnection where it yields extremely hard lepton power-law energy spectra approaching \(F(\gamma )\propto \gamma ^{-1}\), with \(\gamma \) the lepton energy. The synchrotron radiation limit becomes substantially exceeded. Relativistic reconnection is a probable generator of current and magnetic turbulence, and a mechanism that produces high-energy radiation. It is also identified as the ultimate dissipation mechanism of the mechanical energy in collisionless magnetohydrodynamic turbulent cascades via lepton-inertial-scale turbulent current filaments. In this case, the volume-filling factor is large. Magnetic turbulence causes strong plasma heating of the entire turbulent volume and violent acceleration via spontaneous lepton-scale reconnection. This may lead to high-energy particle populations filling the whole volume. In this case, it causes non-thermal radiation spectra that span the entire interval from radio waves to gamma rays. 相似文献
6.
An attempt is made to construct a phenomenological model of turbulence as a self-organization process in an open system. The representation of a turbulized continuum in the form of a thermodynamic complex consisting of two subsystems—the subsystem of averaged motion and the subsystem of turbulent chaos, which is considered, in turn, as a conglomerate of vortex structures of different space–time scales—made it possible to obtain, by methods of nonequilibrium thermodynamics, the defining relationships for the turbulent fluxes and forces that describe most comprehensively the transport and structurization processes in such a continuum. Using two interpretations of the Kolmogorov parameter (as a quantity that describes the rate of dissipation of energy into heat and as the rate of transfer of turbulent energy in the eddy cascade), the defining relationships were found for this quantity, thereby making the thermodynamic approach self-sufficient. An introduction into the model of internal parameters of the medium, which characterize the excitation of macroscopic degrees of freedom, made it possible to describe thermodynamically the Kolmogorov cascade process and to obtain a variety of kinetic equations (of the Fokker–Planck type in the configuration space) for the functions of distribution of small-scale turbulence characteristics, including the unsteady kinetic equation for the distribution of probability of dissipation of turbulent energy. As an example, a detailed derivation of such relationships is given for the case of stationary turbulence, when a tendency toward local isotropy is observed. In view of the wide occurrence of this phenomenon in nature, one might expect that the developed approach to the problem of modeling strong turbulence will find its use in astrophysical and geophysical applications. 相似文献
7.
The CrossScale mission will advance our understanding of fundamental plasma processes in collisionless plasmas. It will exploit the excellent natural plasma laboratory provided by the Earth’s magnetosphere and the near-Earth solar wind and, in particular, carry out multi-scale studies that will strongly complement plasma studies in ground-based laboratories. Previous studies of collisionless plasmas in space environments across the solar system have shown the ubiquitous nature of suprathermal particles and that these particles exhibit a power-law energy spectrum. In this paper we discuss the great significance of these suprathermal particles for CrossScale studies. We show that the presence of these particles is a natural consequence of the collisionless regime as they can propagate across the heliosphere with little spectral change and are not thermalised by collisions. They are a key indicator of the non-equilibrium nature of collisionless plasmas and an important source of free energy that can drive plasma processes. We discuss how these suprathermal particles influence the overall properties of the plasma. In particular, the energy distribution of particles follows a Kappa, rather than Maxwellian, distribution and thus the plasma does not have a single thermodynamic temperature. We also discuss the importance of the suprathermal tail as a tool to diagnose the processes responsible for particle energisation in collisionless plasmas. Such energisation is a common feature in collisionless plasmas, especially in terms of the primary science targets for CrossScale: reconnection, shocks and turbulence. Finally we also touch on the value of using CrossScale studies to provide ground truth measurements for a number of astrophysical techniques that exploit the effects of energetic electrons in the distant universe. Throughout the paper, we stress that suprathermal (30 keV-1 MeV) measurements are essential to fully characterise particle distributions. We show that such measurements will benefit greatly from the improved spatial and temporal resolution (compared to Cluster) that is proposed for the HEP instrument on CrossScale. 相似文献
8.
V. Krishan 《Solar physics》1985,95(2):269-280
A statistical mechanics of the velocity and magnetic fields is formulated for an active region plasma. The plasma subjected to the conservation laws emerges in a most probable state which is described by an equilibrium distribution function containing a lagrange multiplier for every invariant of the system. The lagrange multipliers are determined by demanding that the measured expectation values of the invariants be reproduced. For a numerical exercise, we have assumed some probable values for these invariants. The total energy of a coronal loop is estimated from energy balance considerations. Doppler widths of the UV and EUV lines excited in the coronal loop plasma give a measure of the root-mean-square velocities. Measurements of magnetic helicity are not available for the solar corona. 相似文献
9.
A. M. S. Smith A. Collier Cameron D. J. Christian W. I. Clarkson B. Enoch A. Evans C. A. Haswell C. Hellier K. Horne J. Irwin S. R. Kane T. A. Lister A. J. Norton N. Parley D. L. Pollacco R. Ryans I. Skillen R. A. Street A. H. M. J. Triaud R. G. West P. J. Wheatley D. M. Wilson 《Monthly notices of the Royal Astronomical Society》2006,373(3):1151-1158
The evolution of the Alfvén turbulence due to three-wave interactions is discussed using kinetic theory for a collisionless, thermal plasma. There are three low-frequency modes, analogous to the three modes of compressible magnetohydrodynamics (MHD). When only Alfvén waves are considered, the known anisotropy of turbulence in incompressible MHD theory is reproduced. Inclusion of a fast mode wave leads to the separation of turbulence into two regimes: small wave numbers where three-wave processes involving a fast mode are dominant, and large wave numbers where the three Alfvén wave process is dominant. Possible application of the anisotropic Alfvén turbulence to the interstellar medium and dissipation of magnetic energy in magnetars are discussed. 相似文献
10.
Characteristic features of the plasma model for radio emission from the extending fronts of solar flare energy release are studied. It is shown that the electron distribution is formed near the thermal fronts as stationary beam injection through the boundary into the cold plasma semi-space. A principal new result is a conclusion about the localization of a plasma turbulence region — the source of emission in a narrow layer before the thermal front, that makes it possible to explain the burst narrow-band feature in a natural way. Wide capabilities of the flare loop structure analysis using the narrow-band emission parameters are demonstrated. 相似文献
11.
12.
Ivan R. King 《Celestial Mechanics and Dynamical Astronomy》1974,9(3):349-357
This review attempts to place stellar dynamics in relation to other dynamical fields and to describe some of its important techniques and present-day problems. Stellar dynamics has some parallels, in increasing order of closeness, with celestial mechanics, statistical mechanics, kinetic theory, and plasma theory; but even in the last case the parallels are not very close. Stellar dynamics describes, usually through distribution functions, the motions of a large number of bodies as they all act on each other gravitationally. To a good approximation each star can be considered to move in the smoothed-out field of all the others, with random encounters between pairs of stars adding a slow statistical change to these smooth motions. Smooth-field dynamics has a well-developed theory, and the state of smooth stellar systems can be described in some detail. The ‘third integral’ presents an outstanding problem, however. Stellar encounters also have a well-developed theory, but close encounters and encounters of a single star with a binary pose serious problems for the statistical treatment. Star-cluster dynamics can be approached through a theory of smooth-field dynamics plus changes due to encounters, or alternatively through numerical simulations. The relation between the two methods is not yet close enough. The dynamical evolution of star clusters is still not fully understood. 相似文献
13.
We present a kinetic theory for boundary layers associated with MHD tangential discontinuities in a collisionless magnetized plasma such as those observed in the solar wind. The theory consists of finding self-consistent solutions of Vlasov's equation and Maxwell's equation for stationary, one-dimensional boundary layers separating two Maxwellian plasma states. Layers in which the current is carried by electrons are found to have a thickness of the order of a few electron gyroradii, but the drift speed of the current-carrying electrons is found to exceed the Alfvén speed, and accordingly such layers are not stable. Several types of layers, in which the current is carried by protons are discussed; in particular, we considered cases in which the magnetic field intensity and/or direction changed across the layer. In every case, the thickness was of the order of a few proton gyroradii and the field changed smoothly, although the characteristics depended somewhat on the boundary conditions. The drift speed was always less than the Alfvén speed, consistent with stability of such structures. Our results are consistent with the observations of boundary layers in the solar wind near 1 AU. 相似文献
14.
A new conceptual framework for the foundations of statistical mechanics starting from dynamics is presented. It is based on the classification and the study of invariants in terms of the concepts of our formulation of non-equilibrium statistical mechanics. A central role is played by thecollision operator. The asymptotic behaviour of a class of states is determined by the collisional invariants independently of the ergodicity of the system. For this class of states we have an approach to thermodynamical equilibrium. We discuss the existence of classes of states which approach equilibrium. The complex microstructure of the phase space, as expressed by the weak stability concept which was introduced by Moser and others, plays here an essential role. The formalism that we develop is meaningful whenever the “dissipativity condition” for the collision operator is satisfied. Assuming the possibility of a weak coupling approximation, this is in fact true whenever Poincaré's theorem on the nonexistence of uniform invariants holds. In this respect, our formalism applies to few body problems and no transition to the thermodynamic limit is required. Our approach leads naturally to a ‘classical theory of measurement’. In particular a precise meaning can now be given to ‘thermodynamic variables’ or to ‘macrovariables’ corresponding to a measurement in classical dynamics. 相似文献
15.
Rudolf A. Treumann 《Astronomy and Astrophysics Review》2006,13(4):229-315
The electron–cyclotron maser is a process that generates coherent radiation from plasma. In the last two decades, it has gained increasing attention as a dominant mechanism of producing high-power radiation in natural high-temperature magnetized plasmas. Originally proposed as a somewhat exotic idea and subsequently applied to include non-relativistic plasmas, the electron–cyclotron maser was considered as an alternative to turbulent though coherent wave–wave interaction which results in radio emission. However, when it was recognized that weak relativistic corrections had to be taken into account in the radiation process, the importance of the electron–cyclotron maser rose to the recognition it deserves. Here we review the theory and application of the electron–cyclotron maser to the directly accessible plasmas in our immediate terrestrial and planetary environments. In situ access to the radiating plasmas has turned out to be crucial in identifying the conditions under which the electron–cyclotron maser mechanism is working. Under extreme astrophysical conditions, radiation from plasmas may provide a major energy loss; however, for generating the powerful radiation in which the electron–cyclotron maser mechanism is capable, the plasma must be in a state where release of susceptible amounts of energy in the form of radiation is favorable. Such conditions are realized when the plasma is unable to digest the available free energy that is imposed from outside and stored in its particle distribution. The lack of dissipative processes is a common property of collisionless plasmas. When, in addition, the plasma density becomes so low that the amount of free energy per particle is large, direct emission becomes favorable. This can be expressed as negative absorption of the plasma which, like in conventional masers, leads to coherent emission even though no quantum correlations are involved. The physical basis of this formal analogy between a quantum maser and the electron–cyclotron maser is that in the electron–cyclotron maser the free-space radiation modes can be amplified directly. Several models have been proposed for such a process. The most famous one is the so-called loss-cone maser. However, as argued in this review, the loss-cone maser is rather inefficient. Available in situ measurements indicate that the loss-cone maser plays only a minor role. Instead, the main source for any strong electron–cyclotron maser is found in the presence of a magnetic-field-aligned electric potential drop which has several effects: (1) it dilutes the local plasma to such an extent that the plasma enters the regime in which the electron–cyclotron maser becomes effective; (2) it generates energetic relativistic electron beams and field-aligned currents; (3) it deforms, together with the magnetic mirror force, the electron distribution function, thereby mimicking a high energy level sufficiently far above the Maxwellian ground state of an equilibrium plasma; (4) it favors emission in the free-space RX mode in a direction roughly perpendicular to the ambient magnetic field; (5) this emission is the most intense, since it implies the coherent resonant contribution of a maximum number of electrons in the distribution function to the radiation (i.e., to the generation of negative absorption); (6) it generates a large number of electron holes via the two-stream instability, and ion holes via the current-driven ion-acoustic instability which manifest themselves as subtle fine structures moving across the radiation spectrum and being typical for the electron–cyclotron maser emission process. These fine structures can thus be taken as the ultimate identifier of the electron–cyclotron maser. The auroral kilometric radiation of Earth is taken here as the paradigm for other manifestations of intense radio emissions such as the radiation from other planets in the solar system, from exoplanets, the Sun and other astrophysical objects. 相似文献
16.
Abhas Mittra 《Astrophysics and Space Science》1984,107(1):135-140
We intend to probe into the nature of the thermodynamical equilibrium of an idealized isothermal, spherical, self-gravitating, giant molecular cloud. The necessity of invoking a frozen in magnetic field has been pointed out for clouds with uniform mass distribution. An equation of state corresponding to the macroscopic statistical equilibrium of the cloud, steeped into a weak homogeneous magnetic field, has also been derived. 相似文献
17.
C. C. Leiby Jr. 《Astrophysics and Space Science》1986,122(1):157-161
A vector theory of electromagnetism and gravitation has indicated a possible equivalence of gravitational energy and electric charge. If true, the resulting electromagnetic and gravitational forces within a stationary, gravitationally collapsed body of radiusR=GM/c
2 are everywhere in balance within the body, if it has a radial mass density distribution proportional to 1/r
2. In addition, radial perturbation of such a body will result in a force imbalance which is restorative. Hence, the equilibrium is stable. 相似文献
18.
The evolution of Alfvén turbulence due to three-wave interactions is discussed using kinetic theory for a collisionless, thermal plasma. In particular, we consider decay of Alfvén waves through three-wave coupling with an ion sound mode in the random-phase approximation. Two decay processes are of particular interest: an Alfvén wave decays into a backward propagating Alfvén wave and a forward propagating ion sound wave, and an Alfvén wave decays into a backward propagating fast magnetoacoustic wave and a forward ion sound wave. The former was widely discussed in the literature, particularly under the coherent wave assumption. The latter was not well explored and is discussed here. 相似文献
19.
A. M. Krymsky L. S. Marochnik P. D. Naselsky N. V. Pelikhov 《Astrophysics and Space Science》1978,55(2):325-350
On the basis of the theory set out in Papers I and II (Marochniket al., 1975a, b), the kinetic equations for the spectra of classical and quantum short-wave turbulences have been obtained, taking account of the influence of the latter on the process of cosmological expansion of a homogeneous and, on average, isotropic Universe. The equilibrium and stationary spectra of the turbulence do not change the form of the cosmological solution found in II. The latter change if the spectra are non-stationary, or if the dissipation is taken into account. It is possible that a situation exists in which the primordial short-wave turbulence, having had a significant influence on the early metric, would not be observable at the present time. Quantum turbulence has been studied. Its influence on the metric may be significant only near the Planckian timet
g. 相似文献
20.
In this paper we propose to review the fundamental aspects of turbulence theories and their relevance to particle distribution functions observed by the cluster satellites in the quasi-perpendicular shock. The paper focusses on the hierarchical model describing the different levels of plasma turbulence; from the linear theory, through the quasi-linear remedy, to strong turbulence theories in the context of the earth's bow shock. We will discuss very briefly the validity of these approximations, and their relevance as far as satellite observations are concerned. In particular, we will discuss the development of non-Gaussian features in the ion distribution functions through the evaluation of higher order moments such as the kurtosis or flatness and the skewness. We have found that the profile of the kurtosis versus skewness tends to collapse to a parabolic line. This in turn allows us to draw analogies with neutral fluid turbulence where such a collapse of the kurtosis-skewness profile has been observed. 相似文献