共查询到20条相似文献，搜索用时 31 毫秒
1.
Recently an advanced nonlinear diffusion theory for particle transport across the mean magnetic field has been developed. The method used in the derivation of the latter theory is based on the cosmic ray Fokker-Planck equation. In the present article we use the same approach to describe pitch-angle scattering and parallel spatial diffusion nonlinearly. Furthermore, we derive the quasilinear transport theory, the weakly nonlinear theory as well as the Bohm limit as special cases from our more general approach. 相似文献
2.
Energetic particles, ejected from the Sun during solar flare events, may encounter interplanetary plasma/field conditions, which deviate considerably from the quiet time values used normally to describe the particle propagation. This is due to the presence of a hydromagnetic shock, which is emitted from the Sun at the time of the explosion. In a theoretical blast wave model, which incorporates the interaction with plane polarized Alfvén waves, we have analysed the changes in different terms of the Fokker-Planck equation, which describes energetic particle propagation. In this treatment, the shock influence on energy changes and on the transport coefficients are discussed. 相似文献
3.
I. H. Urch 《Astrophysics and Space Science》1991,178(2):185-195
The Fokker-Planck equation which describes the motion of charged particles in a random electromagnetic field is derived from the Liouville equation by a new method. The size of the perturbing magnetic field, for the Fokker-Planck equation to be valid, is calculated in a regime appropriate for cosmic-ray diffusion. 相似文献
4.
The Fokker-Planck equation for small stochastic changes to particles in Kepler orbits has to be formulated in terms of the integrals of motion. We generalize the modelling of proton and electron collisional perturbations to gas particles on trajectories through the solar system in order to include both spatial and velocity diffusion. The general solution is obtained in terms of a 4-dimensional normal distribution. Treatment of the singularity in the Fokker-Planck operator reduces the dimensionality by one. In addition to extending earlier results for anisotropic collisional heating in the thermal approximation, the present formulation gives the changes in density due to the mean repulsive force and to perturbations of trajectories (spatial diffusion). The net diffusion is almost everywhere towards the sun and the density increase is significant in the downstream hydrogen wake, particularly where destructive depletion is strong and gravitational focussing weak. 相似文献
5.
We study multi-wavelength variability in BL Lacertae object PKS 2155-304 in the frame of the time dependent one-zone synchrotron self-Compton (SSC) model, where stochastic particle acceleration is taken into account. In this model, a homogeneously and isotropically spherical structure is assumed, the Fokker–Planck type equation which describes the evolution of the particles energy is numerically solved, and the synchrotron and self-Compton components from the spherical blob are calculated. Our results can reproduce observed spectra energy distribution (SED) and give definite predictions for the flux and spectral variability of PKS 2155-304. We find that particle injection rate, magnetic field and Doppler factor in the acceleration zone are important parameters for explaining its flaring behaviour. 相似文献
6.
Chang Yang Lewei Zhang Yihua He Si Liu Qinghua Zhou 《Astrophysics and Space Science》2014,353(2):389-394
Using Cluster 4 satellite data, we examine activities of fast magnetosonic (MS) waves in the outer radiation belt near the location L=4.2 on 28 May 2005. We adopt a Gaussian distribution to fit the observed power spectral density of MS waves and find the fitting wave strength to be 245 pT. We then calculate the bounce-averaged diffusion coefficients and show that these diffusion coefficients are pronounced within a region of pitch angles about 25°–70°. By solving a 2D Fokker-Planck diffusion equation, we simulate the dynamic evolution of the electron phase space density (PSD), and demonstrate that significant increases in electron PSDs at energies of MeVs occur mainly within the aforementioned pitch-angle range over a time scale of several hours. The current results suggest that the interaction between MS waves and electrons could be an important mechanism of electron acceleration in the radiation belt. 相似文献
7.
K. G. McClements 《Solar physics》1987,109(2):355-363
The conditions required for the stability of a steady-state electron beam propagating in the solar corona are determined using the quasi-linear theory. The growth rate for electron plasma waves in a magnetized plasma is evaluated, with the electron distribution function being given by an analytic solution of the linearized Fokker-Planck equation. It is shown that, when the gyrofrequency is less than the plasma frequency, the instability has a narrow angular range, with the maximum growth rate occuring along the magnetic field. A stability boundary in parameter space is determined, indicating that electron beams must be highly collimated at injection to be Langmuir unstable at any point in space. The implications of the results for alternative models of hard X-ray bursts are discussed and it is argued that Langmuir instability will not occur on either the trap model or the thermal model. Such models would, therefore, be refuted by the detection of a large flux of plasma microwave radiation associated with hard X-ray emission. 相似文献
8.
We analyze the time variation of microwave spectra and hard X-ray spectra of 1989 March 18, which are obtained from the Solar Array at the Owens Valley Radio Observatory (OVRO) and the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission (SMM), respectively. From this observation, it is noted that the hard X-ray spectra gradually soften over 50–200 keV on-and-after the maximum phase while the microwaves at 1–15 GHz show neither a change in spectral shape nor as rapid a decay as hard X-rays. This leads to decoupling of hard X-rays from the microwaves in the decay phase away from their good correlation seen in the initial rise phase. To interpret this observation, we adopt a view that microwave-emitting particles and hard X-ray particles are physically separated in an inhomogeneous magnetic loop, but linked via interactions with the Whistler waves generated during flares. From this viewpoint, it is argued that the observed decoupling of microwaves from hard X-rays may be due to the different ability of each source region to maintain high energy electrons in response to the Whistler waves passing through the entire loop. To demonstrate this possibility, we solve a Fokker-Planck equation that describes evolution of electrons interacting with the Whistler waves, taking into account the variation of Fokker-Planck coefficients with physical quantities of the background medium. The numerical Fokker-Planck solutions are then used to calculate microwave spectra and hard X-ray spectra for agreement with observations. Our model results are as follows: in a stronger field region, the energy loss by electron escape due to scattering by the waves is greatly enhanced resulting in steep particle distributions that reproduce the observed hard X-ray spectra. In a region with weaker fields and lower density, this loss term is reduced allowing high energy electrons to survive longer so that microwaves can be emitted there in excess of hard X-rays during the decay phase of the flare. Our results based on spectral fitting of a flare event are discussed in comparison with previous studies of microwaves and hard X-rays based on either temporal or spatial information. 相似文献
9.
Cosmic energy equation is an important equation for studying the gravitational galaxy clustering in the expanding universe.
We derive the distribution function for fluctuations in particle number by using the cosmic energy equation for extended structures
(galaxies with halos). From spatial distribution function, containing particle fluctuations, we derive the velocity distribution
function to understand the influence of particle fluctuations on the velocities of galaxies.With the help of cosmic energy
equation we try to find out the physical constraints for the application of quasi-equilibrium approximation. 相似文献
10.
Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media. 相似文献
11.
Jörn E. Kunstmann 《Solar physics》1978,59(2):395-405
The transport of energetic charged particles in fluctuating magnetic fields is analysed by means of the Fokker-Planck equation for the early time, when the diffusive modes are not yet valid. Exact solutions are found for the particle fluxes integrated over space; after these have reached a time-independent final steady state, the usually considered diffusive modes of the velocity-integrated density become valid. The time for that is finite. The analysis is done both for a constant and a divergent mean magnetic field. 相似文献
12.
The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that are necessary for a practical implementation of the method in a working SPH code. Much of SPH’s success relies on its excellent conservation properties and therefore the numerical conservation of physical invariants receives much attention throughout this review. The self-consistent derivation of the SPH equations from the Lagrangian of an ideal fluid is the common theme of the remainder of the text. We derive a modern, Newtonian SPH formulation from the Lagrangian of an ideal fluid. It accounts for changes of the local resolution lengths which result in corrective, so-called “grad-h-terms”. We extend this strategy to special relativity for which we derive the corresponding grad-h equation set. The variational approach is further applied to a general-relativistic fluid evolving in a fixed, curved background space-time. Particular care is taken to explicitly derive all relevant equations in a coherent way. 相似文献
13.
N. R. Sibgatullin 《Astronomy Letters》2002,28(2):83-88
We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrary orbital inclination (with a minimum latitudinal angle reached at the orbit) in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki-Kato formulas. The NS gravitational field is described by the exact solution of the Einstein equation that includes the NS quadrupole moment induced by rapid rotation. Convenient asymptotic formulas are given for the metric coefficients of the corresponding space-time in the form of Kerr metric perturbations in Boyer-Lindquist coordinates. 相似文献
14.
采用含有频率涨落噪声和指数形式关联随机力作用的广义朗之万(Langevin)方程模型描述黑洞吸积盘的垂向振荡,推导出吸积盘随机振荡光度功率谱密度的解析表达式,并讨论了系统参数对功率谱密度中低频准周期振荡(Low Frequency Quasi-Periodic Oscillations,LFQPOs)现象的影响。研究结果发现选取合适的系统参数时,功率谱密度曲线上出现了一个基频和一个二次谐频的共振双峰低频准周期振荡,基频峰对应的中心频率为吸积盘振荡的特征频率;随机力关联时间决定了基频峰的高度和宽度,频率噪声强度和粘滞阻尼只对二次谐频峰产生影响。结果说明吸积盘的随机振荡模型可以作为低频准周期振荡起源的一种解释。 相似文献
15.
S. A. El-Wakil Essam M. Abulwafa E. K. El-Shewy Abeer A. Mahmoud 《Astrophysics and Space Science》2013,346(2):383-393
The reductive perturbation method has been used to derive the Burgers equation for dust acoustic shock waves in unmagnetized plasma having electrons, singly charged ions, hot and cold dust species with Boltzmann distributions for electrons and ions in the presence of the cold (hot) dust viscosity coefficients. The time-fractional Burgers equation is formulated using Euler-Lagrange variational technique and is solved using the variational-iteration method. The effect of time fractional parameter on the behavior of the shock waves in the dusty plasma has been investigated. 相似文献
16.
The evolution of magnetic flux at the solar surface is widely modeled by the flux transport equation. This describes the distribution of flux from instant to instant over the whole surface but does not describe how the synoptic map for one Carrington rotation evolves into the synoptic map for the next rotation. We derive the correct synoptic evolution equation, show that a simple version yields extremely accurate predictions of synoptic maps and discuss the implications for previous studies of the evolution of surface magnetic structures. We also note that the procedure yields a method of reconstructing an approximate map of the flux over the whole surface at any instant. 相似文献
17.
Bernie D. Shizgal 《Planetary and Space Science》2004,52(10):923-933
Nonequilibrium distributions of space plasmas are often characterized by extended high-energy tails. This paper provides a detailed analysis of the relaxation of such isotropic nonequilibrium plasmas. We consider an energetic charged species dilutely dispersed in a fully ionized plasma, which acts as a heat bath at equilibrium. The minor constituent is referred to as a “test particle” and collisions between test particles are not included. We study the approach to equilibrium with a finite difference method of solution of the Fokker-Planck equation appropriate for collisions between charged particles. The solution of the Fokker-Planck equation is also presented formally as an expansion in the eigenfunctions of the Fokker-Planck operator. The main objective of the paper is the calculation of the energy-dependent relaxation times of the distribution function. A strong energy dependence for these relaxation times is anticipated since, for Coulomb collisions, the Rutherford cross-section varies with relative speed g as g−4. Analogous results for neutral species are presented for comparison in the following paper. 相似文献
18.
An analytical theory is developed for the velocity evolution of nonaccreting planetesimal populations, based on the Boltzmann and Fokker-Planck equations. Adapting Shkarofsky's calculation of plasma viscosities, the rate of increase in random velocities due to gravitational encounters between planetesimals of equal mass is found to be one-third to one-half Safronov's result. Comparison with Wetherill's numerical experiments suggests that the Fokker-Planck equation underestimates the effectiveness of encounters and that Safronov's value is approximately correct. For populations of nonuniform sizes, the Fokker-Planck equation indicates an efficient redistribution of energy from the largest bodies to the smaller ones. By conserving angular momentum, the rate of radial spreading of orbits is also derived. 相似文献
19.
The propagation time for solar protons observed during the events of January 24, February 25 and March 17, 1969 are compared with those estimated from numerical solutions of the Fokker-Planck transport equation, using values of the diffusion coefficient of the form K
r
= K
0
r
b
where r is radial distance from the Sun, K
0 is obtained from the plasma-field parameters near the Earth and b varies from - 3 to + 1. K
0 is derived either by assuming that all the magnetic fluctuation power is in small amplitude transverse waves or alternatively in discontinuous changes in ¦B¦ along the flux tube of propagation. In the first case it is found that the K
0 values calculated require either b -3, implying a very rapid wave growth with r, or the Fokker-Planck equation reduces to the situation of purely convective transport which is at variance with the experimental observations. More reasonable results are found in the second case although even here K
0 is probably underestimated. Alternative ways of deducing K
0 empirically from particle anisotropy measurements are put forward and these seem to favour the discontinuity model. 相似文献
20.
T. Takakura 《Solar physics》1990,127(1):95-107
The Fokker-Planck equation is numerically solved to study the electron velocity distribution under steady heat conduction with an applied axial electric current in a model coronal loop.If the loop temperature is so high that the electron mean-free path is longer than the local temperature scale height along the loop, a velocity hump appears at about the local thermal electron velocity. The hump is attributed to cooler electrons moving up the temperature gradient to compensate for the runaway electrons moving down the gradient. If the ratio between the mean free path and temperature scale height is greater than about 2, negative absorption for the plasma waves can appear (waves grow). This effect is enhanced by the presence of axial electric current in the half of the coronal loop in which the electrons carrying the current are drifting up the temperature gradient. Thus, the plasma instability may occur in the coronal elementary magnetic flux tubes. Although the present paper is limited to show the critical condition and linear growth rate of the instability, the following scenarios may be inferred.If the flux tubes change from marginally stable to unstable against the plasma instability, due to an increase in the loop temperature, anomalous resistivity may suddenly appear because of the growth of plasma waves. Then a high axial electric field is induced that may accelerate particles. This could be the onset of impulsive loop flares.For a low electric current, if the loop temperature is sufficiently high to give the negative absorption for the plasma waves in a large part of the coronal loop, steady plasma turbulence may originate. This could be a source for the type I radio noise storm. 相似文献