Cosmic-ray propagation in compressible turbulent media

The influence of compressibility of media on both the statistical acceleration and the turbulent diffusion of cosmic-ray particles is investigated. The averaging over an ensemble of random velocity fields of the medium was performed in the kinetic equation. The kinetic coefficients, which are responsible for the particle acceleration, were obtained in the cases of weak and strong scattering due inhomogeneous magnetic fields.     

Propagation of sonic waves in an optically thick medium in the presence of magnetic field

This paper studies sonic waves in an optically thick medium under the influence of a magnetic field. The conductivity of the medium has been taken to be infinite. The effects of radiation, radiation energy density, radiative heat transfer and magnetic field have been taken into account. It has been obtained that the magnetic field has significant effect on sonic velocity. The fundamental differential equations governing the growth and decay of sonic waves are determined and solved.     

Cosmic-ray fluctuations in interplanetary space

Cosmic-ray (CR) fluctuations in both the drift and diffusion approximations are investigated and the results compared with experimental data. Kinetic equation is used to obtain equations for the second moment of the CR distribution function (the correlation function of the distribution function fluctuations) in both approximations. An application of these approximations to the correlation function equation gives the relations between the CR power spectra and random magnetic fields in interplanetary space. Different magneto-turbulence models are taken in consideration and the relations between the spectral indices are obtained in various frequency intervals.The theoretical results are compared with experimental data obtained by the network of neutron monitors. The CR power spectra observed at the ground level during the years 1978–1981 has been calculated. The investigated frequency range of 3×10^–8 to 10^–4 Hz consists of two parts, with a transient region of 10^–6 to 10^–5 Hz. Together with the background CR fluctuations the contribution of both the periodic and aperiodic phenomena is observed.     

On the effect of oblique disturbances on Kelvin-Helmholtz instability at magnetospheric boundary layers and in solar wind

This paper is concerned with the Kelvin-Helmholtz instability in the indissipative plasma with an external magnetic field. A detailed analysis is made of the results known from the approximation of a tangential discontinuity. The finiteness of the interface thickness effect is considered numerically at the arbitrary distribution of the density, velocity and magnetic field vectors inside this shear layer. The influence of plasma compressibility with an arbitrarily varying magnetic field is investigated. The main role of oblique disturbances with respect to the flow rate direction is shown under conditions of a large plasma compressibility. As such perturbations move away from the interface, their amplitude is damped much more slowly than in the case of weak compressibility. However, their wavelength remains, approximately, the same as that of longitudinal waves in the case of incompressibility. The linear approximation suggests the importance of oblique waves in the energetics of the interaction between the shear layer and the outward medium. A comparison is made of the instability period on discontinuities in the solar wind, and at magnetospheric and plasmaspheric boundaries, with the range of geomagnetic pulsations.     

Variations of cosmic-ray energy in interplanetary space

A consistent theory of energy exchange between high-energy charged cosmic-ray particles and the random inhomogeneities of a magnetic field frozen in the moving solar wind plasma is developed. It is shown that the mode of the particle energy variations at a given law of plasma velocity variation in space is determined by the specific form of the particle distribution function. The equation for the density of cosmic-ray energy is obtained. Consideration is given to the generation of a charged particle energy spectrum in the course of multiple scatterings by the random inhomogeneities of the magnetic field.     

The spherical infall model in a cosmological background density field

We discuss the influence of the cosmological background density field on the spherical infall model. The spherical infall model has been used in the PressSchechter formalism to evaluate the number abundance of clusters of galaxies, as well as to determine the density parameter of the Universe from the infalling flow. Therefore, the understanding of collapse dynamics plays a key role for extracting cosmological information. Here, we consider a modified version of the spherical infall model. We derive the mean field equations from the Newtonian fluid equations, in which the influence of cosmological background inhomogeneity is incorporated into the averaged quantities as the backreaction . By calculating the averaged quantities explicitly, we obtain simple expressions and find that, in the case of a scale-free power spectrum, density fluctuations with a negative spectral index make the infalling velocities slow. This suggests that we underestimate the density parameter when using the simple spherical infall model. In cases with the index n >0, the effect of background inhomogeneity could be negligible and the spherical infall model becomes a good approximation for infalling flows. We also present a realistic example with a cold dark matter power spectrum. In this case, the mean infall tends to be slow owing to the anisotropic random velocity.     

Shock jump relations for a dusty gas atmosphere

This paper presents simplified forms of jump relations for one dimensional shock waves propagating in a dusty gas. The dusty gas is assumed to be a mixture of a perfect gas and spherically small solid particles, in which solid particles are continuously distributed. The simplified jump relations for the pressure, the temperature, the density, the velocity of the mixture and the speed of sound have been derived in terms of the upstream Mach number. The expressions for the adiabatic compressibility of the mixture and the change-in-entropy across the shock front have also been derived in terms of the upstream Mach number. Further, the handy forms of shock jump relations have been obtained in terms of the initial volume fraction of small solid particles and the ratio of specific heats of the mixture, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. The simplified shock jump relations reduce to the Rankine-Hugoniot conditions for shock waves in an ideal gas when the mass fraction (concentration) of solid particles in the mixture becomes zero. Finally, the effects due to the mass fraction of solid particles in the mixture, and the ratio of the density of solid particles to the initial density of the gas are studied on the pressure, the temperature, the density, the velocity of the mixture, the speed of sound, the adiabatic compressibility of the mixture and the change-in-entropy across the shock front. The results provided a clear picture of whether and how the presence of dust particles affects the flow field behind the shock front. The aim of this paper is to contribute to the understanding of how the shock waves behave in the gas-solid particle two-phase flows.     

Spontaneous and induced Čerenkov emission in a turbulent medium

It is shown that the presence of spatially random fluctuations in refractive index, about a mean exceeding unity, influences the power output of erenkov waves emitted by a charged particle in several ways.(1) The frequency spectrum of the spontaneous emission is altered by the fluctuations. (2) There is an induced erenkov emission, due to the interaction of the spontaneous field with the random refractive index variations. This induced field can, in certain frequency bands, be as large as the spontaneous field. And it also contains a backscattered component which propagates in theopposite direction to the particle. (3) The conditions for emission of the erenkov waves, be they spontaneous or induced, depend critically on both the mean refractive index, the particle velocity, the intensity and correlation length of the fluctuations. And the dependence is sensitive to the precise functional form of the two-point correlation function.Instruments detect the optical erenkov emission produced by cosmic ray particles penetrating the Earth's atmosphere (below about 5 km). Also gas erenkov counters are triggered by the passage of highly energetic particles through the gas. Since both the Earth's lower atmosphere and the gas counters contain turbulent fluctuations, the present calculation is of some interest in connection with particle energy loss mechanisms in turbulent media and the basic structure of such media.     

Five dimensional Bianchi type-V cosmological models described by a binary mixture of perfect fluid and dark energy with Λ-term

Some recent experimental observations have been shown that inclusion of electron collisions damping in inertial Alfvén wave (IAW) dynamics may be important for laboratory as well as space plasmas. This paper presents the numerical simulation of model equation governing the nonlinear dynamics of IAW in low-beta plasmas. When the nonlinearity arises due to the ponderomotive force and Joule heating driven density perturbations, the model equation turns out to be a modified nonlinear Schr?dinger equation (MNLS). The electron collisions are introduced only in the electron momentum equation. The damped localized structures of IAW with sidebands are obtained. Also, the effect of collisional damping on power spectra of magnetic fluctuations with different scaling laws has been studied. These turbulent structures may be responsible for particle acceleration in laboratory and space plasmas.     

Nonlinear perturbation theory for cosmic ray propagation in random magnetic fields

A nonlinear perturbation theory is applied to the problem of pitch angle diffusion of energetic particles in random magnetic fields. To keep the analysis simple, the discussion is restricted to fluctuation fields, consisting of Alfvén waves. It is shown that the failure of quasilinear theory at small particle velocities parallel to the average field can be overcome by a statistically exact treatment of the particle orbits in the first order fields. In fact, for spherical power spectra which, in addition, do not fall off too steeply with increasing frequency, the conventional perturbation theory also leads to formally convergent expressions for the scattering mean free path. These results are shown to be quite satisfactory, even in a quantitative sense. For more general physically realistic power spectra, however, a divergence-free diffusion theory is indispensible. A simple representation for the resulting pitch-angle diffusion coefficient is suggested.     

Propagation of magnetogasdynamic spherical shock waves in an exponential medium

In this paper propagation of magnetogasdynamic spherical shock waves is considered in an exponentially increasing medium. The shock wave moves with variable velocity and the total energy of the wave is variable. It is shown that the magnetic field changes the flow velocity, density and pressure.     

The Influences of Shock Thickness and Alfven Waves on the Particle Acceleration by Diffusive Shocks

The influences of the shock thickness and Alfven waves on the particle acceleration by diffusive shock waves are numerically studied through solving one-dimensional diffusive equation including the second-order Fermi effect. It is shown that the spectral index of the energetic particles strongly depends on the shock thickness. For example, the spectral index increases from 2.1 to 3.7 in the low energy range of 3—10 MeV and from 2.5 to 5.0 in the high energy range of 20—60 MeV as the thickness increases. The spectral index decreases from 4.3 to 3.1 as the particle injection energy increases. The spectral index decreases from 4.0 to 1.8 at the quasi-steady stage with the enhancement of the compression ratio from 2 to 4. The results indicate that under the influence of Alfven waves, the energetic particle spectrum at lower energy becomes flat and the spectral index decreases from 2.5 to 0.6 in the low energy range of 3—10 MeV and from 11.6 to 5.0 in the high energy range of 20—60 MeV. At the same time, the turning point energy reaches 19.6 MeV. The spectral index decreases from 5.8 to 2.9 as the energy density of Alfven waves increases. All these results are basically consistent with the theoretical models, as well as the observations of typical energetic particle events.     

The effect of turbulent fluctuations in the interstellar gas and magnetic field on Faraday rotation

The effect of fluctuations in both the interstellar electron number density and galactic magnetic field on the propagation of high frequency radio waves is discussed in terms of the frequency dependent Faraday rotation. It is shown that when the fluctuations are representative of large scale disturbances (1–10² pc) in the interstellar medium, then the observed Faraday rotation is not a measure of the line of sight integral of the product of the magnetic field with the electron number density.Since evidence has been presented elsewhere for believing that such large scale disturbances do exist in our galaxy, some care must be exercised in the physical interpretation of Faraday rotation measurements.Alfred P. Sloan Foundation Fellow.     

Radiation of magnetoacoustic waves in the interstellar medium by physical variable stars

Radially pulsating stars are shown to radiate fast and slow magnetoacoustic waves into the interstellar gas. No Alfvén waves are excited, because the oscillations are radially symmetric. Calculations were performed for the following two limiting cases: hot, weakly magnetized interstellar plasma and cold plasma with a strong magnetic field. In these limiting cases, pulsating stars excite mostly fast magnetoacoustic waves, while the excitation of slow magnetoacoustic waves is weak. Magnetogasdynamic fields of density, velocity, and magnetic-field perturbations in the interstellar medium were found. Relations were derived to calculate the radiated power and its estimates are given for various conditions in the medium. It is shown that radially stratified wave structures with wavelengths from 1 AU to several tenths of a parsec must exist in the vicinity of pulsating stars.     

Transient Evolution of Nonlinear Localized Coherent Structures of Kinetic Alfvén Waves

We present numerical simulations of kinetic Alfvén waves (KAWs) and inertial Alfvén waves (IAWs) applicable to the solar wind, the solar corona, and the auroral regions, respectively, leading to the formation of coherent magnetic structures when the nonlinearity arises from ponderomotive effects and Joule heating. The nonlinear dynamical equation satisfies the modified nonlinear Schrödinger equation. The effect of nonlinear coupling between the main KAW/IAW and the perturbation, producing filamentary structures of the magnetic field, has been studied. Scalings in the spectral index of the power spectrum at different times have been calculated. These filamentary structures can act as a source for particle acceleration by wave?–?particle interaction because the KAWs/IAWs are mixed modes and Landau damping is possible.     

Rayleigh-Taylor instability of a two-fluid layer under a general rotation field and a horizontal magnetic field

In this paper the Rayleigh-Taylor instability (RTI) of a two-fluid layer system under the simultaneous action of a general rotation field and a horizontal magnetic field is presented. An approximate and an exact solution of the eigenvalue equation are calculated. These solutions are important not only to understand more deeply the physical problem but also to determine the correct numerical solutions. Numerical calculations are done for an unstable density stratification in the cases of horizontal magnetic field parallel and perpendicular to the horizontal component of the angular velocity. For an adverse density stratification, it is shown that in comparison to previous works, the horizontal magnetic field creates new angular areas (of the angle of propagation of the perturbation) at which the perturbation is stable and propagates as traveling waves. It is also shown that the vertical component of the angular velocity has a destabilizing effect because it works to eliminate the stable angular areas.     

Solar Wind Acceleration by the Dissipation of Alfvén Waves

Axford and McKenzie [1992] suggested that the energy released in impulsive reconnection events generates high frequency Alfvén waves. The kinetic equation for spectral energy density of waves is derived in the random phase approximation. Solving this equation we find the wave spectrum with the power law "−1" in the low frequency range which is matched to the spectrum above the spectral brake with the power low "−1.6." The heating rate of solar wind protons due to the dissipation of Alfvén waves is obtained. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fluctuations of density and waves in nonlinear nuclear reactions in stellar cores

The space correlation of fluctuation of density in the nuclear reaction system inside the stars is investigated by using the theory of a generating function. Referring to the dynamical rate equation, we have introduced the gravitational force and temperature gradient terms into master equation of the probability distribution function of density, and a generalized master equation has been obtained. We take P-PI reactions of hydrogen-burning in the solar core as an example to solve this master equation for infinite medium. A series of waves have been obtained. The first branch is the average density wave which has already been obtained from the dynamical rate equation. Other branches describe the propagation of the fluctuation moments of the local density. They represent the propagation processes of the local distortion of the probability distribution function. Stability of the system may be related to an increase and decay of the waves. We have analysed the phase velocity of these waves.     

Smoothing of force functions and the fluctuation spectra of an open star cluster model

We perform the correlation and spectral analysis of phase-space density and potential fluctuations in a model of an open star cluster for various values of the smoothing parameter ? of the force functions in the equations of motion of cluster stars, and compute the mutual correlation functions for the fluctuations of potential U and phase-space density f of the cluster model at different clustercentric distances. We use the Fourier transform of the mutual correlation functions to compute the power spectra and dispersion curves of the potential and phase-space density fluctuations. The spectrum of potential fluctuations proves to be less complex than that of phase-space density fluctuations. The most powerful potential fluctuations are associated with phase-space density fluctuations, and their spectrum lies in the domain of low frequencies ν < 3/τ _v.r.; at intermediate and high frequencies (ν > 3/τ _v.r.), the contribution of potential fluctuations to those of the phase-space density is small or equal to zero (here τ _v.r. is the violent relaxation time scale of the cluster). We find a number of unstable potential fluctuations in the core of the cluster model (up to 30 pairs of fluctuations with different complex conjugate frequencies). We also find and analyze the dependences of the spectra and dispersion curves of phase-space density and potential fluctuations on ?. We find a “repeatability” (significant correlation) of the spectra at some values of parameter ?. The form of the dispersion curve is unstable against small variations of ?. We discuss the astrophysical applications of our results: the break-up in the cluster core of the phase-space density wave running from the cluster periphery toward its center into several waves with frequencies commensurable to that of the external (tidal) influence; emission and reflection of phase-space and potential waves near the cluster core boundary; possible wavelength and phase discretization of the phase-space and potential waves in the cluster model.     

Rayleigh waves in an orthotropic thermoelastic medium under gravity field and initial stress

The aim of the present paper is to investigate the influence both of gravity field and initial stress on the propagation of Rayleigh waves in an orthotropic thermoelastic medium subject to certain boundary conditions. We suppose that the body is under initial stress alonqx ₁-direction and incremental thermal stresses. The wave velocity equation has been obtained. Many special cases and comparison with the previous results have been studied.