Cosmic Ray Distribution Function Research Articles

Мониторинг параметров анизотропии космических лучей в реальном времени и краткосрочный прогноз геомагнитных возмущений

SHICRA SB RAS, using data from the NMDB database, has implemented continuous monitoring of the dynamics of cosmic ray (CR) distribution parameters and the automatic forecasting of geomagnetic disturbance. Monitoring is based on the global survey method, which considers the world-wide network of neutron monitors as a single device oriented in different directions at each measured time. This method provides real-time parameters of nine components of the first two angular moments of the CR distribution function for each hour of observation. This paper discusses methodological aspects related to the use of the global survey method and some results of the forecasting of geomagnetic disturbances for 2017–2018.

REAL-TIME MONITORING OF COSMIC RAY ANISOTROPY PARAMETERS AND SHORT-TERM FORECASTING OF GEOMAGNETIC DISTURBANCES

SB RAS, using data from the NMDB database, has implemented continuous monitoring of the dynamics of cosmic ray (CR) distribution parameters and the automatic forecasting of geomagnetic disturbance. Monitoring is based on the global survey method, which considers the world-wide network of neutron monitors as a single device oriented in different directions at each measured time. This method provides real-time parameters of nine components of the first two angular moments of the CR distribution function for each hour of observation. This paper discusses methodological aspects related to the use of the global survey method and some results of the forecasting of geomagnetic disturbances for 2017–2018.

The Distribution Function of Cosmic Rays at the Initial Stage of a Solar Proton Event

The propagation of solar cosmic rays in the interplanetary medium is considered on the basis of the kinetic equation describing the small-angle multiple scattering of charged particles. Energetic particles are assumed to be injected into the interplanetary medium by an instantaneous point-like source. The spatial-temporal distribution of the density and anisotropy of high-velocity particles during the anisotropic phase of a burst of solar cosmic rays is studied. An analytical expression for the distribution function of cosmic rays in the small-angle approximation is derived; the evolution of the angular distribution of energetic particles is investigated. It has been shown that, under weak scattering of charged energetic particles on fluctuations of the interplanetary magnetic field, the intensity of solar cosmic rays impulsively increases at the initial stage of their enhancement. The anisotropy in the angular distribution of solar cosmic rays monotonously decreases with time and exhibits the highest value at the moment of the first particles' arrival to a given point of space.

The cosmic ray distribution function on the initial stage of the solar proton event

The cosmic ray distribution function on the initial stage of the solar proton event

Method of Global Survey by Data of Muon Telescopes

A new variant of a global survey method that allows obtaining information on the first two angular moments of cosmic ray distribution function in the interplanetary space using the data of continuous hourly registration of muon telescopes of the GMDN network and the Yakutsk cosmic ray spectrograph is presented. A calculation of receiving characteristics for the telescopes and accounting of the temperature effect that are necessary for a successful realization of the method are carried out. The results of application of the method in definition of cosmic ray anisotropy parameters are analyzed for the period 2012–2018.

The Distribution Function of Solar Cosmic Rays under Prolonged Particle Injection

Abstract—The propagation of solar cosmic rays (SCR) in the interplanetary medium is considered on the basis of the Fokker–Planck kinetic equation. It is known that the SCR distribution function averaged over a solar proton event contains valuable data on the scattering process for energetic charged particles by interplanetary magnetic fields. A steady-state solution for the kinetic equation in the small-angle approximation is obtained, and the dependence of the angular distribution function of cosmic rays on the distance to the particle source is examined. This solution is applicable if the distance to the particle source is short compared to the mean free path of cosmic rays and if particles are moving primarily in the radial direction. The angular distribution of particles at large (compared to the mean free path of cosmic rays) distances to the particle source is also analyzed. An analytical expression for the distribution function of cosmic rays in the form of a sum of an isotropic component and a small anisotropic one is derived. It is demonstrated that the angular distribution of cosmic rays depends to a considerable extent on the anisotropy of their scattering. The scattering characteristics of energetic charged particles by fluctuations of interplanetary magnetic fields are estimated based on observational data for several SCR flares.

Kinetic Propagation of Charged Particles in a Magnetic Field at Various Directions of Their Injection

Abstract—The propagation of high-energy charged particles in the magnetic field, which is a superposition of the mean homogeneous magnetic field and magnetic inhomogenieties of various scales, is considered on the basis of the Fokker-Planck kinetic equation. The analytical expression for the cosmic ray distribution function corresponding to the instantaneous particle injection in the direction perpendicular to the regular magnetic field is obtained. The solution of the kinetic equation in the small angle approximation is applied for the case of particle emission along the mean magnetic field. It is shown that the spatial-temporal cosmic ray distribution depends substantially on the direction of particle injection. The evolution of the angular distribution of solar cosmic rays is analyzed on the basis of the derived solutions of the kinetic equation.

On the Anisotropy of Galactic Cosmic Rays

Abstract In the interstellar medium at rest, containing low-frequency magnetohydrodynamic linearly polarized slab Alfvén waves, the anisotropy of relativistic galactic cosmic rays consists of two parts: the streaming anisotropy g s (z, p,μ), caused by the spatial gradient of the isotropic part of the cosmic ray distribution function, and the interstellar Compton–Getting anisotropy , caused by the momentum gradient of the isotropic part of the cosmic ray distribution function. Both anisotropies depend differently on the cosmic ray pitch-angle cosine μ, cosmic ray momentum p, and cross-helicity state H c of the Alfvenic slab turbulence. First, the streaming anisotropy is independent from H c and varies as with η = 2 − s, where s denotes the power-law spectral index of interstellar turbulence. Second, the interstellar Compton–Getting anisotropy is independent of momentum and linearly proportional to . These different pitch-angle dependencies can be tested by the Liouville mapping technique to infer the pristine interstellar cosmic ray anisotropy from measurements inside the solar system. For cosmic rays with energy of 4 TeV the derived pristine interstellar cosmic ray anisotropy suggest the linear ( ) pitch-angle dependence. This is well explained by the interstellar Compton–Getting anisotropy, provided the Alfvén speed in the local interstellar medium is about 62 km s−1.

Behavior of zonal components of cosmic ray distribution and Dst-index of geomagnetic field during periods of geoeffective disturbances of solar wind

On a basis of processing of data of measurements of the world-wide neutron monitor network database NMDB by a global survey method in real-time, the behavior of the first two angular moments of cosmic ray distribution function are investigated during the periods of geomagnetic storms that were observed in 2017. It is shown that abrupt increases of positive amplitudes of zonal components, which can be considered as predictors of geomagnetic field disturbances with a probability around 75%, precede geomagnetic storms with Dst <-50 nT. The predictor’s lead time is from a few hours to 1.5 days. A monitoring of geomagnetic disturbances is carried out in real-time mode and results of the forecasting is presented in the Internet through the link http://www.ysn.ru/∼starodub/SpaceWeather/global_survey_real_time.html.

Cosmic ray distribution function under anisotropic particle scattering on magnetic field fluctuations

Cosmic ray distribution function under anisotropic particle scattering on magnetic field fluctuations

Image of Forbush Decrease in a Magnetic Cloud by Three Moments of Cosmic Ray Distribution Function

AbstractThe time dynamics of the cosmic ray distribution function in a magnetic cloud is calculated. The magnetic cloud has the form of a torus segment with the force‐free magnetic field structure at the initial moment. The subsequent propagation of the magnetic cloud in interplanetary space is determined by inertial description. The magnetic field is determined by the frozen‐in condition. When calculating the particle distribution function, the electromagnetic field of the magnetic cloud is taken into account, with the scattering of particles not being taken into account. Relations between the particle distribution function and its three moments (particle density and unidirectional and bidirectional anisotropies) are derived. It is established that cosmic ray losses at the regions connecting the magnetic cloud with the Sun determine the amplitude of the second step of Forbush decrease. The time dependence of the Forbush decrease characteristics on magnetic cloud type is determined. The calculation results of the particle density and unidirectional anisotropy generally correspond to measurements. The referred results show a prominent role of the magnetic field structure in the time dynamics of the Forbush decrease.

Description of Solar Cosmic Ray Propagation in the Interplanetary Medium on the Basis of the Kinetic Equation

The propagation of solar cosmic rays in interplanetary space is considered based on the kinetic equation. The expression for cosmic ray density under instantaneous particle injection by a point-like source is obtained. The set of a differential equation system for harmonics of cosmic ray distribution function is obtained starting from the kinetic equation. The cosmic ray transport equation, taking into account the presence of the second harmonic of particle angular distribution, is derived and the solution of this equation is obtained.

Cosmic ray driven Galactic winds

The escape of cosmic rays from the Galaxy leads to a gradient in the cosmic ray pressure that acts as a force on the background plasma, in the direction opposite to the gravitational pull. If this force is large enough to win against gravity, a wind can be launched that removes gas from the Galaxy, thereby regulating several physical processes, including star formation. The dynamics of these cosmic ray driven winds is intrinsically non-linear in that the spectrum of cosmic rays determines the characteristics of the wind (velocity, pressure, magnetic field) and in turn the wind dynamics affects the cosmic ray spectrum. Moreover, the gradient of the cosmic ray distribution function causes excitation of Alfven waves, that in turn determine the scattering properties of cosmic rays, namely their diffusive transport. These effects all feed into each other so that what we see at the Earth is the result of these non-linear effects. Here we investigate the launch and evolution of such winds, and we determine the implications for the spectrum of cosmic rays by solving together the hydrodynamical equations for the wind and the transport equation for cosmic rays under the action of self-generated diffusion and advection with the wind and the self-excited Alfven waves.

MODIFICATION OF THE PARALLEL SCATTERING MEAN FREE PATH OF COSMIC RAYS IN THE PRESENCE OF ADIABATIC FOCUSING

The cosmic ray mean free path in a large-scale nonuniform guide magnetic field with superposed magnetostatic turbulence is calculated to clarify some conflicting results in the literature. A new, exact integro-differential equation for the cosmic-ray anisotropy is derived from the Fokker-Planck transport equation. A perturbation analysis of this integro-differential equation leads to an analytical expression for the cosmic ray anisotropy and the focused transport equation for the isotropic part of the cosmic ray distribution function. The derived parallel spatial diffusion coefficient and the associated cosmic ray mean free path include the effect of adiabatic focusing and reduce to the standard forms in the limit of a uniform guide magnetic field. For the illustrative case of isotropic pitch angle scattering, the derived mean free path agrees with the earlier expressions of Beeck & Wibberenz, Bieber & Burger, Kota, and Litvinenko, but disagrees with the result of Shalchi. The disagreement with the expression of Shalchi is particularly strong in the limit of strong adiabatic focusing.

HELIOSPHERIC INFLUENCE ON THE ANISOTROPY OF TeV COSMIC RAYS

This paper provides a theory of using Liouville's theorem to map the anisotropy of TeV cosmic rays seen at Earth using the particle distribution function in the local interstellar medium (LISM). The ultimate source of cosmic ray anisotropy is the energy, pitch angle, and spatial dependence of the cosmic ray distribution function in the LISM. Because young nearby cosmic ray sources can make a special contribution to the cosmic ray anisotropy, the anisotropy depends on the source age, distance and magnetic connection, and particle diffusion of these cosmic rays, all of which make the anisotropy sensitive to the particle energy. When mapped through the magnetic and electric field of a magnetohydrodynamic model heliosphere, the large-scale dipolar and bidirectional interstellar anisotropy patterns become distorted if they are seen from Earth, resulting in many small structures in the observations. Best fits to cosmic ray anisotropy measurements have allowed us to estimate the particle density gradient and pitch angle anisotropies in the LISM. It is found that the heliotail, hydrogen deflection plane, and the plane perpendicular to the LISM magnetic field play a special role in distorting cosmic ray anisotropy. These features can lead to an accurate determination of the LISM magnetic field direction and polarity. The effects of solar cycle variation, the Sun's coronal magnetic field, and turbulence in the LISM and heliospheric magnetic fields are minor but clearly visible at a level roughly equal to a fraction of the overall anisotropy amplitude. The heliospheric influence becomes stronger at lower energies. Below 1 TeV, the anisotropy is dominated by small-scale patterns produced by disturbances in the heliosphere.

Steady State Acceleration Model of Cosmic Ray in the Atmosphere

Hydrodynamic equations were simplified to a layman understanding together with the diffusion-convection transport equation for the cosmic-ray distribution function f(t,r,p), which depends on time t , radial distance from the point of supernova explosion r and the particle momentum p. From the results, gas density p is inversely proportional to the gas velocity u ; flux tubes have a tendency to rise at an appreciable speed; pressure of the atmospheric gas Pg depends on the cosmic-ray pressure Pc and the internal energy of the electron U is directly proportional to the gas density p . Based on what Vladimir, et al. [1] said: “More work is needed to understand how robust our results are”, this has helped in making their bulky equations clearer and showing how robust their work are. In the cause of breaking down or simplifying the high energy equations, it was found that cosmic rays move with Alfven speed.

Formation of higher harmonics of the galactic cosmic-ray distribution function

We derive equations for the multipole moments of the distribution function of Galactic cosmic rays with energies 1–20 TeV that experience random scattering by turbulence with a power-law spectrum. We take into account the irregularity of the local interstellar medium (LISM) in the neighborhood of the solar system due to the presence of interstellar clouds, the interstellar wind flow around the heliomagnetosphere, and preceding supernova explosions in the local superbubble. The amplitudes of the second and third harmonics of the cosmic-ray distribution function are expressed in terms of the amplitude of the first harmonic without assuming them to be small compared to the first harmonic. Reconciling their values in magnitude and phase with the observed values requires a significant LISM irregularity, which is consistent with other observational data on the LISM structure. Our model is consistent with the assumption that supernova remnants in the Galactic disk located at distances from the Solar system much larger than the particle transport mean free path are the sources of the particles under consideration.

SCR Distribution Function in the Radial IMF Approximation

The transport of cosmic rays in the interplanetary medium is considered in terms of the kinetic equation describing the energetic particle scattering by magnetic irregularities and their focusing by the regular interplanetary magnetic field. The analytical expression for solar cosmic ray distribution function in the approximation of radial regular magnetic field is obtained and the evolution of energetic particle angular distribution is analyzed. The obtained results can be used for the analysis of ground-level enhancements of cosmic ray intensity.

Cosmic‐Ray Pitch‐Angle Scattering through 90o

We study the problem of cosmic-ray diffusion in the Galactic disk with particular attention paid to the problem of particle scattering through the θ =(v∥/v) = 90° pitch angle in momentum space by wave-particle mirror interaction (here v∥ is the cosmic-ray velocity parallel to the average Galactic magnetic field). We consider the case in which cosmic rays are the only source of magnetic turbulence, which originates as the relativistic particles try to stream through the interstellar plasma faster than the local Alfven speed. The wave growth rate is proportional to the cosmic-ray anisotropy, and the amplitude of hydromagnetic waves generated by this streaming instability is limited by the presence of various damping mechanisms. We study the propagation of cosmic rays in the different phases of the interstellar medium, in particular the coronal regions (where the main form of wave dissipation is nonlinear Landau damping) and the warm regions (where charge exchange between the ions and the neutral atoms gives rise to the dominant form of wave dissipation). We also account for ion-cyclotron damping of small wavelength waves. The effect of a spectrum of waves is to limit the anisotropy of the cosmic-ray distribution function and hence their drift velocity. We show that quasi-linear resonant scattering cannot account for particle diffusion everywhere in momentum space and that particles with θ ~ 90° must change their pitch angle by mirror interaction with long-wavelength waves generated by the θ ~ 0° particles. We match the quasi-linear scattering with the adiabatic mirroring in a small boundary layer in momentum space close to the θ ~ 90° point, and then we calculate the diffusion coefficient together with the cosmic-ray drift velocity. We show that scattering through the 90° point is very efficient, and we calculate the correction to the particle diffusion coefficient due to the presence of mirroring.

Diffusive shock acceleration: a method based on integral equation

The structure of a strong shock, significantly modified by cosmic rays (CRs) is studied on the level of a kinetic description, assuming Bohm-type diffusion. The original problem that is commonly formulated in terms of the diffusion-convection equation for the distribution function of CRs, coupled with the thermal plasma through the momentum flux continuity equation, is reduced to a nonlinear integral equation in one variable. The solution of this equation provides selfconsistently both the particle spectrum and the flow profile. We particularly focus on the solution (out of the three possible) with the highest conversion efficiency of the flow energy to the CR energy. It was found that (1) for this or, equivalently, for multiple solutions to exist, the suitably normalized injection rate ν must exceed the value of ∼ ⪡ 1 where p 1 and p 0 are the cut-off and injection momenta, respectively and, the Mach number M must also be rather large. (2) The total shock compression ratio r increases with M and saturates at a level that scales as r ∝ ν p 1 / p 0 . (3) Completely smooth shock transitions do not appear in the steady state kinetic description. The flow deceleration in the CR precursor is equal to the velocity jump at the gaseous subshock multiplied by a factor ∼ ν p 1 / p 0 .