Diffusion coefficient and radial gradient of galactic cosmic rays

We present the temporal changes of the diffusion coefficient K of galactic cosmic rays (GCRs) at the Earth orbit calculated based on the experimental data using two different methods. The first approach is based on the Parker convection-diffusion approximation of GCR modulation [1]: i.e. K~Vr=dI where dI is the variation of the GCR intensity measured by neutron monitors (NM),V is the solar wind velocity and r is the radial distance. The second approach is based on the interplanetary magnetic field (IMF) data. It was suggested that parallel mean free path can be expressed in terms of B as in [2]-[4]. Using data of the product of the parallel mean free path and radial gradient of GCR calculated based on the GCR anisotropy data (Ahluwalia et al., this conference ICRC 2013, poster ID: 487 [5]), we estimate the temporal changes of the radial gradient of GCR at the Earth orbit. We show that the radial gradient exhibits a strong solar cycle dependence (11-year variation) and a weak solar magnetic cycle dependence (22-year variation), being in agreement with the previous other calculations and with PIONEER/VOYAGER observations

Three dimensional solar anisotropy of galactic cosmic rays near the recent solar minimum 23/24

Three dimensional (3D) galactic cosmic ray (GCR) anisotropy has been studied for 2006- 2012. The GCR anisotropy, both in the ecliptic plane and in polar direction, were obtained based on the neutron monitors (NMs) and Nagoya muon telescopes (MT) data. We analyze two dimensional (2D) GCR anisotropy in the ecliptic plane and north-south anisotropy normal to the ecliptic plane. We reveal quasi-periodicities - the annual and 27-days waves in the GCR anisotropy in 2006-2012. We investigate the relationship of the 27-day variation of the GCR anisotropy in the ecliptic plane and in the polar direction with the parameters of solar activity and solar wind.Comment: 8 pages, 10 figures, paper presented on 24th European Cosmic Ray Symposium 201

A stochastic method of solution of the Parker transport equation

We present the stochastic model of the galactic cosmic ray (GCR) particles transport in the heliosphere. Based on the solution of the Parker transport equation we developed models of the short-time variation of the GCR intensity, i.e. the Forbush decrease (Fd) and the 27-day variation of the GCR intensity. Parker transport equation being the Fokker-Planck type equation delineates non-stationary transport of charged particles in the turbulent medium. The presented approach of the numerical solution is grounded on solving of the set of equivalent stochastic differential equations (SDEs). We demonstrate the method of deriving from Parker transport equation the corresponding SDEs in the heliocentric spherical coordinate system for the backward approach. Features indicative the preeminence of the backward approach over the forward is stressed. We compare the outcomes of the stochastic model of the Fd and 27-day variation of the GCR intensity with our former models established by the finite difference method. Both models are in an agreement with the experimental data.Comment: 8 pages, 7 figures, presented on 24th European Cosmic Ray Symposium 201

Numerical methods for solution of the stochastic differential equations equivalent to the non-stationary Parker's transport equation

We derive the numerical schemes for the strong order integration of the set of the stochastic differential equations (SDEs) corresponding to the non-stationary Parker transport equation (PTE). PTE is 5-dimensional (3 spatial coordinates, particles energy and time) Fokker- Planck type equation describing the non-stationary the galactic cosmic ray (GCR) particles transport in the heliosphere. We present the formulas for the numerical solution of the obtained set of SDEs driven by a Wiener process in the case of the full three-dimensional diffusion tensor. We introduce the solution applying the strong order Euler-Maruyama, Milstein and stochastic Runge-Kutta methods. We discuss the advantages and disadvantages of the presented numerical methods in the context of increasing the accuracy of the solution of the PTE.Comment: 4 pages, 2 figures, presented on 4th International Conference on Mathematical Modeling in Physical Sciences, 201

Stochastic approach to the numerical solution of the non-stationary Parker's transport equation

We present the newly developed stochastic model of the galactic cosmic ray (GCR) particles transport in the heliosphere. Mathematically Parker transport equation (PTE) describing non-stationary transport of charged particles in the turbulent medium is the Fokker-Planck type. It is the second order parabolic time-dependent 4-dimensional (3 spatial coordinates and particles energy/rigidity) partial differential equation. It is worth to mention that, if we assume the stationary case it remains as the 3-D parabolic type problem with respect to the particles rigidity R. If we fix the energy it still remains as the 3-D parabolic type problem with respect to time. The proposed method of numerical solution is based on the solution of the system of stochastic differential equations (SDEs) being equivalent to the Parker's transport equation. We present the method of deriving from PTE the equivalent SDEs in the heliocentric spherical coordinate system for the backward approach. The obtained stochastic model of the Forbush decrease of the GCR intensity is in an agreement with the experimental data. The advantages and disadvantages of the forward and the backward solution of the PTE are discussed.Comment: 4 pages, 2 figures, presented on International Conference on Mathematical Modeling in Physical Sciences, 201

On the relationship of the 27-day variations of the solar wind velocity and galactic cosmic ray intensity in minimum epoch of solar activity

We study the relationship of the 27-day variation of the galactic cosmic ray intensity with similar changes of the solar wind velocity and the interplanetary magnetic field based on the experimental data for the Bartels rotation period 2379 of 23 November 2007-19 December 2007. We develop a three dimensional (3-D) model of the 27-day variation of galactic cosmic ray intensity based on the heliolongitudinally dependent solar wind velocity. A consistent, divergence-free interplanetary magnetic field is derived by solving Maxwells equations with a heliolongitudinally dependent 27-day variation of the solar wind velocity reproducing in situ observations. We consider two types of 3-D models of the 27-day variation of galactic cosmic ray intensity - (1) with a plane heliospheric neutral sheet, and (2)- with the sector structure of the interplanetary magnetic field. The theoretical calculation shows that the sector structure does not influence significantly on the 27-day variation of galactic cosmic ray intensity as it was shown before based on the experimental data. Also a good agreement is found between the time profiles of the theoretically expected and experimentally obtained first harmonic waves of the 27-day variation of the galactic cosmic ray intensity (correlation coefficient equals 0.98 0.02). The expected 27-day variation of the galactic cosmic ray intensity is inversely correlated with the modulation parameter z (correlation coefficient equals -0.91 0.05) which is proportional to the product of the solar wind velocity V and the strength of the interplanetary magnetic field B (z VB). The high anticorrelation between these quantities indicates that the predictable 27-day variation of the galactic cosmic ray intensity mainly is caused by this basic modulation effect.Comment: article published in Solar Physics (2011

Modeling and experimental study of the 27-day variation of galactic cosmic-ray intensity for a solar-wind velocity depending on heliolongitude

We develop a three dimensional (3-D) model of the 27-day variation of galactic cosmic ray (GCR) intensity with a spatial variation of the solar wind velocity. A consistent, divergence-free interplanetary magnetic field is derived by solving the corresponding Maxwell equations with a variable solar wind speed, which reproduces in situ observed experimental data for the time interval to be analyzed (24 August 2007-28 February 2008). We perform model calculations for the GCR intensity using the variable solar wind and the corresponding magnetic field. Results are compatible with experimental data; the correlation coefficient between our model predictions and observed 27-day GCR variation is 0.80 0.05.Comment: article published in Advances in Space Research (2010

Annual Variations of the Galactic Cosmic Ray Intensity and Seasonal Distribution of the Cloudless Days and Cloudless Nights in Abastumani (41.75oN, 42.82oE; Georgia): (1) experimental study and (2) theoretical modeling

We study a possible relationships between seasonal distributions of the visually observed cloudless days (CD) and cloudless nights (CN) at Abastumani Astrophysical Observatory (41.75N, 42.82E; Georgia) in 1957-1993. The annual variations of monthly numbers of CD and CN have been observed, with maximum in August for CD and in September for CN. During geomagnetic disturbances it is also observed the growth of number of CD in September andMarch (equinoctial months), and for CN, together with September, in June, April and February. We assume that this phenomenon indicates an influence of cosmic factors on cloudiness, as well as the existence of semiannual and possibly shorter-periodicity variations. This cosmic factor can be the manifestation of different rates of the galactic cosmic rays (GCRs) flux variations in CD and CN periods. The influence of GCR flux on ionization of lower atmosphere and variations of density of cloud condensation nuclei also can be connected to the annual and seasonal changes of temperature at Earth surface of this region. To comprehend behaviors of the annual and semi-annual variations of the GCR intensity and their possible relationships with the seasonal distributions of CD and CN we compose and numerically solve two dimensional (2-D) time dependent transport equation including all important processes in the heliosphere. An analysis of experimentally observed and theoretically obtained results have been carried out.Comment: 9 pages, 6 figures, presented on 34th International Cosmic Ray Conference 2015. Proceedings of Science 201

27-day variation of the GCR intensity based on corrected and uncorrected for geomagnetic disturbances data of neutron monitors

We study 27-day variations of the galactic cosmic ray (GCR) intensity for 2005- 2008 period of the solar cycle #23. We use neutron monitors (NMs) data corrected and uncorrected for geomagnetic disturbances. Besides the limited time intervals when the 27-day variations are clearly established, always exist some feeble 27-day variations in the GCR 5 intensity related to the constantly present weak heliolongitudinal asymmetry in the heliosphere. We calculate the amplitudes of the 27-day variation of the GCR intensity based on the NMs data corrected and uncorrected for geomagnetic disturbances. We show that these amplitudes do not differ for NMs with cut-off rigidities smaller than 4-5 GV comparing with NMs of higher cut-off rigidities. Rigidity spectrum of the 27-day variation of the GCR intensity found in the uncorrected data is soft while it is hard in the case of the corrected data. For both cases exists definite tendency of softening the temporal changes of the 27-day variation's rigidity spectrum in period of 2005 to 2008 approaching the minimum of solar activity. We believe that a study of the 27-day variation of the GCR intensity based on the data uncorrected for geomagnetic disturbances should be carried out by NMs with cut-off rigidities smaller than 4-5 GV.Comment: 8 pages, 6 figures, presented on 24th European Cosmic Ray Symposium 201

On the 27-day Variations of Cosmic Ray Intensity in Recent Solar Minimum 23/24

We have studied the 27-day variations and their harmonics of the galactic cosmic ray (GCR) intensity, solar wind velocity, and interplanetary magnetic field (IMF) components in the recent prolonged solar minimum 23 24. The time evolution of the quasi-periodicity in these parameters connected with the Suns rotation reveals that their synodic period is stable and is aprox 26-27 days. This means that the changes in the solar wind speed and IMF are related to the Suns near equatorial regions in considering the differential rotation of the Sun. However, the solar wind parameters observed near the Earths orbit provide only the conditions in the limited local vicinity of the equatorial region in the heliosphere (within in latitude). We also demonstrate that the observed period of the GCR intensity connected with the Suns rotation increased up to aprox 33-36 days in 2009. This means that the process driving the 27-day variations of the GCR intensity takes place not only in the limited local surroundings of the equatorial region but in the global 3-D space of the heliosphere, covering also higher latitude regions. A relatively long period ( aprox 34 days) found for 2009 in the GCR intensity gives possible evidence of the onset of cycle 24 due to active regions at higher latitudes and rotating slowly because of the Suns differential rotation. We also discuss the effect of differential rotation on the theoretical model of the 27-day variations of the GCR intensity.Comment: article published in Solar Physics (2013