Non-linear momentum diffusion of heliospheric cosmic rays

Besides parallel and perpendicular spatial diffusion, momentum diffusion can be seen as the third important process of cosmic ray transport. In this paper, the recently derived weakly non-linear theory is applied for a simple quasi-magnetostatic composite model to determine the momentum diffusion coefficient. It is demonstrated that non-linear effects are essential and cannot be neglected. Therefore, the weakly non-linear transport theory has to be preferred over the traditional quasi-linear approach. Within this improved theory, we find for the rigidity dependence of the momentum diffusion coefficient   A ∼ R ^1.4  for relativistic and   A ∼ R ^0.4  for non-relativistic cosmic rays.     

Influence of solar heliospheric parameters on cosmic rays anisotropy

In the present work the cosmic ray data of three different neutron monitoring stations, Deep River, Inuvik, and Tokyo, located at different geomagnetic cutoff rigidities and altitudes have been harmonically analyzed for the period 1980–95 for a comparative study of diurnal semi-diurnal and tri-diurnal anisotropies in cosmic ray intensity in connection with the change in interplanetary magnetic field Bz component and solar wind velocity on 60 quietest days. It is observed that the amplitudes of all the three harmonics increase during the period 1982–84 at all the stations during the high speed solar wind stream epoch and remain low during the declining phase of the stream. The amplitudes of the three harmonics have no obvious characteristics associated with the time variation of magnitude of the Bz component. The phases of all the three harmonics have no time variation characteristics associated with solar wind velocity and Bz. Published in Astrofizika, Vol. 49, No. 4, pp. 651–664 (August 2006).     

Diurnal variations of cosmic rays during a solar magnetic cycle

We have used data from five neutron monitor stations with primary rigidity (Rm) ranging from 16 GeV to 33 GeV to study the diurnal variations of cosmic rays over the period: 1965–1986 covering one 22-year solar magnetic cycle. The heliosphere interplanetary magnetic field (IMF) and plasma hourly measurements taken near Earth orbit, by a variety of spacecraft, are also used to compare with the results of solar diurnal variation. The local time of maximum of solar diurnal diurnal variations displays a 22-year cycle due to the solar polar magnetic field polarities. In general, the annual mean of solar diurnal amplitudes, magnitude of IMF and plasma parameters are found to show separte solar cycle variations. Moreover, during the declining period of the twenty and twenty-ne solar cycles, large solar diurnal amplitudes are observed which associated with high values of solar wind speed, plasma temperature and interplanetary magnetic field magnitude B3.     

A model for the tail region of the heliospheric interface

The physical processes in the tail of the region where the solar wind interacts with a partially ionized local interstellar medium are investigated in terms of a self-consistent kinetic-gas-dynamical model. Resonant charge exchange between hydrogen atoms and plasma protons is shown to cause the contact discontinuity to disappear far from the Sun. The solar wind plasma cools down and, as a result, the parameters of the plasma and hydrogen atoms approach the corresponding parameters of the unperturbed interstellar medium at large heliocentric distances.     

Remote sensing of the heliospheric solar wind using radio astronomy methods and numerical simulations

The ground-based radio astronomy method of interplanetary scintillations (IPS) and spacecraft observations have shown, in the past 25 years, that while coronal holes give rise to stable, reclining high speed solar wind streams during the minimum of the solar activity cycle, the slow speed wind seen more during the solar maximum activity is better associated with the closed field regions, which also give rise to solar flares and coronal mass ejections (CME’s). The latter events increase significantly, as the cycle maximum takes place. We have recently shown that in the case of energetic flares one may be able to track the associated disturbances almost on a one to one basis from a distance of 0.2 to 1 AU using IPS methods. Time dependent 3D MHD models which are constrained by IPS observations are being developed. These models are able to simulate general features of the solar-generated disturbances. Advances in this direction may lead to prediction of heliospheric propagation of these disturbances throughout the solar system.     

The time-dependent transport of cosmic rays in the heliosphere

The modulation of cosmic rays (CRs) in the heliosphere is a dynamic and therefore a highly time-dependent process. Numerical models with only a time-dependent neutral sheet prove to be successful when moderate to low solar activity occurs but fail to describe large and discrete steps in modulated CRs when solar activity is high. To explain this feature of heliospheric modulation, the concept of global merged interaction regions (GMIRs) is required. The combination of gradient, curvature and neutral sheet drifts with these GMIRs has so far been the most successful approach in explaining the 11-year and 22-year cycles in the long-term modulation of CRs.     

Shock acceleration of solar cosmic rays

We investigated the acceleration of solar cosmic rays (SCRs) by the shock waves produced by coronal mass ejections. We performed detailed numerical calculations of the SCR spectra produced during the shock propagation in the solar corona in terms of a model based on the diffusive transport equation using a realistic set of physical parameters for the corona. The resulting SCR energy spectrum N(ε) ∝ ε^?γ exp [? (ε/ε_max)^α] is shown to include a power-law portion with an index γ?2 that ends with an exponential tail with α ? 2.5 ? β, where β is the spectral index of the background Alfvén turbulence. The maximum SCR energy lies within the range ε_max = 1–300 MeV, depending on the shock velocity. Because of the steep spectrum of the SCRs, their backreaction on the shock structure is negligible. The decrease in the Alfvén Mach number of the shock due to the increase in the Alfvén velocity with heliocentric distance r causes the efficient SCR acceleration to terminate when the shock reaches a distance of r = 2–3R_⊙. Since the diffusive SCR propagation in this case is faster than the shock expansion, SCR particles intensively escape from the shock vicinity. A comparison of the calculated SCR fluxes expected near the Earth’s orbit with available experimental data indicates that the theory satisfactorily explains all of the main observed features.     

Estimation prospects of the source number density of ultra-high-energy cosmic rays

We discuss the possibility of accurately estimating the source number density of ultra-high-energy cosmic rays (UHECRs) using small-scale anisotropy in their arrival distribution. The arrival distribution has information on their source and source distribution. We calculate the propagation of UHE protons in a structured extragalactic magnetic field (EGMF) and simulate their arrival distribution at the Earth using our previously developed method. The source number density that can best reproduce observational results by Akeno Giant Air Shower Array is estimated at about 10⁻⁵ Mpc⁻³ in a simple source model. Despite having large uncertainties of about one order of magnitude, due to small number of observed events in current status, we find that more detection of UHECRs in the Auger era can sufficiently decrease this so that the source number density can be more robustly estimated. Two hundred event observation above 4 × 10¹⁹ eV in a hemisphere can discriminate between 10⁻⁵ and 10⁻⁶ Mpc⁻³. Number of events to discriminate between 10⁻⁴ and 10⁻⁵ Mpc⁻³ is dependent on EGMF strength. We also discuss the same in another source model in this paper.     

Possible origin of clusters in ultra-high-energy cosmic rays

We estimate the detection rate of ultra-high-energy cosmic rays on ground-based arrays by assuming that the cosmic-ray sources are active galactic nuclei. We analyze the cases of detection of clusters, several particles that arrived, within the error limits, from the same area of the sky. The adopted model is shown to explain the detection rate of clusters on the AGASA array.     

The maximum energy and spectra of cosmic rays accelerated in active galactic nuclei

Astronomy Letters - We computed the energy spectra of the incident (on an air shower array) ultrahigh-energy (E&;gt;4×1019eV) cosmic rays (CRs) that were accelerated in nearby Seyfert...     

The physics of particle acceleration at the heliospheric termination shock

Cosmic rays are ubiquitous in space, and the essential similarity of their energy spectra in many different regions places significant general constraints on the mechanisms for their acceleration and confinement. Diffusive shock acceleration is at present the most successful acceleration mechanism proposed, and, together with transport in Kolmogorov turbulence, can account for the universal specta. A unique laboratory for studying the acceleration and transport of charged particles is the outer heliosphere, including the solar wind termination shock and heliosheath.

A widely accepted paradigm for the transport and acceleration of energetic particles in the heliosphere has evolved over the last few decades. This picture has successfully explained many features of the modulation of galactic cosmic rays and the transport and acceleration of anomalous cosmic rays at the solar-wind termination shock. Recent Voyager observations near and beyond the termination shock have revealed new, and in some cases, unexpected phenomena which have led to questions concerning the established paradigm. The physical interpretation of the observations requires a blunt termination shock, rapid inward motion of the shock and temporal variations over time scales ranging from hours to 22 years. Incorporation of these into the physics has promise of explaining most, if not, all of the observed phenomena while retaining the advantages of the termination shock paradigm for both galactic and anomalous cosmic rays.     

Energy dependence of Ti/Fe ratio in the Galactic cosmic rays measured by the ATIC-2 experiment

Titanium is a rare, secondary nucleus among Galactic cosmic rays. Using the Silicon matrix in the ATIC experiment, Titanium has been separated. The energy dependence of the Ti to Fe flux ratio in the energy region from 5 GeV per nucleon to about 500 GeV per nucleon is presented. The article was translated by the authors.     

Effect of nearby supernova remnants on local cosmic rays

We study in detail the effect of different particle release times from sources on the cosmic ray (CR) spectrum below 10¹⁵ eV in the Galaxy. We discuss different possible forms of particle injection such as burst-like injection, continuous injection for a finite time, injection from a stationary source and energy-dependent injection. When applied to the nearby known supernova remnants, we find that the observed CR anisotropy data favour the burst-like particle injection model for the CR diffusion coefficient   D ( E ) ∝ E ^a   with   a = 0.3 –0.6  in the local region. In this study we have also found that the contribution of the sources G114.3+0.3 and Monogem dominate if the observed anisotropy is a result of the effect of the nearby sources. Further study shows that we should not neglect the contribution of the undetected old sources to the local CR anisotropy.     

Diffusion tensor for Galactic cosmic rays in the interplanetary medium with a magnetic field

The Boltzmann kinetic equation is analyzed in the MHD approximation. This analysis requires an explicit expression for the collision integral F _c. In the classical theory, F _c=?vf _μ ⁽¹⁾ Ω_μ, where f _μ ⁽¹⁾ is the first spherical harmonic in the Galactic-cosmic-ray (GCR) distribution, Ω_μ are the components of a unit particle velocity vector, and the frequency ν of collisions between GCRs and interplanetary magnetic-field nonuniformities is assumed to be a scalar. The assumption that ν_ij is a tensor (which is the result of anisotropy in the interplanetary medium) distinguishes this study from others. Since the anisotropic GCR effects in the heliomagnetosphere are marginal, the nondiagonal elements of tensor ν_ij were set equal to zero. Our analysis has yielded the diffusion-tensor components D _∥, and D _A, which are expressed in terms of interplanetary parameters. The energy dependencies of D _∥, and D _A are in good agreement with the experimental data and calculations by other authors.     

A study of solar modulation of medium energy primary cosmic ray nuclei

The energy spectra of primary cosmic rays were studied in the energy interval 150 to 450 MeV/nucl by using balloon-borne cellulose-nitrate solid-state plastic detector. Effects of solar modulation were studied using the theoretical spectrum ofH ₁ nuclei near the solar minimum in 1964 as the demodulated spectrum. The ‘force-field’ potential which fit the experimental results was estimated to be 270 MeV/nucl.     

Effect of solar heliospheric parameters on different components of daily variation in cosmic rays

In the present work the data of three different neutron monitoring stations, Deep River, Tokyo and Inuvik located at different geomagnetic cutoff rigidities and altitudes has been harmonically analysed for the period 1980–1993, 1980–1990 and 1981–1993 respectively to investigate for a comparative study of diurnal, semi-diurnal and tri-diurnal anisotropies in cosmic ray (CR) intensity in connection with the change in IMF Bz component and solar wind velocity on 60 quietest days. It is observed that the amplitude of first harmonic is highly anti-correlated to the solar wind velocity during the period of high-speed solar wind stream (HSSWS) epoch on quiet days for three neutron monitor stations at different geomagnetic rigidity thresholds. During quiet days the amplitude of all the three harmonics significantly deviates on the onset of HSSWS epoch, whereas the direction of the anisotropy of all the three harmonics remains time invariant at three different cut off rigidity stations. The amplitude as well as the direction of anisotropy of all the three harmonics does not have time variation characteristics associated with Bz component of IMF on geo-magnetically most quiet days.     

North-south asymmetry of the heliosphere from cosmic-ray observations

The evidence that the heliosphere retains a pronounced north-south asymmetry during a long period (five solar cycles) is discussed. A modification of the standard model for the interplanetary magnetic field that provides the observed asymmetry is considered.     

Quasi-linear perpendicular diffusion coefficients of charged cosmic rays calculated directly from the Newton–Lorentz equation

It is the subject of this article to determine diffusion coefficients of charged test particles perpendicular to a mean magnetic field analytically by starting directly from the Newton–Lorentz equation. We employ the so-called standard quasi-linear theory to test the well-known field line random walk limit. It is demonstrated in this article that there is an additional gyroresonant contribution which describes the scattering of the particle away from a single field line. For certain situations, this additional contribution is small and can be neglected. For other cases, we obtain new results such as a rigidity-dependent quasi-linear perpendicular mean free path. The results of this article are relevant for particles in the solar wind which move scatter free or nearly scatter free in the direction parallel to the magnetic field of the Sun.     

Reflection of pre-accelerated pick-up ions at the solar wind termination shock: The seed for anomalous cosmic rays

It has been hypothesized for quite some time that interplanetary pick-up ions due to energization taking place in the region close to the solar wind termination shock, at some fraction and as an outcome of a complicated chain of processes, eventually are converted into species of the anomalous cosmic-ray particles. For the actual conversion efficiency it is of great importance to know the energy distribution of these pick-up ions upon their arrival at the shock. It turns out that pre-acceleration of these ions during their passage through the heliosphere shall substantially increase their chances to become reflected at the shock into the upstream direction which is a prerequisite for a further climb-up in energy by virtue of Fermi-1 acceleration processes. In this paper we start out from stochastically pre-accelerated pick-up ions and investigate their behaviour at the shock. With the use of adiabatic approaches in the de Hoffman-Teller frame of the shock, we calculate the energy distribution function of the reflected part of pick-up ions. From the calculated distribution functions it turns out that the reflected ions in the average suffer an energy increase by about a factor of 10, still not enough to let them move off the shock by spatial diffusion in the upstream direction. Thus, since converted back into the shock, they can undergo repeated reflections and energy gains till the diffusion-convection limit is reached. As we show in addition, the reflection probability for pick-up ions is about a factor of 10 higher than expected from the present literature and strongly varies with the off-axis angle, pointing to the fact that the termination shock represents a surface with a three-dimensionally varying source strength for the production of anomalous cosmic rays. The ACR source pattern is also expected to vary during the solar cycle and the relevant injection energies are expected to be larger by factors of 10 to 100 than the canonically adopted 1 keV nucl^–1.Institute for Problems of Mechanics of the Russian Academy of Sciences, Prospect Vernadskogo 101, 117526, Moscow, Russia.