Extensive air showers (EAS) with median primary energy (E
 m) of (1013÷1015) eV have been observed since 1970 at Mt. Norikura (2770 m above sea level; geographic latitude 36.1°N, longitude 137.6°E) in order to study a cosmic-ray sidereal daily variation of galactic origin. We report here a summary of the observed results. EAS shows a significant sidereal diurnal variation with an amplitude (0.060±0.003)% and a phase (0.8±0.3) h sidereal local time forE
 m≈1.5·1013eV. Sidereal semi- and tridiurnal variations also are statistically significant. These variations are proved to be of galactic origin by a method which uses the difference of two directional (eastward and westward) air shower observations. It is found that these variations are subject, as predicted by Nagashimaet al., to the annual variation due to the heliomagnetospheric modulation of the galactic anisotropy, which dominates in the rigidity region ≈1012V, and further that the annual variation changes its phase due to the polarity reversal of the polar magnetic field of the Sun, which occurs at the period of the maximum solar activity. This indicates that the anisotropy is produced by the charged cosmic rays, contrary to the expectation from the γ-ray origin hypothesis suggested by Alexeenko and Navara. With the increase ofE
 m, the anisotropy seems to be reduced as we have not been able to detect any significant sidereal variation in EAS withE
 m≈2·1014eV. This seems contradictory to the conventional conclusion that the energy spectrum of the anisotropy is flat or slightly increases with energy.

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Galactic cosmic-ray anisotropy and its modulation in the heliomagnetosphere inferred from air shower observation at Mt. Norikura

A theory of cosmic ray anisotropies of solar origin

Very high intensities of galactic cosmic rays measured by Voyager 1 in the heliosheath appear to be incompatible with the presence of a modulation wall near the heliopause produced by a pile up of the heliospheric magnetic field. We propose that the modulation wall is a structure permeable to cosmic rays as a result of a sectored magnetic field topology compressed by plasma slowdown on approach to the heliopause and stretched to high latitudes by latitudinal flows in the heliosheath. The tightly folded warped current sheet permits efficient cosmic-ray transport in the radial direction via a drift-like mechanism. We show that when stochastic variations in the sector widths are taken into account, particle transport becomes predominantly diffusive both along and across the magnetic sectors. Using a test-particle model for cosmic rays in the heliosheath we investigate the dependence of the diffusion coefficients on the properties of the sector structure and on particle energy.

https://iopscience.iop.org/article/10.1088/0004-637X/754/1/31/pdf

Cosmic-ray diffusion in a sectored magnetic field in the distant heliosheath

It is demonstrated that, at high rigidities (50 GV and beyond), all the main features of cosmic-ray anisotropy of solar origin can be explained in terms of regular particle motion —without diffusion being involved — in the large-scale interplanetary magnetic field (IMF). A simple model of the IMF is adopted with a corotating warped neutral sheet separating the regions of alternative polarities; the warped shape is indispensable for obtaining any form of anisotropy. Energy losses occurring along various computed trajectories are calculated to give the sidereal, solar and antisidereal intensity waves. The reliability of the variations obtained are checked by changing the parameters of the IMF model. Both the sense and amplitude of the polarity-dependent sidereal vector are compatible with those established experimentally. Also reproduced are the predictions of corotation in addition to the 3-hour phase of the semi-diurnal wave. The corotation is found to be near perfect at 50 GV, while it reduces at 100 GV. The model presented accounts for the change of solar daily vector that was observed in 1969.

Sector structure of the interplanetary magnetic field and anisotropy of 50–1000 GV cosmic rays

Interaction of cosmic rays with magnetohydrodynamical turbulence in cosmic media

Explicit expressions describing the semi-diurnal variation of cosmic ray intensity are obtained in the frame of the convection-diffusion theory. Convection-diffusion equations are extended by introducing a symmetric traceless tensor accounting for the second harmonics of the cosmic ray angular distribution. Starting from the statistical Boltzmann equation a new transport equation is deduced which relates the second harmonics of the angular distribution to the gradients of cosmic ray streaming. Expressing the free space anisotropy in terms of geographical coordinates, the predicted diurnal and semi-diurnal variations are given. Arguments are brought forward that a sunward cosmic ray streaming along the interplanetary field lines gives rise to a pitch angle distribution with an excess of particles of large pitch angles.

http://iopscience.iop.org/article/10.1088/0305-4470/8/8/019/pdf

On the second spherical harmonics of the cosmic ray angular distribution

Explicit expressions describing the semi-diurnal variation of cosmic ray intensity are obtained in the frame of the convection-diffusion theory. Convection-diflusion equations are extended by introducing a symmetric traceless tensor accounting for the second harmonics of the cosmic ray angular distribution. Starting from the statistical Boltzmann equation a new transport equation is deduced which relates the second harmonics of the angular distribution to the gradients of cosmic ray streaming. Thus, compared to models used hitherto, a more quantitative calculation is carried out. Expressing the free space anisotropy in terms of geographical coordinates, the predicted diurnal and semi-diurnal variations are given. The results obtained are essentially in agreement with those of Quenby and Lietti but also differences arise as a result of the bending and divergence of the large-scale interplanetary magnetic field lines. Arguments are brought forward that a sunward cosmic ray streaming along the interplanetary field lines gives rise to a pitch angle distribution with an excess of particles of large pitch angles.

J. Kota

Papers

On the second spherical harmonics of the cosmic ray angular distribution

On the second spherical harmonics of the cosmic ray angular distribution