Transport equation of the galactic cosmic ray (GCR) is numerically solved for qA>0 and qA<0 based on the stochastic differential equation (SDE) method. We have developed a fully time-dependent and three-dimensional code adapted for the wavy heliospheric current sheet (HCS). Results anticipated by the drift pattern are obtained for sample trajectories and distributions of arrival points at the heliospheric boundary for GCR protons. Our simulation reproduced a 22-year cycle of solar modulation which is qualitatively consistent with observations. Energy spectra of protons at 1 AU are calculated and compared with the observation by BESS.
We discuss two extraordinary increases of cosmic ray intensity observed by Voyager 1 in the last 1.1 AU before heliopause crossing, Aug 2012 at 121.7 AU. The two increases are roughly similar in amplitude and result in a total increase of cosmic ray nuclei around 1 GV of over 50 percent and of 0.01 GV electrons of a factor about 2. During the first increase, the changes in the magnetic, B, field are small. After the first increase, the B field variations and cosmic ray changes become large and during the second increase the B field variations and the cosmic ray changes are correlated to within a day. The intensity variations of H and He nuclei during these time intervals are measured from 0.1 to over 1 GV. The total GCR increse over the two events resemble those expected from a simple force-field like solar modulation model with a modulation potential of about 80MV. This is nearly one third of the total modulation potential of about 250 GV required to produce the modulation of these particles observed at the earth at the 2009 sunspot minimum and adds a new aspect to ideas about heliospheric modulation.
The 11-year and 22-year modulation of galactic cosmic rays (GCRs) in the inner heliosphere are studied using a numerical model developed by Qin and Shen in 2017. Based on the numerical solutions of Parkers transport equations, the model incorporates a modified Parker heliospheric magnetic field, a locally static time delayed heliosphere, and a time-dependent diffusion coefficients model in which an analytical expression of the variation of magnetic turbulence magnitude throughout the inner heliosphere is applied. Furthermore, during solar maximum, the solar magnetic polarity is determined randomly with the possibility of $A>0$ decided by the percentage of the north solar polar magnetic field being outward and the south solar polar magnetic field being inward. The computed results are compared with several GCR observations, e.g., IMP 8, SOHO/EPHIN, Ulysses, Voyager 1 & 2, at various energies and show good agreement. It is shown that our model has successfully reproduced the 11-year and 22-year modulation cycles.
We study the effects of drift motions and the advection by a Galactic wind on the propagation of cosmic rays in the Galaxy. We employ a simplified magnetic field model, based on (and similar to) the Jansson-Farrar model for the Galactic magnetic field. Diffusion is allowed to be anisotropic. The relevant equations are solved numerically, using a set of stochastic differential equations. Inclusion of drift and a Galactic wind significantly shortens the residence time of cosmic rays, even for moderate wind speeds
It is shown that the relativistic jet, emitted from the center of the Galaxy during its activity, possessed power and energy spectrum of accelerated protons sufficient to explain the current cosmic rays distribution in the Galaxy. Proton acceleration takes place on the light cylinder surface formed by the rotation of a massive black hole carring into rotation the radial magnetic field and the magnetosphere. Observed in gamma, x-ray and radio bands bubbles above and below the galactic plane can be remnants of this bipolar get. The size of the bubble defines the time of the jets start, $simeq 2.4cdot 10^7$ years ago. The jet worked more than $10^7$ years, but less than $2.4cdot10^7$ years.
The existence of the spectral break around $sim 3 times 10^{15}$ eV in the cosmic ray spectrum (referred to as the `knee) is one of the biggest questions in cosmic ray astrophysics. At the same time, the origin of cosmic rays above the knee energies (between 10$^{15}$ and 10$^{18}$ eV) is also still unsettled. In this paper, we investigate how the hypothetical extragalactic CRs after modulated by the galactic wind contribute to the knee in the CR spectrum. We numerically calculate the modulated energy spectrum of the hypothetical cosmic rays coming into the galaxy from just outside of the ``galactic sphere where the galactic wind terminates. We show that the observed knee structure is reproduced well by a superposition of the modulated component and the galactic cosmic rays originating in supernova remnants.
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