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The transport of energetic particles in the heliosphere is reviewed regarding the treatment of their drifts over an entire solar cycle including the periods around solar maximum, when the tilt angles of the heliospheric current sheet increase to large values and the sign of the magnetic polarity changes. While gradient and curvature drifts are well-established elements of the propagation of cosmic rays in the heliospheric magnetic field, their perturbation by the solar-activity-induced large-scale distortions of dipole-like field configurations and by magnetic turbulence is an open problem. Various empirical or phenomenological approaches have been suggested, but either lack a theory-based motivation or have been shown to be incompatible with measurements. We propose a new approach of more closely investigating solar magnetograms obtained from GONG maps, leading to a new definition of (i) tilt angles that may exceed those provided by the Wilcox Solar Observatory during high activity and of (ii) a “noninteger sign” that can be used to reduce the drifts during these periods as well as to provide a refinement of the magnetic field polarity. The change of sign from A < 0 to A > 0 of solar cycle 24 can be in this way localized to occur between Carrington Rotations 2139 and 2140 in mid 2013. This treatment is fully consistent in the sense that the transport modeling uses the same input data to formulate the boundary conditions at the heliobase as do the magnetohydrodynamic models of the solar wind and the embedded heliospheric magnetic field that exploit solar magnetograms as inner boundary conditions.

Precise measurements of the time-dependent intensity of the low-energy (

The charge-sign dependent modulation of cosmic rays is an important topic in solar modulation studies, providing insights into gradient, curvature, and current sheet drifts. Such studies, at higher levels of solar activity, have always been associated with challenges due to the limitations of numerical modulation models. We employ a three-dimensional numerical model based on stochastic differential equations and, owing to the numerical stability of this model, avoid such limitations at solar maximum conditions. We are therefore able to model results up to extreme solar maximum conditions, including the period of time over which the polarity reversal in the solar magnetic field takes place. We use our model to illustrate the effects of the tilt angle of the heliospheric current sheet that changes over the course of the solar activity cycle, and also discuss the effects when this is accompanied by a corresponding change in the magnitude of the heliospheric magnetic field. Given the results shown in this progress report, we expect our model to be able to reproduce recent data from AMS-02 and PAMELA, as well as provide us with useful predictions regarding the extent of drift effects during the next solar cycle.

Since the beginning of the space exploration era, solar activity was observed at its lowest level during 2006 to 2009. During this period, the PAMELA space experiment observed spectra for galactic cosmic rays, specifically for protons, electrons and positrons over a wide energy range, during what is called an A < 0 solar magnetic polarity cycle. Drift theory predicts a difference in the behaviour for these oppositely charge particles during A < 0 cycles. An opportunity was thus created to study the predicted charge-sign-dependent modulation, also now for very quiet heliospheric conditions. A comprehensive three-dimensional, drift modulation model has been used to study the solar modulation for cosmic rays in detail with extensive comparison to the observed PAMELA spectra for the mentioned period. First, this was done for protons and secondly for electrons, as already published, to test and to authenticate the modelling approach and then to come to a better understanding and appreciation of the underlying physics, such as diffusion and drift theory. The results were also used to make predictions of how cosmic rays are differently modulated down to low energies (1 MeV) for the two magnetic polarity cycles of the Sun, and what role drifts play in this process. All computed solutions are based on new very local interstellar spectra, now also done for positrons. This report is focussed on detailed aspects of the solar modulation of positrons during the extraordinary quiet solar modulation period from 2006 to 2009. For the first time, a meaningful modulation factor in the heliosphere is computed for positrons, from 50 GeV down to 1 MeV, as well as the electron to positron ratios as a function of time and rigidity for the mentioned period.

The transport of cosmic rays (CRs) in the heliosphere is determined by the properties of the solar wind plasma. The heliospheric plasma environment has been probed by spacecraft for decades and provides a unique opportunity for testing transport theories. Of particular interest for the three-dimensional (3D) heliospheric CR transport are structures such as corotating interaction regions (CIRs), which, due to the enhancement of the magnetic field strength and magnetic fluctuations within and due to the associated shocks as well as stream interfaces, do influence the CR diffusion and drift. In a three-fold series of papers, we investigate these effects by modeling inner-heliospheric solar wind conditions with the numerical magnetohydrodynamic (MHD) framework Cronos (Wiengarten et al., referred as Paper I), and the results serve as input to a transport code employing a stochastic differential equation approach (this paper). While, in Paper I, we presented results from 3D simulations with Cronos, the MHD output is now taken as an input to the CR transport modeling. We discuss the diffusion and drift behavior of Galactic cosmic rays using the example of different theories, and study the effects of CIRs on these transport processes. In particular, we point out the wide range of possible particle fluxes at a given point in space resulting from these different theories. The restriction of this variety by fitting the numerical results to spacecraft data will be the subject of the third paper of this series.

A numerical model for the solar modulation of cosmic rays, based on the solution of a set of stochastic differential equations (SDEs), is used to illustrate the effects of modifying the heliospheric magnetic field, particularly in the polar regions of the heliosphere. SDE-based models are well suited for such studies so that new insights are gained. To this end, the differences in the modulation brought about by each of three choices for the heliospheric magnetic field, i.e. the unmodified Parker field, the Smith–Bieber modified field, and the Jokipii–Kota modified field, are studied as typical well-known cases. It is illustrated that although both these modifications change the Parker field satisfactorily in the polar regions of the heliosphere, the Smith–Bieber modification is more effective in reducing cosmic ray drift effects in these regions. The features of these two modifications, as well as the effects on the solar modulation of cosmic rays, are illustrated qualitatively and quantitatively. In particular, it is shown how the Smith–Bieber modified field is applied in a cosmic ray modulation model to reproduce observational proton spectra from the PAMELA mission during the solar minimum of 2006–2009. These SDE-based results are compared with those obtained in previous studies of this unusual solar minimum activity period and found to be in good qualitative agreement.