Abstract. The heliospheric modulation of galactic and Jovian electrons is studied using a fully threedimensional, steady state model based on Parker's transport equation including the Jovian source. The modulation of low-energy electrons is a handy tool to establish and to construct a suitable diffusion tensor to assure compatibility between model computations and observations from the Ulysses spacecraft. This is because electron modulation responds directly to the energy dependence of the diffusion coefficients below -500 MeV in contrast to protons which experience large adiabatic energy losses below this energy. The model is used to study the latitudinal transport of both Jovian and 4-20 MeV galactic electrons by illustrating how the electron intensities are affected at different latitudes when enhancing perpendicular diffusion in the polar direction. In particular, the electron intensity-time profile along the Ulysses trajectory is calculated for various assumptions for perpendicular diffusion in the polar direction and compared to the 3-10 MeV electron flux observed by Ulysses from launch up to the end of the first out of the ecliptic orbit. Comparison of the model computations and the observations give an indication as to the magnitude of this diffusion coefficient. The relative contributions of the Jovian and galactic electrons to the total electron intensity is shown along the Ulysses trajectory.

We present a newly developed numerical modulation model to study the transport of galactic and Jovian electrons in the heliosphere. The model employs stochastic differential equations (SDEs) to solve the corresponding transport equation in five dimensions (time, energy, and three spatial dimensions) which is difficult to accomplish with the numerical schemes used in finite difference models. Modeled energy spectra for galactic electrons are compared for the two drift cycles to observations at Earth. Energy spectra and radial intensity profiles of galactic and Jovian electrons are compared successfully to results from previous studies. In line with general drift considerations, it is found that most 100 MeV electrons observed at Earth enter the heliosphere near the equatorial regions in the A > 0 cycle, while they enter mainly over the polar regions in the A < 0 cycle. Our results indicate that 100 MeV electrons observed at Earth originate at the heliopause with ∼600 MeV undergoing adiabatic cooling during their transport to Earth. The mean propagation time of these particles varies between ∼180 and 300 days, depending on the drift cycle. For 10 MeV Jovian electrons observed at Earth, a mean propagation time of ∼40 days is obtained. During this time, the azimuthal position of the Jovian magnetosphere varies by ∼1 •. At a 50 AU observational point, the mean propagation time of these electrons increases to ∼370 days with an azimuthal position change of Jupiter of ∼20 •. The SDE approach is very effective in calculating these propagation times.

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The Ulysses spacecraft has been the first to orbit the Sun over its poles and to explore the heliosphere at these high heliolatitudes. It has now completed two fast latitude scans, one at solar minimum and one at solar maximum. Since its launch in October 1990, this mission has led to several surprising discoveries concerning energetic particles, cosmic rays, Jovian electrons, the solar wind, the heliospheric magnetic field and the global features of the heliosphere. This review addresses mainly the propagation and modulation of cosmic rays and other charged particles, from both an observational and theoretical point of view, with emphasis on what has been learned from exploring the inner heliosphere to high heliolatitudes. This is done for solar minimum and maximum conditions. The review is concluded with a summary of the main scientific discoveries and insights gained so far from the Ulysses mission.

Drifts are one of the major cosmic ray modulation mechanisms in the heliosphere. Three types of drifts occur in the background heliospheric magnetic field, namely curvature, gradient and current sheet drifts. The last component occurs because of the switch in magnetic field polarity across the heliospheric current sheet and is the main topic of study. We discuss and implement a new approach to model drifts in a numerical modulation model. The model employs stochastic differential equations to solve the relevant transport equation in five (three spatial, energy and time) dimensions. What is of interest is the fact that the model can handle current sheet tilt angles up to the theoretical maximum of α = 90°and still remain numerically stable. We use the additional insights gained from the numerical model to investigate the effectiveness of drifts along the current sheet by examining the relationship between the current sheet path length and the cosmic ray propagation time. It is found that diffusion can disrupt the drift process very effectively, leading to diffusive short circuiting of the current sheet by the cosmic rays.