Modeling the Modulation of Galactic and Jovian Electrons by Stochastic Processes

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.