### A Computational Study of Cross Field
Diffusion of Energetic Particles Caused by their Interaction with Magnetic
Decreases in Interplanetary Space

**Edio da Costa Junior**^{1},
Bruce T. Tsurutani^{2}, Maria Virgania Alves^{1},
Ezequiel Echer^{1}

^{1}National Institute
for Space Research - INPE, Brazil

^{2}Jet Propulsion Laboratory - NASA, USA

There are regions in the interplanetary space where the
strength of the magnetic field is low as compared to around regions. These
structures are nowadays usually called Magnetic Decreases (MDs). MDs are
probably created by a diamagnetic effect caused by the heating of particles that
are accelerated preferentially perpendicular to B. The particle acceleration is
associated with the dissipation of phase-steepened Alfven waves, presumably
through the ponderomotive force. Our main intent in this work is to investigate
non-resonant cross-field diffusion particles due to their interactions with MDs
at large heliospheric latitudes and at the ecliptic plane. In order to perform
that we start using analytical expressions for the distributions of magnetic
field decreases and sizes of the MDs at large heliospheric latitudes. These
expressions were obtained from analytical fits of Ulysses data. In order to have
an statistical representation of these distribution functions we use Monte Carlo
method (Amar, Computing in Science and Engineering, 8(2), 9, 2006). A
theoretical model for particle diffusion has been presented by Tsurutani et al.
(Nonlinear Processes in Geophys., 6, 235, 1999). We use this model in our
calculations by letting a particle with an specific energy interacts with an MD
to which field decrease and thickness are attributed by the respective Monte
Carlo representation of the distribution functions. This process can go on until
all particles have been scattered. Besides that, we have also obtained results
for the coefficient diffusion using particles (protons) within a large range of
energy (100 keV to 100 MeV) interacting with MDs of constant features to find
out what would be the influence of MDs parameters on the diffusion. Nowadays, we
are analyzing Ulysses magnetic field data corresponding to the ecliptic plane to
derive distribution functions for MD properties to calculate the cross-field
diffusion of energetic particles in low latitudes.