Effects of Pitch Angle Scattering on Nonlinear Charged Particles Dynamics in a Magnetic Field Reversal

Numerical simulation of charged particles dynamics in magnetic field reversals, such as in the Earth's magnetotail, demonstrate the partitioning of phase space into dynamically distinct regions corresponding to transient, chaotic, and integrable orbits. In turn, this partitioning results in an ion distribution function signature that manifests itself as a series of peaks whose separation is proportional to the 4^th root of the particle energy and parameters that describe the mesoscale structure of the magnetic field. The signature has been observed in quiet time satellite data from multiple different spacecrafts. We have developed an ad hoc collision operator that models pitch angle scattering due to random processes in the plasma. In the presence of collisions, we find that the KAM surfaces in the integrable regions are destroyed and particles move throughout the region following a classical diffusion process. In particular we show that particles started in the center of the integrable region have an escape time proportional to the magnitude of the collision and inversely proportional to the square of the time between collisions. However, particles in the previously integrable region still remain trapped for long periods as compared to chaotic orbits. In addition, the boundary between the chaotic and transient regions remains, but becomes less defined. We find that the boundary spreads with a thickness proportional to the square root of the collision amplitude and inversely proportional to the time between collisions. As a function of the energy, the chaotic particle trapping time is shown to decrease for resonant energies and increase for off-resonant energies, however, the number of chaotic orbits increases for all energies. The robust nature of the phase space structures helps to explain the persistence of the distribution function signature in observed satellite data.