Dynamics of energetic particles scattered in the solar wind : Magnetohydrodynamics and test-particle simulations

We model the transport of solar energetic particles (SEPs) in the solar wind. We propagated relativistic test particles in the field of a steady three-dimensional magnetohydrodynamic simulation of the solar wind. We used the code MPI-AMRVAC for the wind simulations and integrated the relativistic guiding center equations using a new third-order-accurate predictor-corrector time-integration scheme. Turbulence-induced scattering of the particle trajectories in velocity space was taken into account through the inclusion of a constant field-aligned scattering mean free path $\lambda_\parallel$. We considered mid-range SEP electrons of $81\:{\rm keV}$ injected into the solar wind at a heliocentric distance of 0.28 AU and a magnetic latitude of $24^{\circ}$. For $\lambda_\parallel =0.5\:{\rm AU}$, the simulated velocity pitch angle distributions agree qualitatively well with in situ measurements at 1 AU. More generally, for $\lambda_\parallel$ in the range 0.1 to 1\:AU, an energy-loss rate associated with the velocity drift of about $10\%$ per day is observed. The energy loss is attributable to the magnetic curvature and gradient-induced poleward drifts of the electrons against the dominant component of the electric field. In our case study, which is representative of the average solar wind conditions, the observed drift-induced energy-loss rate is fastest near a heliocentric distance of 1.2 AU. We emphasize that adiabatic cooling is the dominant mechanism during the first 1.5 hours of propagation. Only at later times does the drift-associated loss rate become dominant.