Physics – Plasma Physics
Scientific paper
Dec 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011agufmsh31b2008k&link_type=abstract
American Geophysical Union, Fall Meeting 2011, abstract #SH31B-2008
Physics
Plasma Physics
[7514] Solar Physics, Astrophysics, And Astronomy / Energetic Particles, [7859] Space Plasma Physics / Transport Processes
Scientific paper
Variable time steps are common features of Runge-Kutta methods and they are used widely in applications where charged particles penetrate into high-gradient fields, like the geomagnetic field. Symplectic trajectory integrations are generally incompatible with variable time steps because the simple inclusion of variable time steps in an initially symplectic scheme destroys its ability to preserve particle energy. We derive generalized equations for the Stormer-Verlet method of trajectory integration from basic principles and show that they allow the use of variable time steps and yet posses conservation properties of the traditional simplectic schemes. We demonstrate that our equations preserve particle energy and transform to the Stormer-Verlet equations for the case of constant time steps. We verify solutions by analysing both single-particle trajectory parameters and particle distributions resulting from uniform isotropic mono-energetic sources in a dipole magnetic field. Following validation of the algorithm we apply it to the study of the propagation of solar energetic particles SEP through ideal (dipole) and empirical (IGRF-11) models of the geomagnetic field for the case of a monodirectional plane sources outside of the magnetosphere, characteristic of the early phases of some SEP events. We find that anisotropic distributions are highly focused by the geomagnetic field, with all particles mapping to regions as small as 400x400 km2, and 51% of particles concentrated in a region 133 km across in the case of a dipole field, although a realistic field (IGRF-11) gives only 45% of particles concentrated in a region 133 km across. These findings have significant consequences for the morphology of polar cap absorption events.
Knudsen David J.
Kouznetsov Andrei
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