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Scientific paper
Apr 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987bvps.rept.....e&link_type=abstract
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Boundary Value Problems, Magnetic Rigidity, Planetary Magnetic Fields, Radiation Shielding, Spacecraft Shielding, Boundary Conditions, Cosmic Rays, Differential Equations, Particle Trajectories, Solar Flares
Scientific paper
Since a planet's magnetic field can sometimes provide a spacecraft with some protection against cosmic ray and solar flare particles, it is important to be able to quantify this protection. This is done by calculating cutoff rigidities. An alternate to the conventional method (particle trajectory tracing) is introduced, which is to treat the problem as a boundary value problem. In this approach trajectory tracing is only needed to supply boundary conditions. In some special cases, trajectory tracing is not needed at all because the problem can be solved analytically. A differential equation governing cutoff rigidities is derived for static magnetic fields. The presense of solid objects, which can block a trajectory and other force fields are not included. A few qualititative comments, on existence and uniqueness of solutions, are made which may be useful when deciding how the boundary conditions should be set up. Also included are topics on axially symmetric fields.
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