Focusing of Paraxial Rays in a Magnetic Dipole Field

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Abstract
It is well known that a magnetic field of axial symmetry has a focusing effect for paraxial orbits. The field of the earth is of this type and it is shown that, if the cosmic rays consist of protons, a bundle of orbits parallel at infinite distance is focused on the surface of the earth if the energy is about to GeV. The co-latitude of the bundle at infinite distance is about 2.2 times the co-latitude of the focal point. The asymptote to the orbits is about 22° further to the east than the focal point. There is also an infinite series of lower energies exhibiting focusingproperties. The calculations refer to paraxial orbits, but a comparison with terrella measurements shows that the focal energy and the above relation between the co-latitudes is appropriate down to about 50° latitude. DOI: 10.1111/j.2153-3490.1956.tb01219.x

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