Possible explanation of the radiation observed by Van Allen at high altitudes in satellites

We consider the possibility, suggested by P. Rothwell and T. Gold in conversation with the author, that the radiation observed by Van Allen and co-workers at high altitudes is due to the decay electrons and protons from neutrons produced in the earth's atmosphere by cosmic rays and stored in the earth's magnetic field. Order of magnitude estimates for the densities to be expected are presented. Only scattering loss is considered. Using a lifetime of 3 · 10⁹ s for loss through scattering, an upper limit of 10^-2 electrons/cm³ near the earth and .05 (R _E /r ₀)³ electrons/cm³ at large distances r ₀ in the equatorial plane is obtained. The proton density at large distances is .03(R _E /r ₀)² cm^-3, for a lifetime of 10¹² s. If plasma accelerations are not important, then the spectrum of electrons will be that of neutron β-decay. The protons are produced by fast neutrons coming directly from nuclear stars and their spectrum will be approximately that of the protons from stars. The electron density is sufficient to give a counting rate a few times larger than is observed, while the proton density is sufficient to give a counting rate 10⁴ times higher than the observed lower limit. The lifetimes of stored particles are therefore probably much less than those given by scattering. There should be a strong latitude effect which is roughly estimated as proportional to cos⁶λ. Reasons are given for believing that collective effects will reduce the density below this near the poles.