It is demonstrated by formal calculation that the large-scale geomagnetic fluctuations observed at ground stations result in a rapid and somewhat remarkable kind of diffusion of the electrons in the outer zone of the Van Allen radiation belt. An initial thin ring of electrons will give an immediate finite particle flux at infinity, at the same time that the group of the particles remaining moves radially inward as a ‘wave’. We predict a decline of particle counting rate beyond about 4 earth radii of the order of 1/rβ, where β≅12 to 16, depending upon the kind of counter, in agreement with the many observations.