What we're actually talking about is cosmic rays, which are matter particles (mostly protons), not any kind of electromagnetic radiation. Those generally slam into something in the atmosphere, producing showers of secondary particles. Occasionally some of these make it to the ground. The article mentions neutrons, but these seem to be mostly muons.
Of course Bruce Perens, to whom you replied, was talking about the radio waves from HAARP, which was mentioned by the OP.