Interesting information about the origin and potential power of cosmic rays if the ionosphere was not shielding us.
It's highly unlikely the ionosphere would stay down much longer than a few weeks at maximum but if it did, you'd want to put some granite between you and outer space until it restored itself. Topside there would be places on the planet that'd be cooking organic matter like the inside of a microwave oven.
We know it has happened before because the prime survivors, bacteria and fungi, all display rare latent abilities that only manifest themselves in the presence of radiation lethal to human beings. Normally benign fungus can suddenly turn coal black, form massive colonies and balloon up in mass like crazy foam. Harmless bacteria can swell up like superheroes and integrate into linked lattices of cooporative action that eat through metal and rock to protect themselves. There's no way these microcritters would retain these capacities if these kinds of events were anywhere near as rare as the majority believe at present. These bugs keep these evolutionary mechanisms in reserve because those that don't must get fried sooner or later.