"The cosmic rays strip off electrons from the air molecules and these electrons are accelerated upwards by the electric field of the lightning discharge. The free electrons and the lightning electric field then make up a natural particle accelerator.
Fullekrug and his colleagues used the radio waves emitted by the particle beam of one of those natural occurring accelerators to figure out how high up the phenomenon occurred, using computer simulations at Los Alamos National Lab's supercomputing facility. Then a group of European scientists set up video cameras to monitor the area above thunderstorms. They observed lightning discharges strong enough to produce so-called "sprites": telltale airglows that sometimes form above thunderstorms. A few of those sprites coincided with with the particle beams.
This is indirect evidence, of course. But over the next several years, no fewer than five different space missions are planned which will have the capability to measure those naturally occurring particle beams directly.