Interesting article here about relativistic acceleration of electrons at regions of "magnetic reconnection".

My question is that if this happens miles from earth using the earth's magnetic field (which is very weak compared to many manmade magnetic fields), can't we use this effect to accelerate electrons (maybe ions?)? Probably there's a way to make them a coherent beam. I think I recall references to electron lasers.

If we found a good cheap way of doing this, it could bring the cost down of those earth-based laser cannons, designed to push solar sails. Push them with relativistic electrons, which are much more massive than photons.

You'd need a sail (probably magnetic) that would reflect the electrons, rather than letting them hit the payload. You'd probably still need a way for the payload to dump excess electrons, to keep from building up a monumental charge.