Positrons are naturally occuring. There are several nuclides that emit them. We have created small, short lived environments where we have created anti-protons. Scientists somewhere even went to the trouble of getting a positron and an anti-proton together to create anti-hydrogen. I can't think of much off the top of my head for uses of anti-matter. The annilhation of an anti-proton yields two gamma photons of almost 1 GeV, so there's some possible use there.
In a vacuum a nuke is really just an intense burst of electromagnetic energy. However, close to a asteroid this would be flash vapourising rock, and that would create a shockwave in the asteroid, and alot of rock turned to gas and plasma blasting out into the vacuum. The best way would be to set a nuke off beside the asteroid, the evaporating rock on one side would give it a nudge. A better way would to be just nudge the asteroid with kinetic projectiles. It would be simpler and more 'green' to send up lumps of heavy stuff in a orbit that crosses the asteroids orbit from 90 degrees. Giving it a sideways nudge off course. Each projectile could be small enough not to disturb and break up the asteroid. Ten 1 ton trucks dropped on your head hurts more than one ten ton trucks
but launching lumps of heavy stuff is more expensive than launchig explosives. it is safer though. it might be best to psuh lumps of heavy stuff already orbiting the earth out of their orbit to hit the target, that seems to me to be cheapest
WHat's "green" got to do with it? Unless you think the penetrator wouldn't stand the heat of reentry and spewing a few Kgs of plutonium over the planet is a worse fate than getting hit by a mile-wide asteriod.
