Air Force working on antimatter weapons

Unapparently unsatisfied with the destructive capabilities of the weapons they have now, the US Air Force is working on—get this—antimatter bombs (we'll spare you the obvious sci-fi references, but feel free to make them yourselves).
And we can see why: as little as one millionth of a gram of positrons has as much destructive force as 83 pounds of TNT, and unlike with nukes, there's no messy radioactive fallout to have to deal with later. We smell a doomsday machine in here somewhere, and there are already plenty of worries that the fact that an antimatter superweapon could kill tons of people without also rendering the planet uninhabitable has some scientists worried that they'll be too temtpting to actually use. Potentially saving us all from destruction: the fact that producing even 100-billionths of a gram of antimatter costs on the order of $6 billion, a princely sum which'll either keep antimatter weapons from being built anytime soon or result in a massive jack-up in military expenditures.