The energy from antimatter comes from bringing it into contact with regular matter. It destroys both and releases a LOT of energy as a result.
Half of the energy comes from the antimatter mass. Which means, sure, you technically get twice as much energy as was stored within the antimatter, but a factor of 2 doesn't count for much when we're already in the kilo-tons. (Although it is something I'd forgotten about.)
Also, the efficiency of energy input to antimatter creation is likely to be far below 50%, meaning that you're still probably putting in more energy than you're getting out. (Energy storage is always low efficiency, because you have to work against entropy - which is fine so long as you have a good source of energy, like stars. It does, however, drive up production time.)
And this being a bomb, close counts. Kinetic barriers do nothing against energy attacks. You don't have to get it onto a Reaper. Just near it. And depending on how big a boom we're going for, maybe not even all that near it.
Bombs in space are tricky.
I was considering blowing up the bomb on the surface of the Reaper in order to get a structural shockwave, which would parse most of the bomb's energy into the Reaper, and do considerable damage. Since you don't get shockwaves in vacuums, I considered that this would only work at direct contact.
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You're suggesting what is essentially a radiation bomb. Radiation obeys an inverse square law - it gets notably weaker the further away you get, so, yeah, you'll want to be close. It gets emitted in all directions, so you can't target it at the Reaper. Radiation does ignore kinetic barriers - but the Reapers have radiation shielding and heavy armour. And since you can't focus the damage, the result will be a large area surface burn.
One disadvantage is that your input energy costs for an effective radiation bomb are going to be much higher than that of an effective shockwave bomb (ie, you'll have to make more anti-matter). This is because a substantial amount of the energy from a radiation bomb completely misses the Reaper, and the rest has to get through the armour.
A second disadvantage is that you need a perfect 1-to-1 matter anti-matter mix. Otherwise, a large amount of the energy will go into whatever matter or antimatter remains and you'll get a fragmentation bomb instead, which the Reaper's kinetic barriers will be able to handle.
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While I was writing this post up and figuring out the mechanics of a radiation bomb, I realised there's a third option, a kind of mix between the radiation bomb and the shockwave bomb.
The initial reaction of a radiation bomb will generate a shockwave through the matter and antimatter fuel. This shockwave will be HUGE, blowing the fuel and bomb apart into a cloud of gas, but the antimatter will continue to react with anything it touches, setting off more shockwaves within the gas. If you've built the bomb right, this means that you get an expanding cloud of matter-antimatter plasma that continues to react even as it expands. If the bomb went off close enough to the Reaper's kinetic barriers, I'm... genuinely not sure what would happen. The difference between kinetic energy (which is blocked) and radiation energy (which isn't) gets rather fuzzy at that level.
Although, considering you need a LOT of energy just to make a single gram of antimatter, if you're planning to manufacture enough to create a cloud of gas, it's going to be a very expensive bomb. That's only expensive in terms of time though, considering that we have stars to tap.
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Of course, as Reorte pointed out, whatever we can do the Reapers can do too. And there's more of them than us. So I'm still not holding out hope for a conventional victory coming out of all this antimatter-think.