How much shielding do you need to survive an antimatter explosion?

Question

The Story (Literally)

Extract: First Draft, Third Person Limited.

"C'mon! We need the engines back, now!" Valerie yelped over the general channel. The interceptor floated adrift, otherwise without any radio-signature. The jellyfish-like leviathan of lashing tendrils that was the apex sparred with the main ship, leaving whips of PDC fire dashing over them.

Jayden floated idly in a cloud of debris and discarded tools, above the fusion reactor core. Kitsuki floated in a corner, wrestling the cargo bay door open. "I have a plan, and Val ain't gonna like it." Jayden muttered, only Kit on the channel.

He wrenched out the reactor's antimatter catalyst cylinder from its cooling system. Its magnets glowing idle blue. "No no n-n-no. This is going to get us killed." "Maybe, but we're all dead anyway. If we don't kill it."

He knocked his mag-boots together and they disengaged, floating up next to the canister. Getting himself in between the canister and the apex, he kicked off the ground, spun and kicked the canister with both legs, right at the leviathan. It lashed its tendrils to meat the canister, and just as he swung behind the tank, he swung the rifle off his back and leveled it.

There was a bright bolt of plasma and-

He came to. He noticed his ears hurt, a lot. They rung with deafening silence. Water floated everywhere, blobs freezing as they coalesced, in the shimmering cloud of shrapnel that used to be the starboard side of the engineering bay. He took a second to thank the nameless engineer who invented anti-spalling net, which was the only thing between the fiery debris of the tanks, and both of them being shredded.

"...What happened?" Valerie asked, dead calm.

The Question

It's quite simple, how much water and ship do you need to put between you and the gamma ray flash of a canister of antimatter exploding. Let's just say that it was a few miligrams of X kind of antimatter. I would like it to be full anti-hydrogen, to be consistent with most other antimatter in the book, but it would in all reality just be positronium. And only throw off gamma rays.

If you chucked it out and it managed to get a kilometer away from the ship before exploding, and you get behind seven inches of steel and ceramic shield plating, (possibly the drive cone of the ship, because it was facing the explosion), a nondescript tank of reaction mass (water), and a thick anti-spalling net, could you reasonably survive?

I can only get as far as figuring out the energy of such an explosion, and sort of attenuating it with distance, beyond that I have no clue as to whether my fluffy crew gets reduced to ashes.

Answer 1

Disclaimer: Not an expert, I probably got something wrong.

Edit: As it turns out, I did get at least one thing wrong. After I wrote this answer, I learned that the radiation released by the annihilation of a proton is not comparable to that released by the annihilation of an electron. While an electron/positron annihilation releases gamma rays with an energy of around 0.5 MeV, proton-antiproton annihilation produces gamma ray photons with an energy of around 200 MeV, though it can be even higher than that (Page 113). I also found a calculator for determining the amount of shielding needed to protect from photons of a given energy. It only goes up to 100 MeV, but, if it is to be believed, you are going to need a lot more shielding to not receive a lethal dose of radiation if the source of said radiation happens to be proton-antiproton annihilation (Seven inches of steel seems to actually be within the ballpark). So, my original answer is only true for the case of electron-positron annihilation.

Original Answer:

TL;DR: Jayden will probably be fine

When you have a matter-antimatter annihilation, remember that whatever amount of antimatter you have is annihilating with an equal amount of ordinary matter. So, you can expect to release twice the mass-energy of your antimatter. HOWEVER, only electron-positron annihilation releases all of its energy as gamma rays. The annihilation of a proton with an antiproton is a bit more complicated than that. One source claims that only a third of the energy released by the annihilation of a proton is in the form of gamma rays, half is in the form of neutrinos (Which can be discounted) and a sixth of which is in the form of electrons and positrons. For our purposes, we're assuming that all of the energy is released as gamma rays, though this is not actually true. After all, it's better to overestimate the amount of shielding you need than to underestimate it.

So, suppose we have 5 milligrams of antimatter and 5 milligrams of normal matter. The total energy released is 898755 megajoules. This is around 215 tons of TNT.

Atomic Rockets provides an equation to calculate the radiation dose received by an average person a given distance from a nuclear blast. I reckon that this situation is similar enough. The site gives the formula as 1.78e9 * (Y / R^2), where Y is the yield of the nuke in kilotons. This assumes that 80% of the weapon's energy is delivered as X-Rays with no shielding, and explains how the equation was derived. This equation also assumes that none of the photons actually pass through a person. You can tweak the numbers a bit to account for how your crewmember body's surface area would differ from the average. Adjusting the numbers to assume that 100% of the weapon's energy is released as radiation, we get 2.18e9 * (Y/ R^2). Now, this does assume that there is no difference between getting irradiated by X-Rays and getting irradiated by gamma rays, which might not be true.

Now, let's suppose our protagonist is 50 meters away from the detonation. According to this formula, he would receive a dose of 187480 grays, whereas the lethal dose is around 5.5. Yeah, he is going to die. The amount of energy absorbed is probably also enough to just turn a person into a steak. At 100 meters away form the detonation, the dose delivered is 46870 grays.

So, how much of a given material do we need to reduce the dose of radiation received? Luckily for us, there is a chart of the thickness of a given material needed to reduce the incoming radiation dose by 50%. Depending on the energy of a gamma ray, the halving thickness for water is between 4.15 and 7.15 centimeters. For iron, it's 0.26-1.06 cm. For copper, it's 0.18-0.42cm. Suppose we want to reduce the incoming dose from 46870 grays to 3 (Mortality rate is still around 30% here), and we want to use water to do so. Solving 46870/(2^x)=3 we get x=13.93 as the amount of times the radiation intensity must be halved. For this...we only need around 1 meter of water at most. Solving all that for a distance of 1 kilometer away from the explosion, we get that it would only take around 50cm of water to bring the dose down to something which one has a chance of surviving.

So, if this is in space, the characters will be fine if they are a good distance away and have something between them and the explosion. If this is in atmosphere, consult nukemap.

Answer 2

You don't need anything special. In space, there won't be any kind of shockwave one inch away from the exploding ship (you can be hit by the shrapnel, though), so the only thing you have to worry is about gamma radiation.

The bad news is that atmosphere is a great absorber of gamma rays, and in the near-vacuum of space the gamma rays will have virtually infinite range. But of course, the amount of energy generated by the explosion will be dispersed by the surface of the sphere whose radius is the distance you are away from the bomb. At one kilometer away, the amount of gamma rays that are going to hit you are not that much, and probably they are not the right energy to cause much harm to your body - they'll just past through. I would be more worried about secondhand radiation by irradiated metals on your ship but bodies are great to deal with radiation as long as it comes in low dosages over time.

If you want to add some credibility, just state that some 5% of the ship's crew gets ill, some of them dying, but your protagonist is not one of them. If you read the accounts of the two incidents of the infamous "demon's core" you'll see that in both cases there were people around, very close to the source, that went seemingly unscathed while other people died. That's just how particle physics work. Sure, the closer you are to the source, the higher the probabilities you are harmed, but it's a game of statistics. Just state that some of your crew is affected and some are not so, and be done with it.

Answer 3

As Much as You Want

Just like normal explosions, antimatter explosions can be any size. More antimatter gives a bigger boom. Less antimatter gives a smaller boom.

You know how much armor the space ship has. You know the reaction you want. The space ship gets banged up but remains in one piece. The crew mostly survives. There is some size of explosion that will achieve this.

Use that much antimatter.

Leave the exact amount out of the story. The characters don't know or they don't say.

Do not waste your time with exactly how many micrograms of hydrogen you need, the purity of the antimatter, the efficiency of the detonation mechanism, the attenuation rate of empty space, the proportion of the gamma rays that pass through harmlessly. This is needless busy work.

What we know is some combination will give you what you want. You don't need to calculate those numbers.

Answer 4

According to the Internet, 1 kg of Antimatter is Thermonuke territory, 1 milligram is 50 Tonnes of TNT.

So, a couple milligrams of TNT is in the realm of 50-150 Tonnes of TNT.

A big boom, but not unsurviveable. Even in the open air at 1 km.

1 gram gets into 5 kiloton realm which is a small nuclear explosion - which is probably what you were thinking of in terms of your distance and Armour