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What actually happens when an anti-matter projectile collides with matter?
Suppose 1 kg of a stray meteorite anti-matter moves to the earth.
Over here, I'm assuming that the antimatter is atomic antimatter--e.g. made of antiatoms. If it were made of some other antiparticles, then it wouldn't have much of an effect (aside from decaying on its own).
What would happen after the collision matter and the anti-matter?
Whenever antimatter meets matter (assuming their particles are of the same type), then annihilation occurs, and energy is released. In this case, a 1 kg chunk of the earth would be annihilated , along with the meteorite. There would be energy released in the form of gamma radiation (probably).
Is there a way to produce antimatter here on earth?
Yes, particle colliders routinely produce antiparticles every day. In these colliders, beams of particles accelerated to a high speed collide (with a target or with each other), spewing out a bunch of more exotic particles (which include antiparticles). These are usually short-lived.
Antiatoms are harder, since preserving the antiparticles for the time that it takes to bring them together is difficult. Nevertheless, we have been able to make and preserve antihydrogen for ~15 minutes.
But producing this for use is harder (especially large quantities). Antimatter is extremely difficult to store (since it'll just annihilate whatever walls you put it in).
Why antimatter bombs more powerful than the atomic bomb?
Atomic bombs convert the binding energy of the nucleus into free energy. The binding energy is part of the mass of the atom (mass=energy), so basically a small part of the total mass is converted into free energy.
On the other hand, in a matter-antimatter collision, all the mass is converted into energy. For a 1kg ball of antimatter being annihilated, we get $E=mc^2=(1 \mathrm{kg}+1 \mathrm{kg})\times c^2=1.7\times 10^{17} \mathrm J$
In contrast, Little Boy (The Hiroshima bomb) contained $64 \mathrm{kg}$ of uranium, of which only $\approx 700 \mathrm{mg}$ was converted into energy, releasing $\approx 65 \times 10^12 J$ of energy. The strongest atomic bomb (IIRC an H-bomb) created till date was a few thousand times as strong as Little Boy. Still off from the antimatter bomb by a few orders of magnitude.
So we have a 100% mass-to-energy efficiency for antimatter, whereas Little Boy has $\approx 0.001%$ efficiency. Quite a big difference.
1kg of antimatter will annihilate 1kg of matter and release $2c^2 = 1.8 \times 10^{17}$ joules of energy. To put this in perspective, this is enough energy to melt about $10^{11}$ kg of granite. For comparison the weight of Mount Everest is about $10^{15}$ kg, so it wouldn't cause wholesale melting of the Earth. In fact the energy of the meteor that killed the dinosaurs is estimated at $4 \times 10^{23}$ joules, so while I wouldn't want to be near the antimatter when it annihilated, it's unlikely to wipe out all life on Earth.
Having said this, the point about the antimatter annihilation is that all the energy is released in a very small area (while the Chicxulub meteor was 10km across) so the explosion would be very violent indeed.
Antimatter is produced naturally in very small amounts. Energetic particles hitting the atmosphere naturally produce anti-matter. The LHC also produces anti-matter, but again in tiny tiny amounts. According to http://www.engr.psu.edu/antimatter/papers/nasa_anti.pdf the global production of anti-matter is about 10 nanograms per year, so making your 1kg of antimatter would take 100 billion years or about 10 times the age of the universe.
Assuming enough anti-matter could be produced to make a bomb, the reason an anti-matter bomb is so effective is because it creates an enormous energy density i.e. it releases all it's energy into a small volume. The biggest nuclear bomb ever detonated was the Tzar Bomba, and by co-incidence this released about the same amount of energy as the annihilation of your 1kg of antimatter. The Tzar Bomba was 8m long and weighed 27,000kg!
