From a [previous comment of mine](https://www.reddit.com/r/EngineeringPorn/comments/cpb3gz/inside_cerns_antimatter_generator/ewozufe/):
> Take a proton beam with several tens of GeV of energy and direct it at a block of metal (iridium is good). Some of the crap that comes out the other end will be antiprotons. You can select antiprotons within a certain momentum range using magnets and collimators, rather like a mass spectrometer. Then you need to cool and decelerate the beam. They can be trapped using a Penning trap or similar.
> To make antihydrogen atoms, you can introduce positrons from a beta+ source. Neutral anti-atoms (as with regular atoms) are more difficult to trap than charged particles. They require the use of lasers as well as magnets.
The scientists at CERN have an [antimatter production program](https://home.cern/science/physics/antimatter ), as do their FermiLab counterparts and collaborators in other countries. You can make anti-particles in high energy colliders, but the first step is to take a beam of anti-protons out of one of those experiments and slow the anti-protons down. This is like a proton accelerator, in reverse (well not really in reverse because they are anti-protons). Then you can add positrons and make anti-hydrogen. Some experiments are also adding anti-neutrons to try and make anti-lithium.
Antimatter elements, besides hydrogen and helium, have not been fabricated. To make antimatter of a subatomic particle, two other subatomic particles are smashed together at stupid-high speed. In the collision, antimatter is sometimes formed. A simpler way to make antimatter, specifically positrons (anti-electrons), is to let certain radioactive materials exist – they will passively form positrons as they decay.
Antimatter is produced typically by blasting electrons through the nucleus of a heavy atom at incredible speeds, nearly the speed of light. This causes the electrons to emit energy quanta that decay into both matter and antimatter, so it is then just a matter of separating and isolating the antimatter.
> Can any antimatter element theoretically be fabricated?
Current theories suggest that yes, antimatter chemistry is likely to behave basically the same to normal matter chemistry. The problem is verifying this because getting any large quantity of antimatter which is cool enough to study is very difficult (remember you are producing it at nearly light speed, you need to get it to slow down to work with it), and manipulating it is difficult considering it will annihilate any material it touches.
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