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.
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