How is antimatter made in laboratory? Can anyone explain, at the particle level, specifically how anti-protons and anti-electrons are made?
[Physics] How is antimatter made
antimatterexperimental-physicsparticle-physicsquantum mechanics
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There is some freedom in deciding which particle in a particle-antiparticle pair is called "matter" and which is called "antimatter" but the freedom is smaller than you think. A basic problem is that your sentence
Antimatter of course annihilates ordinary matter, but the more precise statement is that antiparticles annihilate the same types of particles.
isn't really true. In fact, the opposite statement, while inaccurate, is much closer to the truth: matter and antimatter often can annihilate even if they belong to different species.
For example, a proton will rapidly annihilate with an antineutron (or an up-quark with anti-down-quark, if we look at the same process at the quark level), leaving some positron and neutrino (whose rest mass is much lower than the rest mass of either proton or antineutron) with lots of energy.
The up-quark and down-quark are different species or flavors but it would make no sense to call one of them "matter" and the other "antimatter" because they can "almost annihilate" to "almost nothing". More generally, all quark flavors are similar and it's better to call all of them "matter", especially because they may be related by symmetries that don't have a reason to include charge conjugation C.
Now, the atoms are composed of protons and electrons – and we call the atomic bound states "matter". That implies that an electron has the same "pro-anti" label as the six quarks. There are no bound states between positrons and protons so there would be no atomic "matter" if you flipped the convention for electrons but not protons.
Grand unified theories actually do link some 2-component spinors to larger representations and these representation contain fields that create both matter and antimatter so the binary label "pro-anti" becomes more subtle in such theories. We must still carefully distinguish a field and its Hermitian conjugate.
The "pro-anti" dichotomy remains meaningless for some particles, anyway. There are totally neutral particles – photons, Z-bosons, gluons, gravitons – that are identical to their antiparticles so here there is no "polarization", of course. There are also charged particles, W-bosons, for which it makes no sense to ask which of them is matter and which of them is antimatter. A W-boson may decay to a quark-antiquark pair so it's equally "far" from matter as it is from antimatter.
Neutrinos seem to be Majorana particles so far so they are identical to their antiparticles, too. However, the helicity (left-handed, right-handed) is correlated with the usual labels "pro-anti" which means that we can distinguish matter from antimatter, after all. There can also be right-handed neutrinos in which case the separation of neutrinos to "matter" and "antimatter" is exactly as possible (in principle) as it is for electrons and positrons.
This Centauri Dreams article claims that a 0.01% efficiency is possible with current technology if there was a dedicated production facility.
Having searched for information on this problem myself, I have found nothing more of significance.
If you can get past the google scholar paywalls, you may want to look through the articles by Robert Forward who is referred to as the source of the information.
Best Answer
Creating anti-protons is straightforward in principle because any high energy collision produces a shower of protons, antiprotons and various types of pions. The pions decay in a few nanoseconds, so you just have to wait for the pions to decay then separate the antiprotons from the protons.
At Fermilab a 120GeV proton beam was collided with a nickel target to produce the protons and anti-protons. The proton/antiproton mixture was first passed through a lithium lens to produce a collimated beam, and subsequent magnetic separation produced separate beams of protons and antiprotons.
Although making antiprotons is easy, if by making antimatter you mean making neutral antimatter like antihydrogen that's much, much harder. The energies of antiprotons created from the nickel target are far higher than the ionisation energy of (anti)hydrogen, so the antiprotons need to be cooled and trapped then reacted with positrons to create antihydrogen.
The first significant amounts of antihydrogen to be made were created by the Alpha group at CERN. There's a nice video that describes their experiment here. They hold the antiprotons in a magnetic trap then adjust the field to allow them to come into contact with the positrons.