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In Star Trek, the fundamental concept of warp drive requires anti-matter and matter combinations to produce the needed energy. Yet, for this importance, I haven't come across any reference to how antimatter is produced (Memory Alpha contained no hints). So how is antimatter produced in the 24th Century (or 23rd century if there is any reference to it then)?

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In terms of realistic physics, it's pretty hard to make any sense out of Star Trek's use of antimatter. Any time a ship crashed or was destroyed in battle, the antimatter would be released, and the result would be an explosion big enough to sterilize an entire planet. –  Ben Crowell Apr 4 at 3:50
    
@BenCrowell: Do we know exactly how much antimatter a ship is carrying? –  PlasmaHH Apr 4 at 8:34
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@PlasmaHH: The Next Gen Technical Manual says on pages 67-68 that they have thirty storage pods with a volume of 100 m^3, for a total supply of 3000 m^3. They also say that antihydrogen is stored as liquid or slush. And liquid hydrogen has a density of 70.85 kg/m^3, so that would work out to 212,550 kg of antihydrogen. That would contain 1.9*10^22 Joules of energy, and double that would be released reacting with matter, about 9 million megatons according to en.wikipedia.org/wiki/TNT_equivalent (360,000 H-bombs). –  Hypnosifl Apr 4 at 12:42
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@PlasmaHH - The energy might be distributed differently but I don't think it'd heat up the atmosphere lethally, the atmosphere has a mass of about 5.3*10^18 kg according to scipp.ucsc.edu/outreach/balloon/atmos/The%20Earth.htm and the average mass of an air molecule is about 4.74*10^-26 kg, so about 1.1*10^44 molecules...adding 1.9*10^22 Joules adds 1.7*10^-22 Joules per molecule, then using the thermodynamic "equipartition theorem" (idealizing the atmosphere as constant temp) we should have (7/2)*kT1 + 1.7*10^-22 = (7/2)*kT2 or (T2 - T1) = (2/7)*(1.7*10^-22)/k = 3.5 degrees C or so. –  Hypnosifl Apr 4 at 13:54
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If the Enterprise has the same mass as the Queen Elizabeth 2, then to accelerate it up to half the speed of light, you would need about 10^24 J. Assuming the same mass, the amount of energy inferred by Hypnosifl would be enough to get the ship up to about 7% of the speed of light. Re the amount of destruction, you would have to worry about effects analogous to nuclear winter en.wikipedia.org/wiki/Nuclear_winter , but the Enterprise is clearly the ultimate weapon of mass destruction, and I wouldn't want it in my solar system. –  Ben Crowell Apr 5 at 1:45

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The semi-canonical Star Trek: The Next Generation Technical Manual is deliberately vague on this, just referring to some unknown form of "charge reversal devices" on p. 67, but they do at least specify that Starfleet has special facilities for antimatter production:

As used aboard the USS Enterprise, antimatter is first generated at major Starfleet fueling facilities by combined solar-fusion charge reversal devices, which process proton and neutron beams into antideuterons, and are joined by a positron beam accelerator to produce antihydrogen (specifically antideuterium). Even with the added solar dynamo input, there is a net energy loss of 24% using this process, but this loss is deemed acceptable by Starfleet to conduct distant interstellar operations.

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Today, very small amounts of antimatter are produced. Most are in the form of positrons, some are produced in the form of anti-protons, and there are a few labs making anti-hydrogen (a full positron/anti-proton pair).

It takes more energy to make it than would be released if it was utilized. This is a basic principle of physics, after all.

There is a nuclear fission principle though, that of the "breeder reaction". They experimented with this sort of nuclear reactor until the 1980s or so. It exploited some weird side reactions, such that as you cooked the uranium (plutonium? I'm not familiar with the details) it also cooked the other radioactive elements in the fuels rods turning them into more fuel.

Hypothetically, if there were a similar reaction for antimatter, such that annihilating it with matter caused nearby particles to convert into antimatter, then you would be able to make more of the stuff easily. It would be sort of like if when using gasoline in a internal combustion engine it caused the air to spontaneously turn into gasoline. Only, with antimatter there might be some formulation of this that didn't necessarily violate entropy.

I've also read other theories that suppose that you might "rotate" normal matter through higher dimensions, such that when it reappeared to us in our dimension it would have become antimatter. Of course, every few weeks someone is claiming that there are 30 higher dimensions or none, so this might be bunk too.

Star Trek itself has mostly been silent on the details of its own process, for the same reason that we never see the cops on Law and Order ever bother to fill up the gas tanks of their department-issued vehicles.

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