Setting aside concerns of containment for now; how much energy would it take to create antimatter? And how much of it would we get back using it as a fuel in a matter-antimatter reactor?
What I'm worried about is that the amount of energy you put into making antimatter is less than the amount of energy you get back during annihilation. I was also looking to get a general idea of how much of a gain/loss there would be.
In general, L.Dutch's assessment of the energy returns on sythesized anti-matter are correct. But there are some considerations.
L.Dutch is referring to the pair-production method of creating anti-matter. Pair production is the creation of a particle and anti-particle from a boson. A photon (which is a boson) with more than 1.022 MeV of energy can form an electron and positron. However, there is another method, which is positron emission, from the radioactive decay of certain isotopes.
OP suggests in comments that you only have to create the anti-matter, and not the matter, so you might be able to get back more than it cost to make the anti-matter. For pair production, as you have seen, there is always both a particle and anti-particle produced, so this doesn't help you. You have to produce both the matter and anti-matter.
But this isn't necessarily a bad thing. Even if it costs you more energy (counting production inefficiencies) to make a gram of antimatter than you would get by annihiliting it for energy, that can still be a good idea. This is basically the principle of the electric car: it takes more energy at the power plant to generate electricity for your car than your car gets by using up its battery full of energy. But this is still a good idea, because the car is a mobile transportation system, and you simply can't have a high efficiency power plant or green wind turbine on your car to provide power. You need the lower efficiency battery. Similarly, if you are using an anti-matter rocket to travel the stars, you don't have any alternatives. You need the anti-matter to power your rocket, no matter how much electricity/energy it takes to create it in the first place.
But lets get back to positron emission. This allows you to avoid 'creating' anti-mattter at all. If you find a way to get a lot of a certain isotope, and then catch all the positrons it emits as it decays, then you are basically getting anti-matter for free.
The way this is done now is with a cyclotron, with a method such as positron emission tomography (PET). The cyclotron is used to create the desired isotopes that will undergo positron emission as they decay. However there are two downsides for using this as an energy source. First, you are directly creating the isotopes in question with a particle accelerator, so you run into the same energy-in/energy-out constraint. Second, there is no method for capturing the generated positrons.
In order to 'mine' free energy from positron emitting isotopes, we must find a source of them in nature that we can exploit.
Most of the isotopes used for PET have short half-lives, by design. After all, the purpose is to have trace amounts of such isotopes emit enough radiation to be detectable by medical instrumentation. But there are some options with both short and long half-lives that might be found in nature.
Potassium-40 one of the most important isotopes on this list, with a half-life of 1.25 billion years. It is one of the main reasons the Earth's core is so hot, as radioactive decay of potassium over time has kept adding heat up to the present day. It has a natural abundance of 0.012%, so anywhere you find potassium, you will find K-40. Of note, since it is produced in supernovae, it is more common in young systems. If you looked in the dust cloud of an exploded star, K-40 would be at least 30 times as common as it is on Earth.
Nitrogen-13 has a short half-life, but is sometimes produced by lightning. Not only could you potentially find in in Earth's atmosphere, but on other planets with both lightning and nitrogen compounds. Venus has lightning, but little to no nitrogen in its atmosphere. Jupiter and Saturn both have ammonia in high clouds and ammonium hydrosulfide in their lower clouds. I don't know of any way to capture N-13 within a few minutes of a lightning strike on Saturn, but it is at least theoretically possible.
The magic formula here is the well known $$ E=mc^2 $$
To create a given mass of antimatter (assuming the yield of the energy matter conversion is 100%) you need exactly the same amount of energy you would get back with the annihilation.
So, unless we find a mine of antimatter or a source of energy available "for free", it doesn't make sense to synthetize antimatter and then burn it (also because we would start putting yields in the picture, so we could not reach break even if we had to pay for the initially used energy. Using a cost 0 energy instead make whatever small energy outcome a net profit).
Your question is the same as "why don't we synthetize gasoline to run our cars?" We use gasoline because oil is already stocked up in the ground.
The first comment is right. In every case, when dealing with finities, you lose energy by synthesizing fuel.
If you think of a balloon as a storage mechanism, then the energy lost is from:
To put it plainly, every kind of fuel is trapped energy, and the trapping process always leaks energy in another form. The efficiency of that process is dependent both on the natural circumstances and on our own technical knowledge, but in an ideal case peaks around 95%
By comparison, our current energy storage mechanisms have a round-trip efficiency that ranges from 45% (hydrogen) to up to 95% (lithium-ion battery that isn't filled to it's full capacity) real-world more like 87% (Tesla Powerwall). For fuel-oil down-conversion to gasoline, there's around 85% efficiency, but the energy doesn't have to be generated, as we're using found energy.
The real driver of these technologies is convenience and applicabilitiy to a particular purpose. Even for rockets, we use the most convenient and applicable fuels for that specific purpose. Hydrogen is generated at 60-90% efficiency, and lots of energy is lost in the process of burning the fuel to launch the rocket to space. But, it gets the job done. For cars, now that electricity can be stored in energy densities that parallel gasoline (not quite there, but close enough) we're switching to electric, because it's easier. The applicability of the fuel for the specific purpose and the difficulty of handling the material matter a lot.
The crux of the issue is that the efficiency of creation can't realistically be separated from the difficulty of handling the material itself. And dealing with antimatter is HARD. If it's charged, or if it's ferrous antimatter, you can contain it with magnets. If not, you can.. ..what.. ..push it around? Nope. If it's ferrous, it's probably solid. How exactly do you plan to use that again? ..or wait.. ..to generate it? How are you going to get an iron antimatter block, even if you can generate iron antimatter molecules? ..melt it with lasers while containing it in a magnetic field, I guess, but.. ..eesh.
All of this boils down to the simple extreme probability that long before we have the ability to readily handle antimatter, we will have developed extremely efficient nuclear fusion or fission options. Bear in mind, the reality you're dealing with on energy density is:
1 part antimatter + 1 part matter = 2 parts energy
1 part matter + 1 part matter via fusion or fission = 2 parts energy
edit: that is to say, any talk of 'free' energy should consider that all nuclear, including antimatter, will have a large overhead, but are the harvesting of free energy. The advances in nuclear at this point will come in cleanness and in controllability, such as with molten salt reactors and laser fission. These processes will be convenient from our current standpoint, and will be improved as time goes on. /edit
..and the second is easier to work with, and therefore easier to generate efficient processes for. Again, we can count on the idea that for a readily-accessible, handlable technology with good natural conditions, we'll peak around 95% efficiency, round-trip. ..and that'll be long after the thing was used ubiquitously.
