Is antimatter 100% efficient as a source of energy?

[IvanTih]

I know that this is a stupid question,but please don't take this too hard on me.

[Formless]

No.

1) a lot of the energy (half I think?) is wasted in the form of neutrinos.

2) 100% efficiency from any energy source would violate the laws of thermodynamics, specifically the second, otherwise known as-- remember this word because its as important as any word in science you need to know-- entropy.

[SCRawl]

The short answer is "no".

The longer answer follows. Even if you had a source of free antimatter, with a free means of containing it, and a free means of reacting it with matter -- all of which are impossible -- it still wouldn't be 100% efficient. Think about what a matter/antimatter is in the simplest terms possible: electron-positron annihilation. You get a couple of 511 keV photons shooting off in opposite directions. Now I don't pretend to know what the the efficiency of the most efficient way is for turning photons into some sort of energy we can use, but I'm quite certain that whatever it is it's less than 100%.

If you want the complete answer, that requires more serious thermodynamics, a topic about which I've forgotten most of what I ever learned.

[SCRawl]

No.

1) a lot of the energy (half I think?) is wasted in the form of neutrinos.

2) 100% efficiency from any energy source would violate the laws of thermodynamics, specifically the second, otherwise known as-- remember this word because its as important as any word in science you need to know-- entropy.

Actually there needn't be any neutrinos produced in the reaction. The entire rest mass of the electron and positron can be converted into photons.

[Jaepheth]

I forget where on the internet I saw it, but my favorite rephrasing of the laws of thermodynamics goes like this:

1. You can't win
2. You can't break even
3. You must lose
0. You have to play

[Feil]

There are three related answers to this question, none of which actually require knowing anything about antimatter.

1: The mass+energy after any event is the same as the mass+energy before the event (First Law of Thermodynamics). Thus every event may be viewed as '100% efficient', if one defines efficiency crudely as efficiency = (energy out)/(energy in).

2: The entropy of the universe after any event is greater than the entropy of the universe before the event. Or; any event consumes negentropy. (Second law of Thermodynamics). Any time something changes in its own inertial reference frame, that is an event. Thus, no event is '100% efficient' if one uses the strict physical definition of efficiency: efficiency = (usable mass+energy out)/(usable mass+energy in) = 1-(waste mass+energy out)/(usable mass+energy in).

3: Efficiency only has meaning if you use the usable mass+energy out, e.g. to do work, to decrease the entropy of a system (while nonetheless increasing the entropy of the universe), to store chemical potential, etc. Thus the question is meaningless until you say what you want to do with the energy from the event.

[Ariphaos]

Actually there needn't be any neutrinos produced in the reaction. The entire rest mass of the electron and positron can be converted into photons.

If you find a way to store grams worth of free positrons for extended periods, let us know.

For proton-antiproton, the minimum amount of neutrinos created accounts for 56% of the annihilation energy. I posted a link showing what happens in a previous discussion on this, which goes over the neutrinos created and their energies.

[SCRawl]

Actually there needn't be any neutrinos produced in the reaction. The entire rest mass of the electron and positron can be converted into photons.

If you find a way to store grams worth of free positrons for extended periods, let us know.

For proton-antiproton, the minimum amount of neutrinos created accounts for 56% of the annihilation energy. I posted a link showing what happens in a previous discussion on this, which goes over the neutrinos created and their energies.

Oh, I never meant to suggest that I had a serious suggestion about how to go about building such a reactor. But I dismissed Formless' statement out of hand without warrant: I had electron-positron annihilation on the brain, and considered no other modes. (It's always the easiest for me to remember, maybe that's the reason.)

[Junghalli]

Also unless the antimatter is surrounded by a much larger mass of matter (or visa versa) I imagine there'd be a fairly high probability that at least a few atoms of matter and antimatter fail to be annihilated, so there's another possible inefficiency.

[someone_else]

According to Comparison of Fusion-Antiproton Propulsion Systems for interplanetary travel (which contains much more meat than this):

Around one third of the annihilation energy goes into two 200 Me gamma rays per proton-antiproton annihilation, and around a half of the total energy is lost in neutrinos if you don't do nothing.

The result of the article is more or less "it's not worth the effort", also because they clearly state to blissfully ignore the whole cadres of devils in the details of storage system and fuel lines.
They also say that by 2010 the antimatter production could be enough for use as a fuel though. Anyone got some antimatter for me?

It lists a few concepts:

-Something resembling a NERVA, but with a tungsten core that stops all the annihilation energy somewhay (probably unrealistic assumption, but I don't really know), with a 88% conversion efficiency from antimatter to heated propellant. But say that neutron production from interactions is significant. It also states that by using Tungsten-184 (isn't a neutron poison) as a structural material in a more conventional NERVA, you get the same higher-temperature-without-melting-the-core benefit that was the main advantage of antimatter over fission in this particluar design.

-an "antimatter-energized, magnetically assisted hydrogen thermal rocket" which is similar to a Gas-core nuclear rocket. Antimatter heats a tungsten plasma that in turn heats propellant.
That assumes a total loss of gamma ray power, and says that only 35% of the remaining energy (so 35% of the 75% of the total, which is around 26% of the total) can be converted into thrust power (kinetic energy of exaust).
The liquid-core version still enjoys the higher-temperature-without-vaporizing-the-core benefit over the LCRs, but that's about it.

-an "Antiproton Heated Magnetically Confined Plasma Rocket" which is more or less a "throw antimatter into the propellant until it is white-hot plasma" approach.
It ran into three brick walls:
1)too much braking radiation to make it substantialy better than the others above
2)too short time for the relativistic annihilation products to bump on plasma atoms and thus transfer them their energy before decaying into annoyingly uncaring neutrinos.
3)gamma rays damage and overheat your reactor.
That will net you only a pityful 18% of the annihilation energy (that you can then harvest using a MHD in your generator), and recovering gamma rays requires heat-conversion equipment that would be heavy on a spacecraft. And frankly, if you wanted to use heat-conversion systems to extract the energy out of it, you should have used one of the above.

Please remeber, these are engines. If you want to get electricity, you need to place a generator on that, so you need to look at the generator's own efficiency too, which (rather unrealistically) I'll say is around 45%.
A power plant for any of them will be huge, and probably not that different from nuclear power plants of today at first glance.
The NERVA-like method would give you a good 40% antimatter-to-electricity efficiency, if the assumptions they made aren't so wrong (I suspect they are a little optimistic).
The second's ("antimatter-energized, magnetically assisted hydrogen thermal rocket") overall antimatter-to-electricity efficiency could be around 12%.
The third's efficiency could be 15% or so because MHDs are very efficient energy-conversion systems.


You say you had in mind electron-positron annihilation. That would only generate two 511 keV photons that you will stop with something (not that hard for a power plant), then convert the heat with the usual coolant-turbine-generator. That's the usual 20-40% efficiency of those thermal conversion systems.

You want your generator for a spacecraft or for ground installations?

[someone_else]

Also unless the antimatter is surrounded by a much larger mass of matter (or visa versa) I imagine there'd be a fairly high probability that at least a few atoms of matter and antimatter fail to be annihilated, so there's another possible inefficiency.

That was atomic rocket's busting antimatter bombs, in a reactor you have much more control over the reaction and can shoot a few anti-protons/anti-electrons per second in the coolant/target instead of dumping your whole antimatter tank in it.
You don't wanna blow up after all.

[Bottlestein]

"Short Answer": No - 3 reasons:
1) No such thing as "ground state" electron & positron system - 2 fermions cannot exist in the same state. Thus, the "e=mc^2" is strictly higher than "usable work" or "availability" (for the more engineering minded). This will show up in a rigorous analysis as differing spins of the outgoing photons. (It takes either electric or magnetic energy to alter the spins of photons).

Assuming our solar sail was 100% efficient (patently false assumption, but we are talking "best case scenario" here) -i.e. photons of the correct polarization hitting the boundaries completely converting all KE into work, we get into the thermodynamics issues:

2) Internal energy of photon gas < Sum of "e=h* frequency" of individual photons. Again, this is a result of the photons having different spins, and the transitions between states as a result of this. So, even if we insulated the system from heat loss (impossible), we still would not get "Sum of individual photon energies = Usable work", which is the condition required for any rational definition of 100% efficiency.

3) Carnot upper bound efficiency: 1 - T(cold reservoir)/T (hot reservoir)
It is clear from the above formula that 100% efficiency exists if and only if Temperature of Cold Reservoir of our heat engine= 0 Kelvin. This is impossible - even from a quantum perspective (c.f Casimir effect and Feynman's Lectures on Physics for "Zero Point Energy"). Plus, "empty" space has a rough temperature around 3K.

Note for interested parties: The 2nd law of thermodynamics is the principle used to calculate the Carnot upper bound efficiency, so that is where it enters the analysis.

Further references for those interested:
Spins of Photons: Shankar's "Principles of Quantum Mechanics" is the undergraduate text of record for the subject - it covers all 1) and 2) in sufficient depth for anyone who has read it to follow and expand all the ideas presented here. (Though for physics non-major undergrads: Caution - Tensor products and the Hilbert Space formulation required for quantum mechanics is pretty much assumed for phys. undergrads exiting their 2nd year - so gauge your own mathematical maturity before selecting QM texts. For Phys - major undergrads: you'll have to go through Shankar anyway - so buck up and start reading it early ).

For thermodynamics (and part 3): Kittel and Kroemer's "Thermal Physics" is a good text, used for freshmen who are physics majors (possibly sophomore non-majors). The mathematics is simple enough that a high school calculus course more than suffices. The writing is clear such that high school physics should again be more than enough to understand everything presented. Bonus: the solutions to the problems are online since millions of freshmen have worked through it