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From what I've learned, fusion reactions are not currently economically viable as of right now because the energy required to start the reaction is more than the energy actually released. However, in stars they have immense pressures and temperatures which are able to allow these reactions to take place. However, if these reactions are considered endothermic for us, how are they exothermic in stars? i.e. how are stars able to release energy?

Moreover, why are such fusion reactions for us endothermic in the first place? Given we are fusing elements smaller than iron, wouldn't the binding energy per nucleons products be higher and hence shouldn't energy be released?

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    $\begingroup$ They are not endotermic for us. $\endgroup$
    – nasu
    Oct 28 at 12:26
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    $\begingroup$ You've answered your own question: "in stars they have immense pressures and temperatures" which are very difficult to reproduce on Earth. Also, stars are very large, so a small amount of star might not produce all that much power. A quick search doesn't find an answer. It's not as simple as taking the energy output of the sun and dividing by the volume, because the fusion happens towards the core. The outer layers are just to keep the temperature & pressure in :-) $\endgroup$
    – jamesqf
    Oct 29 at 3:31
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    $\begingroup$ Economy of scale :) $\endgroup$
    – fraxinus
    Oct 29 at 6:36
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    $\begingroup$ When you burn wood splinters with a flame thrower you end up net negative, but you cannot say the combustion of the splinter was endothermic... $\endgroup$ Oct 29 at 15:03
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    $\begingroup$ Correction: The pressure in a star's core is immense (measured in petapascals, far beyond what we've achieved). Temperatures are actually rather cool compared to fusion reactions on Earth -- ITER, for example, runs more than 5x hotter than the Sun's core. We have to run it much hotter because we can't control it well and we can't pressurize it nearly as much, nor can we wait around for the energy like a star can. $\endgroup$
    – Charles
    Oct 29 at 16:39

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The Sun is fabulously inefficient as a fusor: in a given year it consumes only about $10^{-10}$ of its fuel. For the Sun that’s actually a good thing, because it took us five billion years to notice. But an Earthside reactor where you have to confine and control a billion times more fuel than you actually use is quite different from the approach we’ve taken through history.

The Sun also operates at very low power density: in the hottest part of the core, about a hundred watts per cubic meter. You can imagine reproducing this power density by filling the inside of your house with scaffolding and operating one light bulb every cubic meter. It’d be warm, for sure, but not solar-warm; you might not even need to re-wire your house. You could get higher power density than the core of the Sun just by setting your house on fire.

The reason the Sun is still useful as a power source, despite its fabulous inefficiency, its low power density, and its astronomical distance, is that the Sun’s power-generating core is mind-bogglingly large.

At constant power density, the amount of effort it takes to confine a hot plasma goes roughly like its surface area (because you only have to push on the outside surface). Suppose I have a tokamak which produces a certain amount of fusion power and has a certain cost to keep the plasma contained. If I build the same design but three times bigger across, I expect the cost of confining the plasma to increase by a factor $3^2 = 9$. But if I keep the energy density the same, the energy output should go up like the volume, by a factor of $3^3 = 27$. The engineering question then becomes whether I can make the tokamak large enough that the power produced outstrips the containment cost, while still having it fit on Earth, in a building. (A big building would be okay.)

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    $\begingroup$ Beautifully written answer. $\endgroup$ Oct 29 at 12:13
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    $\begingroup$ Cube square law in action… $\endgroup$
    – Drunix
    Oct 29 at 13:34
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    $\begingroup$ It's not really so much inefficient as it is slow. $\endgroup$ Oct 29 at 19:16
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    $\begingroup$ @Acccumulation I would strongly disagree with you on what 'wattage' means - but it might be a regional thing. In Australia wattage refers to the actual power draw. LED lights are often 10W or 15W but are marketed as "60W equivalent" or "100W equivalent" despite having a wattage of 10 or 15 watts. Where are you from? $\endgroup$
    – fabspro
    Oct 30 at 1:49
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    $\begingroup$ @rob Coincidentally, the power output of an adult human not exerting themselves too much is also about 100W. So the power density of the sun is about the same as that of a slightly crowded party. It's only that on the sun it is impossible to remove the resulting heat by opening a window. $\endgroup$
    – mlk
    Oct 30 at 22:07
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None of the other answers (so far) mentions gravity. At least one of them mentions confinement though. It talks about the cost of confinement and, about the consequences of not confining a reaction well enough or long enough to extract any benefit from it.

Stars, on the other hand, get confinement "for free" by virtue of the gravitational binding of their enormous mass.

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    $\begingroup$ So you're saying all we need to do is build a reactor several hundred thousand times the mass of the Earth and we'll be golden. $\endgroup$ Oct 29 at 0:16
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    $\begingroup$ @DanielR.Collins: We already have one. It's the Sun. $\endgroup$ Oct 29 at 1:54
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    $\begingroup$ @Daniel You only need ~4,000 Earth masses to make a brown dwarf, which has enough heat of formation to fuse deuterium. OTOH, you do need a lot more mass for sustained deuterium fusion $\endgroup$
    – PM 2Ring
    Oct 29 at 3:30
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    $\begingroup$ Wow, that joke did not land. $\endgroup$ Oct 29 at 4:18
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    $\begingroup$ @DanielR.Collins I wonder if finishing with we'll be bronzed would have helped :) $\endgroup$
    – Caius Jard
    Oct 29 at 8:54
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It is the fact that fusion reactions are very exothermic that makes them so hard to control.

Coal releases its chemical energy so slowly that a coal fire does not need any confinement - it does not blow itself apart. Refined hydrocarbons, such as petrol, release energy more violently, but the walls of a metal cylinder are strong enough to contain the explosion (e.g. in an internal combustion engine) or at least direct the explosion products in a useful direction (jet engines, rocket engines).

We have various ways of achieving nuclear fusion (see this Wikipedia article for an overview) but they all either blow themselves up (thermonuclear devices), require too much power to achieve confinement (magnetic and inertial confinement devices) or produce a low density of reactions (colliding beam devices).

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    $\begingroup$ Detonation is not a normal operation mode for an internal combustion engine! $\endgroup$
    – Ruslan
    Oct 28 at 21:44
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    $\begingroup$ @Ruslan Detonation IS the normal operation mode for an internal combustion engine! That's the Combustion part. Black smoke is incomplete combustions. The engine block is super reinforced in ICE engines and are basically compact rapid explosive devices. It creates explosions hundreds to thousands of times a minute. $\endgroup$
    – Nelson
    Oct 29 at 13:35
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    $\begingroup$ This feels like a very pedantic debate. "Detonation" (a word which I'll note gandalf61 did not use) is a specific technical term used to describe combustion happening when the spark plug is not firing. To describe an ICE as involving "explosions" seems entirely adequate to me. $\endgroup$
    – Kirk Woll
    Oct 29 at 14:17
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    $\begingroup$ @Ruslan Both detonations and deflagrations are explosions. The difference is that detonations involve supersonic shock waves and deflagrations do not. The process of igniting a hydrocarbon/air mixture in an ICE usually creates a deflagration rather than a detonation (which would be inefficient) but this is still an explosion. $\endgroup$
    – gandalf61
    Oct 29 at 17:43
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    $\begingroup$ Gasoline is a low explosive. Its combustion releases gasses that produce high pressure, which is not quite the same as high explosives, which arguably is what people think of when they think of "explosives". The confinement of gasoline is the cause of, not the response to, it exploding. There's nothing stopping one from using gasoline in an external combustion engine, other than efficiency. It's also a bit odd to contrast "hydrocarbons" with coal, as coal is a hydrocarbon. If one tried hard enough, one could make an internal combustion engine that uses coal as fuel. $\endgroup$ Oct 29 at 22:39
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However, if these reactions are considered endothermic for us, how are they exothermic in stars?

The reactions are still exothermic for us. In fact, they are very exothermic. The fact that they are not net energy producers is due to inefficiencies in our existing technologies for producing these reactions, not because the reactions themselves are endothermic. In other words, our fusion devices waste a lot of energy, heat that leaks out to the environment and so forth. So even a highly exothermic reaction does not compensate for all of the waste and inefficiencies.

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    $\begingroup$ In addition to not harvesting all the power of the reactions, there is also all the power we need to put into magnets to hold the fusioning plasma in place, as well as other power needs a running reactor might have. $\endgroup$
    – Arthur
    Oct 28 at 20:53
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As others have pointed out, the fusion reactions inside the sun and man-made on Earth are exothermic. Per mass of reactant, they release far more energy than any chemical reaction, and even more energy than fission.

Even the experimental reactors technically produce energy. If you take the Q=0.67 result from JET, then 24MW went in, 16MW was generated, and 40MW came out. For ITER, the projection is 50MW in, 500MW out.

But both of these are a long way from being economical. ITER is not even designed to generate electricity, but if it was, it would struggle to generate more than it consumes. That 50MW to heat the plasma comes from complex machines (fancy microwaves and particle beams) that run on electricity, with about 50% efficiency. So the input in terms of electricity is 100MW. On the output side, you have to deal with the Carnot efficiency, so that 500MW of heat will only generate about 200MW of electricity (40% efficiency). By the time you run pumps for the reactants, exhaust, coolant for the superconducting coils, a whole bunch of measurements... there's not a lot left over.

So a fusion reactor based on the ITER design that produces electricity has to be much larger. Designs at the moment aim for about 3000MW of energy for an output of 1000MW net electricity. Based on those designs you can start talking economics, but it's complicated. That reactor has cheap fuel, but expensive components. Superconducting coils, microwaves, radiation protection... it's hard to predict what the end cost of electricity would be based on these costs if we're still figuring out how to build the reactor.

As others have pointed out, the sun doesn't care about economics. Hasn't turned a profit in millennia. And by human standards of power density it is actually fantastically inefficient. But that's fine by me. It's about the right amount of power to keep Earth in a stable life-supporting temperature range.

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The problem is not with “creating” fusion: we have H-bombs that will do this. The technical difficulty is with controlling the very exothermic fusion process, so the whole thing doesn’t blow up violently.

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Whether a fusion reaction is exothermic or endothermic depends on the binding energy of products relative to reactants as you suggest. It does not depend on the environment. However, the rate at which the reaction occurs does depend on density and temperature. These determine how often nuclei collide and what proportion of collisions result in fusion (overcoming electrostatic). Even for the easiest fusion reactions (e.g., the D+T reaction) temperatures of millions of degrees are required for a non-negligible reaction to occur.

The reason current fusion reactors consume more energy than they release is due to the energy required to heat and contain the hot plasma. The plasma in current reactors loses energy more quickly than fusion reactions release it.

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For the second part of your question, you have noted that all the lighter elements have binding energy less than iron. Binding energy is the energy that needs to be supplied to unbind something, so the binding energy of an iron nucleus is the energy you would need to supply to split that nucleus into protons and electrons (recalling that a neutron will break down to a proton and an electron). Fusion releases that energy when the hydrogen in a star is converted to other elements including iron.

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The reactions are exothermic. But in a volume the size of the sun, the fusion reactions are so deep within the star (within its core), and in such dense material (the core), that they cant easily lose all their energy to the outside.

  • Photons can take thousands if not millions of years to exit the core.
  • Heat is retained because it's produced based on VOLUME, but lost via SURFACE AREA - a larger sphere has much less surface area per unit volume to lose/disperse energy,and the sun is vast by human standards.
  • Confinement is due to sheer mass, gravity is effective at this.
  • Gravity not only confines, it also maintains immense pressure.

So the sun itself, even though it's not very efficient a heat engine, produces enormous heat, just because of its sheer vast size negating all these issues. The core cant easily lose heat, or reduce pressure. Even a relatively slow heat buildup keeps accumulating, because the heat cant be lost easily, and also there is immense pressure, all throughout the immense volume of the core. Any loss of pressure or temperature within the core, or reduction in fusion equilibrium, results in the core shrinking which increases pressure and temperature, so it's largely a stable situation while fuel exists.

So fusion is easy, and sustains itself, with very high TOTAL energy output, even though the heat production is technically quite low per unit volume and pretty inefficient.

What we are trying to do on earth, is find a way to confine the heat and fusing particles, without any of these advantages of immense size or gravity. It's very easy to lose energy, on the scale of any plausible human-built fusion reactor. It's very hard to confine properly.

This is what the challenge is about.

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As I see the core of your question is based on the “exothermic/endothermic” problem.

Fusion reaction is exothermic both on earth and on stars. When one binds two light elements, one ends up releasing energy always. The negative energy balance of fusion apparatus on earth is not due to the fusion reaction mechanism itself. It comes from the enormous energy necessary to keep atoms close enough to allow the fusion reaction to be sustained after initiated. As you noticed, in stars, this containing energy comes for free from the huge gravitational push that stars have. On earth, the containing energy is usually taken from incredibly high strength magnetic fields, which need an equivalent high consumption of electricity.

Because of this high energy consumption to keep the plasma contained, we cannot sustain the fusion reaction long enough to get back the energy spent to start the reaction plus the energy needed to keep it running on a reasonably amount of time.

An interesting fact is that the ratio of the energy consumed to contain the plasma by the energy gained from the reaction reduces inversely with the size of the reactor. The problem is that we still need incredibly big installations to make it cost effective using current technology.

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