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Nuclear fission reactors are fairly common, but what technological/physical limitations are currently impeding developing the nuclear fusion reactor? The H-bomb is capable of creating nuclear fusion on earth, so the process of creating nuclear fusion is already understood to some extent, although you are detonating a fission bomb to start the fusion process.

Having a cycle between a fusion and a fission reactor would solve some serious energy problems.

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Have you ever played with magnets, especially tried to put two north poles together with your hands, and noticed how difficult this is? Well, although it is difficult, you can manage it. But this is only possible because the magnetic dipole force is weaker (proportional to $1/r^3$) than the coulomb force (proportional to $1/r^2$) that keeps your hands from falling apart.

When it comes to fusion, the situation is similar in that you would need to push positive nuclei intensely together in order to make them eventually fuse due to their shorter ranged strong interaction. But, sadly, there is simply nothing stronger at technological scales than the repulsive Coulomb force between the positive nuclei, because every machine we can build is made of atoms, which are also subject to the Coulomb force. Hence, no simple machine can push nuclei together to achieve fusion, unlike you are able to push magnets together with your hands.

The only way to achieve nuclear fusion is to increase the speed of the components in order to surmount the Coulomb barrier by their kinetic energy. But if kinetic energy is high, the probability that the nuclei just fly apart increases also, unless you are able to confine them in a limited volume. And this is the actual difficulty: you can't just put a plasma of several million Kelvin into a Cola bottle.

In the case of the fusion/fission bomb, the containment is simply achieved by the fission bomb creating an enormous pressure that acts on the fusion components. It is clear that this is a one-time event, and, as such, it is not a sustainable process like it is desired for a power plant. And you can't just slow down the fusion process, because this would again decrease the pressure, which wouldn't be sufficient then so as to confine the fusion components.

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A rephrasing of this question is:
A) We can make nuclear fission reactors, and B) nuclear fusion bombs are driven by nuclear fission bombs. So, C) why can't we use nuclear fission reactors to power nuclear fusion reactions? (If I have this rephrasing wrong, please let me know.)

Answer:

In short, fission bombs and fission reactors are very different. In particular, the temperature of a fission reactor is about $300\,{\rm C}$, whereas the temperature of a fission bomb is about $10^6-10^7\,{\rm C}$. There's not really a way to scale between these.

More generally, the pressures and temperatures required to sustain fusion are difficult to achieve and contain, and at this time, humanity has simply found no way to do it.

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A reactor requires sustained fusion which requires sustained pressure. A fusion bomb produces the required pressure with an fission implosion which cannot be sustained. On top of that, it needs to be controllable which a nuclear implosion is not.

We haven't figured out a controllable way to produce such sustained pressures without putting more energy in than you get out (another requirement). We have only one working example: stars, which use gravity. Needless to say, gravity is difficult to tinker with. We have to come up with something from scratch.

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    $\begingroup$ I understand that a nuclear fission explosion is not a viable source to produce a controlled fusion reaction. But the sun clearly has it figured out, so is there no hope of replicating a controlled nuclear fusion reaction on earth? Due to physics required by fusion reactions, such as gravitational mass ..etc. $\endgroup$ – Feynman137 Apr 14 at 20:36
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    $\begingroup$ See edit, though I thought it was obvious enough that I wouldn't need to add it in. $\endgroup$ – DKNguyen Apr 14 at 20:37
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    $\begingroup$ @Feynman137 The solar core density is ~150 g/cm³, which isn't easy to achieve without gravity. But even if we could do that (at a temperature of 15 million kelvins) here on Earth, it wouldn't make a practical reactor. From Wikipedia, the mean lifetime of a solar core proton is around a billion years, and the solar core only produces around 276.5 watts/m³, which (by volume) is about the same as an active compost heap. And given the huge core density, by mass the energy production rate is pathetically small. $\endgroup$ – PM 2Ring Apr 14 at 22:23

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