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Many experiments seem to have been done where the experimental setup consists of an extremely short, but intense laser pulse, impinging on e.g. deuterated plastic of some sort or some "jet" of nano droplets with some sort of deuterated chemical. Typically a Coulomb explosion happens and then fusion reactions are detected also.

Is the logic behind this approximately as follows; the strong "radiation field" of the laser light strips away the (outer) electrons on the target, which is then left with a large net positive charge and is also at the same time ionized. Then the whole shebang explodes simply because like charges repel. The deuterons, or generally fuel nuclei, get so high velocities that when they collide with one another or a target, nuclear fusion is induced.

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Pretty much, yes.

The idea is that electrons are much lighter than nuclei, so during the timescale at which they fly off the nuclei are essentially frozen; once that happens, the nuclei need to contend with the fact that there's now a lot of positive charge in a very confined space, and that has only one way to go: outwards, and fast. And, once you get them going that fast, you hope (or try to engineer things so that) they'll collide with things fast enough to induce fusion.

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    $\begingroup$ in the case of a deuterated fuel pellet of finite size, the initial impingement of laser power on its outside surface heats the shell of the pellet to extremely high temperature and correspondingly large pressure in a very brief instant. the outermost layers of the pellet explode away and the remainder of the pellet is very strongly compressed. its own inertia prevents it from escaping, and extraordinarily large pressures inside the pellet result- which is why this method of triggering fusion via high temperature and pressure is called "inertial confinement". $\endgroup$ – niels nielsen Oct 31 '17 at 3:45

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