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Alien technology.

Instead of simply admiring the brilliant display of aurora could an advanced alien civilization create strong focused magnetic field from their planet to trap hot plasma and at the same time draws energy for its consumption? If what is the strength of the magnetic field required? Ignore engineering issues and how do they protect themselves?

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No. They can't and they won't even try to do it. A planet's magnetic field is basically too feeble to even bother about turning their planet into tokamak reactor of any size.

To quote this description of Magnetic Flux Compression Fusion, because this sets out the magnetic field strengths for a fusion reactor.

"Magnetic fields above 10 mega Gauss can be reached compared with the Earth's magnetic field strength of 0.5 Gauss and refrigerator doors magnets of 10 Gauss."

The difference between a fusion reactor's magnetic field and a planet's magnetic field is a factor of 20 million. Nice idea, but no banana.

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    $\begingroup$ ...I'm glad you mentioned the banana, because OP's error was a matter of scale. $\endgroup$ – xDaizu Sep 2 '16 at 9:01
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    $\begingroup$ @xDaizu Bananas never get enough of the credit they deserve. Scale errors are very common and all too easy to make. We all make them. $\endgroup$ – a4android Sep 2 '16 at 10:13
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The other answer is correct, but I'll try to give a little bit more explanation of the problem. The issue is that while there is a vast amount of energy up there, it is spread out into an even larger area.

Think about what happens when you cut food with a knife, now try to do the same with the flat side of a spoon. Even if you apply the same amount of power it is not going to work. To provide another analogy a warm bath contains more heat energy than a boiling kettle, however you aren't going to make very good quality tea with bath water and you can climb into the bath without scalding yourself.

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