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NASA says that it can build a magnetic dipole shield at the Mars L1 Lagrange Point, but how do they support the electricity?

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They haven't got that far yet.

This article says scientists have proposed a method for creating an artificial magnetic field. The next steps are:

  1. Design a system that can generate the magnetic field required.
  2. Calculate how much power that system needs.

And then, if the result of 1. and 2. is a feasible system and not e.g. far too large for us to launch into orbit, they can start thinking about how that power will be provided.

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