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How can I protect a ringworld (which creates 1g artificial gravity and has an earth-like atmosphere) from the things that earth's magnetic field protects us? (using real-world physics)

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If you read Ringworld or Bigger Than Worlds you'll see that the ringworld, as a giant spinning super conductor, has a magnetic field, a much more powerful one than Earth's, powerful enough to turn its star into a particle beam weapon when needed. This spinning conductor model is substantially similar in operation to Earth's geodynamo.

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