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In the long run Mars needs a magnetic field to keep a thick atmosphere and for radiation shielding, if humanity were to terraform it. Starting a dynamo in Mars' core seems forever impossible, but a magnetic field could instead be induced by the Solar wind.

Venus has a naturally induced magnetic field. Could an ionosphere be densified to create a much stronger magnetic field? For example by bringing material from Phobos and ionising it above Mars?

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    $\begingroup$ In the long run Mars needs a magnetic field to keep a thick atmosphere. Although this seems to be common knowledge, it doesn't explain Venus. If we are ever able to terraform Mars and thicken its atmosphere considerably, then the speed at which impatient humans thicket the atmosphere is surely orders of magnitude larger than the speed at which the atmosphere escapes. $\endgroup$ – gerrit Dec 16 '15 at 11:22
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    $\begingroup$ @gerrit I added radiation shielding as another motive. $\endgroup$ – LocalFluff Dec 16 '15 at 11:34
  • $\begingroup$ @gerrit - There is some evidence that Venus is still volcanically active which helps add to the atmosphere, whereas Mars is not. This does not fully resolve the issue, but volcanic activity would help (though I am not sure if volcanos alone can explain the absurdly thick atmosphere compared with Earth... ). $\endgroup$ – honeste_vivere Dec 17 '15 at 21:26
  • $\begingroup$ @honeste_vivere Venus is much larger than Mars, almost as large as Earth, which would suggest size is a far more important factor than the magnetic field. $\endgroup$ – gerrit Dec 17 '15 at 22:16
  • $\begingroup$ @gerrit - That's not what the results from MAVEN seem to suggest, but perhaps I missed something in those articles. $\endgroup$ – honeste_vivere Dec 18 '15 at 16:03
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The premise of the question is incorrect. If you were able to terraform Mars on a human civilization time scale in the first place, then you can replenish the atmosphere, if you like, at a rate several orders of magnitude faster than the rate of loss to the solar wind. Or you can simply ignore that loss, since it won't be noticeable for many millions of years.

The terraformed atmosphere, assuming Earth sea-level density or even mile-high density, would provide ample radiation protection.

You don't need a magnetosphere to terraform Mars.

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The way to solve this problem has recently been proposed by NASA. Put a magnet on the L1 Legrange point (between Mars and the Sun) of about 2 Tesla. This is what it looks like:

Magnetic Mars shield

At present, atmospheric loss on Mars is balanced to some degree by volcanic outgassing from Mars interior and crust. This contributes to a surface atmosphere that is about 6 mbar in air pressure (less than 1% that at sea level on Earth). As a result of the magnet, Mars atmosphere would naturally thicken over time, this would include an average increase of about 4 °C (~7 °F), which would be enough to melt the carbon dioxide ice in the northern polar ice cap. This would trigger a greenhouse effect, warming the atmosphere further and causing the water ice in the polar caps to melt.

This is what it looks like now: enter image description here

Source: https://phys.org/news/2017-03-nasa-magnetic-shield-mars-atmosphere.html#jCp

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