How could we establish a stable atmosphere on Mars without a sufficient magnetosphere to keep it safe from solar wind?
To establish a stable atmosphere on Mars safe from solar wind humans would need to use caves.
Caves and other underground structures, including Martian lava tubes, canyon overhangs, and other Martian cavities would be potentially useful for manned missions, for they would provide considerable shielding from both the elements and intense solar radiation to which a Mars mission would expose astronauts. ...the "Essential Tasks" necessary for cave habitation are: finding extraterrestrial caves, protecting the scientific environment inside of a cave, dealing with the dark (providing lighting solutions for the interior of the habitats), cave life support.
The atmosphere which is needed for life would also be protected inside sealed sections of the caves.
The issue from the solar wind is one that matters over > 100,000 years, not short term.. if we can drop enough comets and shit onto Mars to give it a useable atmosphere, we can totally keep up on losses!
But where to get all that nitrogen? have to find the correct comets!
Now if you have air, you still cannot go outside in the day as the Rads will toast you somewhat.. no mag field!