Technology
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Solar panels would be my guess, though you can always build a space based nuclear reactor if you can refuel it and get rid of its waste.
It would certainly need a lot more to figure out an actual feasible plan, but I don't think there's anything fundamentally impossible about doing it with today's technology, let alone the future's.
Mars gets roughly half the light of Earth, so I don't think Solar panels would be realistic (how much solar panel surface would you need to power a magnet of that size?)
I'm also not sure a nuclear reactor is realistic - forget the nuclear waste, how do you get rid of the heat waste?
You'd need quite a big magnet operating at a level akin to superconducting magnets in particle accelerators.
Perhaps someone could calculate more accurate numbers and feasibility, but to me, it currently sounds very out of reach for us (not impossible, mind you).
This is false. https://www.wolframalpha.com/input?i=Lagrangian+points+of+mars L1 is 137Million Miles from the sun. Though it is only 650,000 miles from Mars, which is probably where you are getting your 2.2million Km from.