NASA proposes a magnetic shield to protect Mars' atmosphere (2017)
phys.org
phys.org
May be a bunch of solar-powered rail guns ([0]) to fling a fraction of the Phobos mass into space.
Now, to feel the need to install something like this on Phobos - is beyond our means, as a species.
It's a bit like the announcements "Wow! We've found a planet that we could live on easily!". The only problem being that planet is 'only' 200 light years away. Two hundred light years. It's going to take the Voyager space craft thousands of years to reach an equivalent distance of the nearest star which is but a mere FOUR light years away.
Whistling in the wind.