Unfortunately this will not work. That isn't to say that the construction, placement, and powering of an artificial magnetosphere at Mars-Sun L1 is infeasible. It can totally be done with today's tech and modest meter scale superconducting rings. Mini-Magnetospheric Plasma Propulsion (M2P2): High Speed Propulsion Sailing the Solar Wind (http://earthweb.ess.washington.edu/space/M2P2/STAIF2000.PDF) probably represents the core concept. Except instead of trying to go somewhere you stay where you are. The M2P2 paper says a 10cm diameter superconducting coil can divert solar wind in a bubble up to 20 km in diameter. It wouldn't take too much to scale that up.

Of course diverting that much solar wind would create a force on the object. In the paper above that force is used to accelerate a craft. It'd be some handful of newtons at 20 km and linearly more to do what this project wants. One way you might get around that is to "lean into" the wind by going down the sun-side of the L1 halo orbit and allowing the force from the diverted solar wind to counter the sun's gravity's acceleration.

But for the vast majority of the lost Mar's atmosphere the kinetic energy needed to achieve escape velocity is not from impact with solar wind ions or other solar wind related/magnetic field means. All those hereafter referenced under the umbrella term "jeans escape".

Instead the majority of the kinetic energy needed comes from the ejected electrons from the sun's light ionizing the upper atmosphere. That ejected electron has quite a bit and it is distributed to the ions it later interacts with and as those ions interact with others. If there was no solar wind at all the rate of atmospheric loss at Mars would drop but not significantly if the sun still shone upon it.

That isn't to say that, having no magnetosphere, Mars (or Venus) does not lose an additional small amount of it's atmosphere to jeans escape mechanisms. But that amount is limited due to the currents created in the upper atmosphere by photoionization creating their own local magnetic field. That creates a bow shock about the ionopause which slows the incoming solar wind down such that it's constituent ions no longer have the energy needed to deliver the boost required for escape. And because of the induced magnetic field other solar wind magnetic field based mechanisms which would pick-up the ions ionized by the sun's light are mitigated.

I love the idea of this but it isn't going to make Mars have a decent atmospheric pressure in just some years.

On a (much) lighter note, I was thinking if you put these artificial magnetospheres all over the inner system and then coordinated turning them on and off you could "paint" the termination shock surface of the heliosphere with different scales of tubulence in charge density. It'd be a multi-hundred AU wide screen visible only from very far away with sensitive polarimeters (detecting the changes in lines of sight charge density through faraday rotation). Might be a decent way to METI since it'd not require much energy or high angular resolution at the other end.

tldr: It's technically and economically feasible. But it doesn't work like suggested for atmospheric protection because almost all the mass loss is from light caused photoionization, not the solar wind (and other Jeans escape mechanisms).