First of all: This would probably be the wrong approach. A better approach will be described below.
Now to the meat (or rather plasma) of the question:
Background stuff:
Plasma on its own doesn't necessarily mean you can see it. What you DO see is the (partial) recombination and the excited ions. The light they radiate highly depends on the precise make-up of the ions inside the plasma. Since it is recombination-radiation we're not only talking visible either: large portions of it will be ultra violet.
This already gives us a hint though: even though there will be other spectral lines by the ions in question, some (maybe even the majority) of the light will be purple-tinted, as high-energy recombination tends to release high-energy (=high frequency) photons, which you see as blue to purple.
At the same time the higher frequency spectral lines will be more active in the ions in question. Speaking of which:
Color, or "What ions do you use?"
If you use Phobos, it is natural to assume you use the local rock of Phobos. Note here that Phobos is not a solid moon but a "rubble pile", basically a bunch of rubble barely stuck together and rather lightweight. The average density of Phobos is about 1'887 kg/m³ and an astronaut in full gear could jump about 800 meters high, before slowly descending.
Spectral analysis and the low density imply a makeup of mostly of carbonaceous chondrite regolith, meaning you're met mostly by silicone, oxygen, hydrogen, carbon and iron.
The German website internet-chemie got a nice page of spectral lines for individual elements (which is where I pulled the following image-links) at: https://www.internetchemie.info/chemie-lexikon/daten/s/spektrallinien.php
- Hydrogen has 3 spectral lines: purple, blue and faint red.
- Oxygen got about a dozen lines in blue to purple, as well as 3 green ones, 5 yellow-to-orange ones and 6 red ones.
- Silicone has some blue and some red ones but mostly green-to-yellow lines.
- Iron has its spectral lines wide spread, but there is some in the purple range and most in the blue-to-green range.
- Carbon got the majority on cyan, orange and red, and a few individual lines at blue and green.
The combined plasma will be a bit more white-ish, but should look kind-of similar to the typical oxygen plasma (which is red tinted purple).
Shape
The shape would be some kind of ring, possibly spread out to a band. The pinch-effect would try to keep it together while the interaction with solar wind would spread it apart.
From the surface it would look like a band going across the sky from east to west. It would be only a faily faint glow however, less intense than the aurora we know on earth. Also it would introduce its own aurora, albeit even dimmer.
A different approach
What's wrong with this one?
While awesome in theory, this would not be the best way to achieve your actual goal, which is keeping the solar wind from mars.
The magnetic field contains a lot of energy and will leak some of it to solar wind, so you'll need to constantly feed new power into it.
Also it will behave a lot like the Van-Allen belt, and be a danger to satellites and noise to radio transmissions. It would probably not work well as signal reflection either, since it were probably both, to thin and interfering with the signal.
So what else to use?
One or multiple stations at the Lagrange point 1. Since it is far before the planet, the magnetic field doesn't need to be anywhere near as massive. The power demands should be something a nuclear plant, or preferably a few square kilometers of solar sail can produce.
Isaac Arthur made a video about it recently (citing the same paper by the way).
Finally, if really to be built in a multiple station bound, open ion particle accelerator fashion, (like the paper you gave describes it at page 16) it would look like an ever so faint purple band. (No white crackling arks, sorry).
It would be mostly even in density, since you would have many many streams of ions in order to keep your stations small and redundant.
These streams will probably bleed into each other, but even if they don't they'll be too close to each other and to diffuse for you to see the gaps between.
Note: In my personal opinion, their argument for the plasma ring doesn't match up, as you can do the same for L1 station based systems.
Also compound magnetic fields could be generated with a more precise modulation, allowing for better shielding and a reduction in mass.
If one was to go for the argument: you could even build the system to deflect part outwards and part to the center massively reducing the fields required.
This may sound absurd since you "want to keep solar wind away" but the main reason you want to do that, is to reduce the amount of athmospheric water vapor that is kicked into space.
The solar wind deflected towards Mars center has fairly little effect on that, since it would hit mostly shoving towards mars rather than away from it.
