My Apologies...
The Artifact Series is a 4th Edition Campaign addon, and I forgot that Background Count worked differently in 4th Edition than it does in 5th Edition. To whit, MAGIC Score was reduced per the rating of the Background Count (in this particular instance, by 12, since I got a stupid amount of successes on the spell by spending Edge - But at least Frosty did not have to bail us out 
). If that score was reduced to 0 for a Spirit, they were Disrupted. Not as Handy in 5th
Edition. Also of note, the Mage in question had few to no Combat Spells (His Mentor Frowned upon using Combat Magic - How can you convert someone when they are dead?). So to make sure he could cover his and his team's ass in a crisis, he was fairly skilled (Skill 3 with a Specialty) in Assault Rifles for when the Mojo was not an option.
Ah, too bad, I could've used a spell that instantly took out spirits like that. :-)
Here's a rules hack that depends on how tolerant your GM is: recklessly cast Mana Static and then Physical Barrier at the same force. Because Physical Barrier is a dome instead of a sphere like other AOE, you can place it just an inch higher than your Mana Static spell and it won't intersect the background count. Enemy magician trapped inside the barrier is stuck with the background count penalty, and is too weak both physically and magically to shatter the barrier. (And if they try to cast at you outside the barrier they take an additional -1 penalty from the light fog effect.) Spirits can take down the barrier from the outside but if they're trapped inside with the Magician will need to dematerialize and rematerialize on the other side to be effective, which at the very least buys you some precious time.
Don't think you could make an argument for doing this with Mana Barrier, which is a conventional LOS (A) spell, which means either it overlaps and intersects with the background count if cast at the same Force (thereby rendering it ineffective), or if cast at a higher Force leaves sufficient space for a spirit to be between the barrier and the Mana Static field.
