How to efficiently deorbit space junk
Setting: Nearish future where corporate space ventures have had maybe a hundred years of launching satellites and missions and tourists into earth's orbit.
Issue: Launching anything is difficult now because you've got to make it through a million bits of space junk. Picture that scene in Wall-E where <PERSON>'s ship has to smack its way through a bunch of junk in earth's atmosphere.
Partial solution: Contractors are hired to go up into space in their ships and get rid of that trash so that things like communications satellites and manned missions don't get obliterated and rockets can be launched more easily.
Problem with the partial solution: De-orbiting space junk takes fuel. Some of this stuff has a lot of Delta-V. Matching speed, docking, and deorbiting the space junk would take tons of fuel... more than is probably possible or efficient for removing the volume of junk that needs to be removed. 199
Blowing up the junk doesn't work, it just turns one big trash bullet into a thousand tiny trash bullets traveling at the same speed as before in a less predictable orbit.
My idea: A ship that interfaces with and steers a giant tunnel of an electromagnet onto space junk, then acts as a huge railgun and fires the junk either to escape velocity or back into earth's atmosphere. Is this feasible? Is there an easier solution? If you like this solution, how do you think something like this would work? I like it because the trash-moving method can be accomplished electronically and charged with solar cells... but I feel like there must be a less cumbersome solution that doesn't require a massive orbital railgun (very expensive for the space trash company)
No magic, no infinite fuel sources, and as cheap as possible for the most profit per bit of junk deorbited.
Edit: I'm particularly interested in keeping my crew and their ship in space for as long as possible to avoid costly launch/reentry. Economy is a huge factor here - it needs to be cheap. Picture a company looking to make the most off of a low wage crew. 199