In 1994, there was an announcement that aHYPERVELOCITY LAUNCHER (gas gun) has accelerated a quarter-inch disk of metal to a velocity of 15.8 km/sec, or about 36,000 miles per hour, a record for a macroscopic object. For comparison, the Space Shuttle's orbit velocity is 17,500 mph, while the velocity for total escape from the Earth is 25,000 mph. The tremendous acceleration ensues from the following sequence: a gun fires a piston, which compresses a column of hydrogen gas, which moves a specially- sculpted impactor down a barrel where it strikes the projectile.
In 1996, there was a paper on a ground-based electrically-powered launcher. It could significantly reduce the complexity and cost of space launches for moderate-weight payloads. The electromagnetic launch complex could greatly reduce the amount of fuels handling, reduce the turn-around time between launches, allow more concurrence in launch preparation, reduce the manpower requirements for launch vehicle preparation and increase the reliability of launch by using more standardized vehicle preparations. The launch requires high acceleration, so the satellite package must be hardened.
The launcher energy and power requirements fall in the range of 40-260 GJ and 20-400 GW electric. Parametric evaluations have been conducted with a launcher length of 1-2 km, exit velocity of 1-6 km/s, and payloads to low earth orbit of 100-1000 kg.
So it sounds like an update of the 1996 electical launcher is what could launch for $20/pound.
Here is a pdf from the lifeboat foundation on gun and electromagnetic launchers