Why is no agency actively building a coilgun or other space gun in near equator mountains to launch payloads into orbit?

Here's the easy answer: Force equals Mass multiplied by Acceleration (F=M*A) What is called a coil-gun, rail-gun, electro-magnetic mass driver (EMMD), or whatever name you want to call it isn't really practical for anything other than a replacement for a cannon or artillery (i.e. something meant to fling a piece of metal at something with great force to punch a big hole in it). brings to light the last real attempt at anything of the "go build it on the mountain" scale, and that was really so Iraq could shoot things at Israel without having the missile knowledge (their Scuds were really quite pitiful, despite all of the fears during Desert Shield / Desert Storm - more on par with the V1 Buzz-Bombs of Germany 40 years before). As far as what has referenced, there's something about the diagram I'd like to point out: Evacuated Launch Tube. Some of the larger designs, to overcome not only the possible gauss (magnetic field jump) that might occur between coils (since you're dealing with thousands of times more magnetism that what you'd find in an MRI, as the projectile is pulled along the sled, but to also make the launcher more efficient, call for the launch tube to be at a vacuum or quite near it. Oh, and just imagine what that sort of magnetic field would do to anything living, if you were able to slow the acceleration down to tolerable levels. Bad stuff. So, for right now, EMMDs are solely being considered for use as cannon replacements on ships that have nuclear reactors (where they'd have enough electrical power). http://www.engadget.com/2011/11/01/us-navys-electromagnetic-railgun-hits-testing-milestone-1-000/ While some argue that the new LASER that the Navy is working on, now at 500 Watts, although 1,000,000 Watts (1MW) is the goal a supposed capacity to melt / burn / vaporize through about 20 feet of steel a second, will be the weapon of the future, an EMMD gives you the ability to fire beyond line of sight (LOS) to where a target is going to be, or where your other ships, aircraft, or personnel are observing it (and depending on how large of a projectile, and the speed it maintains when it hits the target, the force delivered could be substantially higher than anything currently in the arsenal). Most likely, you'll see a mix of both technologies in the future, with LASERs providing the bulk of the short and mid-range firepower, and EMMDs providing the long range and beyond LOS firepower.

It is not clear why this isn't happening now. It is also unclear whether the premise of the question is true to begin with. It seems like a great approach to me. Basically the approach is to mount a railgun on a mountain like this: You would fire the payload off into space with such a tremendous velocity that your "shell" would be able to exceed escape velocity and therefore put something into space. Apparently there has been a great deal of progress in recent years. It appears from the abstract of this IEEE paper [1], that the main problem with this type of launcher is the extreme acceleration forces imparted onto the shell. We're talking about 1000s of g-forces. This would not only crush any human, but sophisticated instrumentation of anything sensitive to crushing forces. Abstract—Many advances in electromagnetic (EM) railgun and power supply technology have been made in recent years. Laboratory experiments with railguns have demonstrated muzzle velocities of 2–3 km/s and muzzle energies 8 MJ. The extension of this technology to the muzzle velocities ( 7500 m/s) and energies ( 10 GJ) needed for the direct launch of payloads into orbit is very challenging, but may not be impossible. For launch to orbit, even long launchers ( 1000 m) would need to operate at accelerations 1000 gees to reach the required velocities, so that it would only be possible to launch rugged payloads, such as fuel, water, and material. A railgun system concept is described here and technology development issues are identified. Estimated launch costs could be attractively low ( $600/kg) compared with the Space Shuttle ( $20 000/kg), provided that acceptable launch rates can be achieved. Further evaluations are needed to establish the technical and economic feasibility with confidence. However, I can think of one material which would be nice to eject - and would survive the acceleration quite nicely. That is spent nuclear waste. With a heavy railgun which could fire a shot, say once a day, and fire nuclear waste off into deep space, we'd have quite an interesting solution. With rockets, the cost of removing nuclear waste from the planet is prohibitively expensive, but if a railgun could be realized with a couple orders of magnitude in improved cost efficiency, it might be a winner. [1] http://research.lifeboat.com/ieee.em.pdf

Because most payloads don't survive well at those levels of acceleration.  Launching broken stuff into space is a waste of money.

Rockets generate thrust throughout the entire burn.  A gun only generates thrust until the projectile has left the barrel.  You have to generate the same amount of energy in that short time as the rocket does for it's whole burn.   That's a hard thing to do.  We also don't have experience with guns on this scale.  Starting now would require a big learning curve.  On the other hand, we know a lot about rockets.    As for the coilgun/linear accelerator, the problem is the energy.  We don't have an efficient way to store the scale of electricity that they would need.  Given the requirements of a linear acclerator, you need to get the energy out very quickly, which eliminates most battery technologies.  We'd need to develop large scale capacitors or some other technology.  Or we'd need to have a huge generating station specifically for that launcher.  It would need to be very close to minimize losses from cables.  Here's a question - if the launch fails, would you rather have a fossil fuel plant or a nuclear plant near the launcher?

Just google 'Chelyabinsk' for a bunch of nice recent footage of what happens to objects that pass through the earth's atmosphere at orbital velocity...