Whenever somebody mentions "Railgun" there are two things that would come to our minds. The first one is the Railgun in the Quake video game. The second one, we would think about the massive Railguns being tested by the U.S. Navy that can  shoot 23-pound projectile at over 5,000 miles per hour or something like Mach 7. If you still have no idea about the second one, here's a concept of the navy railgun as imagined by Michael Bay for "Transformers 2":

So far, portable railguns have been imagined for video games and movies, just like the Chem Railgun used by Matt Damon in the movie "Elysium":

Now, the railgun may just really get portable as it is proven it can be done by one tinkerer who used 3D printing technology and capacitors to create his own railgun. According to Kotaku, NSA_listbot posted on Reddit  Portable 3D-Printed Railgun that can fire graphite or aluminium projectiles at over 250 meters per second. As he explains, the railgun he created "uses 6 300J, 350V, 5500uF capacitors which combined weigh 20lbs and can deliver >1050V and 1.8kJ of energy to the projectile." He added an Arduino Uno R3 with which he can monitor the capacitor voltage, amperage, temperature and battery voltage to ensure even charging and operation.

Here are two quick videos that shows it firing graphite and aluminium projectiles:

The Portable RailGun can also fire tungsten, carbon and teflon/plasma.

Looking at the whole railgun, even if it does look portable, it still is a bulky weapon that you would rather mount on a vehicle rather than carry around on foot. I guess he needs either to call DARPA or wait for some men in suits to show up and gets forcibly recruited to improve his design to make it even more portable or mobile. Such a concept can be incorporated for small unit use or even enlarged to be used as long range artillery or for armoured fighting vehicles such as tanks.

Is the weapon legal to manufacture? The Portable Raygun is developed in the USA, which allows one to manufacture his/her own firearm for personal use as long as there is no intention to distribute or sell and the person is allowed to receive or possess a firearm. Most probably the ATF would ask the owner to register the portable raygun if it gets an NFA classiciation of "any other weapon".

If it can fire projectiles at full auto, the term "AEG" might just get a whole new meaning.