Of course, NTRs are a pretty broad category. That term encompasses everything from solid core designs like NERVA to the nuclear light bulb. So, here's a brief primer on some of the basic designs, and some of their important features.
First, the open-cycle, solid core design.
It's fairly simple: pass hydrogen (or whatever fuel, but hydrogen is usually best) over the fuel rods of an operating nuclear reactor. The hydrogen heats up and is expelled out the rocket nozzle at high velocity. This is what the NERVA designs and their Soviet counterparts used. Thrust to weight is decent; much worse than a chemical rocket, but far superior to an ion engine. Specific impulse is around 800-900 seconds, maybe up to 1100 if you use better materials. The main limitation is the reactor temperature; above a certain temperature, your fuel rods will melt. Most concepts I've seen have the reactor operating at a maximum temp of about 3,000 K.
Next, the closed cycle, solid core design. I haven't seen much written about this one at all. Essentially, you separate your propellant and the radioactive bits (such as by putting a transparent window between them). Assuming the reactor operates at 3,000 K, most of you emissions are going to be in the infrared.
Next is the liquid-core NTR. Something of an intermediate step between solid and gas core designs; you heat up the uranium hot enough that it liquefies; this lets you get hotter temperatures and more energy out of your propellant. Of course, you have to contain the fuel; either by using a closed cycle design, or some other method. Possibly spinning the reactor at high speed like a centrifuge (the uranium will go to the outside, while the lighter hydrogen stays in the middle). Again, I haven't seen as much written about this one, though Atomic Rockets has a bit on it.
|(picture via Atomic Rockets page)|
Performance would probably be somewhere inbetween solid and gas core designs, ballpark about 1,500-2,000 seconds of isp.
Next come the gas core designs. First, the open cycle. Heat up your fuel so hot it gasifies (well over 5,000K, possibly even over 20,000 K). Keep your fuel confined somehow (by centrifuging again, or injecting the propellant and fuel carefully), you'll still lose a bit anyway. Let the propellant pass directly over the fuel, so your heat transfer is very efficient. Above 4500K (the gas core is much hotter), diatomic H2 will dissociate, giving you another 40% or so bonus on your specific impulse.
Specific impulse for this one could be well north of 3,000 seconds (I've seen figures near 10k isp quote). Decent thrust, too. Shame about the radioactive exhaust.
Which is where the closed cycle gas core comes in. Also known as the nuclear lightbulb.