Rather than relying on a chemical reaction between combustible elements, the NTR engine instead employs a two-part system for generating power.
First, a small, fully contained nuclear fission chamber utilizes a tiny amount of fissile material to generate heat -- much in the way a nuclear power plant operates. In the second part of the process, a lightweight element -- usually liquid hydrogen -- is forced around the reactor core where it is instantly heated. The resulting superheated hydrogen is then expelled at great velocities through the engine nozzle, generating over twice as much specific impulse (force) as a traditional rocket engine, permitting a rocket to travel further and at higher velocities.
In addition, because the process can be thought of as simply expelling a heated gas through a nozzle, many different gases could be utilized for propellant, potentially allowing such rockets to "refuel" by occasionally skimming the atmospheres of distant worlds to collect additional gas (a concept proposed by Robert Zubrin, president of The Mars Society, as a viable method for the long-term exploration of Titan's atmosphere).
Perhaps the most common misconception associated with fission-powered rockets involves the notion that radioactive material could be dispersed into Earth's atmosphere, or that a nuclear explosion may occur. Despite the inclusion of a fission reactor within the core of an NTR rocket engine, such a design is actually incredibly safe and can be utilized in several ways without outputting any radioactive exhaust material into Earth’s atmosphere.
One such control method would be to only utilize certain engines safely beyond the atmospheric layers of the Earth, thereby preventing any potential contamination (outer space is replete with radiation naturally, therefore any contributions from rocket propulsion are entirely inconsequential).
Another approach would be to utilize special materials with radiation absorbing properties that would completely contain the engine's radiation in orbit. An unproven but promising theoretical design involves enclosing the reactor entirely with a special quartz material which only permits the heat to escape in the form of intense ultraviolet light, passing harmlessly through the quartz shell to heat the hydrogen fuel, while all of the radioactive material is safely contained within the reactor.
Certain methods could permit ground based launches utilizing NTR engines, while other methods might employ chemical rockets to lift an NTR into orbit before engaging the fission engines.
The primary concern associated with any NTR rocket would involve a sub-orbital structural failure, however in such cases it would be highly improbable for any fissile material to escape as the reactor core is extremely robust, and only contains a very small amount of radioactive material in the first place.
In fact, an NTR engine was actually designed in the 1970’s for use with the original Space Shuttle program, as it generated twice the power of a conventional engine, but was eventually scrapped amid an increase in popular resistance to the use of nuclear technology.
Rather than relying on a potentially dangerous combustion reaction, such as that required in chemical rocket engines, in its simplest form an NTR engine functions by passing coolant over a hot surface, resulting in an exponentially safer engine that could ensure that Challenger-type accidents and the associated causes could be prevented.
Until more exotic propulsion methods are fully developed and tested, utilizing safe fission rocket engines is the most promising near-term method for delivering heavy cargo (i.e. humans, living habitats, larger robotic explorers) to more distant planetary systems. The chemical rockets of today and the last several decades are suitable for, at best, delivering humans to the moon and perhaps Mars under ideal circumstances.
However, to embark on a truly thorough mission to search for life in promising regions such as the moons Titan or Enceladus, fission powered rockets will be required, as they provide both a safe and efficient means for becoming one step closer to answering the question of whether or not we are alone in the universe.