Nuclear electric rocket
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In a nuclear electric rocket, nuclear thermal energy is changed into electrical energy that is used to power one of the electrical propulsion technologies. Technically the powerplant is nuclear, not the propulsion system, but the terminology is standard. A number of heat-to-electricity schemes have been proposed.
Possible uses 
One of the more practical schemes is a variant of a pebble bed reactor. It would use a high mass-flow nitrogen coolant near normal atmospheric pressures. This would take advantage of highly developed conventional gas turbine technologies. The fuel for this reactor would be highly enriched, and encapsulated in low-boron graphite balls probably 5-10 cm in diameter. The graphite serves to slow, or moderate, the neutrons.
This style of reactor can be designed to be inherently safe. As it heats, the graphite expands, separating the fuel and reducing the reactor's criticality. This property can simplify the operating controls to a single valve throttling the turbine. When closed, the reactor heats, but produces less power. When open, the reactor cools, but becomes more critical and produces more power.
The graphite encapsulation simplifies refueling and waste handling. Graphite is mechanically strong, and resists high temperatures. This reduces the risk of an unplanned release of radioactives.
Since this style of reactor produces high power without heavy castings to contain high pressures, it is well suited to spacecraft.
Research in nuclear propulsion began with studies for nuclear thermal propulsion, where the reactor heated a propellant (usually hydrogen) that was allowed to expand through a nozzle. This was essentially an ordinary chemical rocket with the nuclear reaction replacing chemical combustion as the rocket's heat source. Because the reactor could supply more heat to the propellant than chemical combustion, higher exhaust velocities, i.e., higher specific impulses were possible. See KIWI, NERVA. The reports at the time (and since) indicated that keeping the system light would require high temperature, densely packed designs, such as fast metal cooled reactors or hexagonal pin fueled, high temperature gas cooled reactors. In the past several decades the attention has turned to using the nuclear reactor to drive a turbine to produce electricity, which is used to create a plasma which is accelerated. See Project Prometheus. The present best of tech is the SAFE-400, which uses a 400kW thermal reactor and a gas turbine (called a closed Brayton cycle) to produce electric power. Heat rejection is kept low-mass using advanced heat pipe systems (such as are now used in some laptop computers for cooling as well). Safety comes from ruggedness, proper shielding, control pins and spoiler pins inside the reactor which arrest the reaction.
The key elements to NEP, as they are being pursued today are: 1. A compact reactor core 2. A gas turbine or Stirling engine used as an electric generator 3. A compact heat rejection system such as heat pipes 4. A power conditioning and distribution system 5. A high power propulsion system based on plasma propellants.
The SAFE-400 is the current best of tech for items 1-3. Item 4 is common to all spacecraft. Some examples of thrusters that might be suitable for this are VASIMR, DS4G and Pulsed inductive thruster. PIT and VASIMR are unique in their ability to trade between power usage, specific impulse (a measure of efficiency, see specific impulse) and thrust in-flight. PIT has the additional advantage of not needing the power conditioning system between itself and the electric generators.
See also 
- Spacecraft propulsion
- Nuclear propulsion
- Nuclear reactor
- Radioisotope thermoelectric generator
- Ion thruster
- Magnetic sail