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The Franklin's reaction control system (top)

A RCS thruster used on a Galaxy-class starship

Multiple realities
(covers information from several alternate timelines)

The reaction control thrusters or reaction control system are the standard thrusters used by the Federation for low-velocity propulsion, station-keeping and maneuvering control in space.

They were in use as early as the 2160s. (Star Trek Beyond)

In 2366, in an attempt to escape from a Promellian battle cruiser surrounded by aceton assimilators, Jean-Luc Picard used only two of the USS Enterprise-D's RCS thrusters to maneuver the vessel through the remains of Orelious IX. (TNG: "Booby Trap")

A Type 15 shuttlepod uses eight DeFI 657 hot gas RCS thrusters, (TNG: "Descent", display graphic) also known as microfusion thrusters. (TNG: "In Theory")

In 2367, the reaction control thrusters on the Galaxy-class starships was managed by the reaction control thruster system. In that year, when Data hijacked the USS Enterprise-D, he issued a command override on this system giving him complete control of the system from the bridge. (TNG: "Brothers")

In 2369, Deep Space 9 was moved from the orbit of Bajor to the mouth of the Bajoran wormhole with six of the station's RCS thrusters. A subspace field was used to reduce the stations inertial mass to shorten the travel time from two months to some minutes. (DS9: "Emissary") Another way of getting more velocity from RCS thrusters is to accelerate the deuterium feed and burn them beyond safety limits. (VOY: "The Cloud")

In order to conduct an emergency shutdown of all RCS thrusters, all deuterium from the RCS system must be vented out. (VOY: "The Cloud")

Starfleet regulations state that only thrusters are allowed for propulsion inside a spacedock. (Star Trek VI: The Undiscovered Country)

Background information

According to Star Trek: The Next Generation Technical Manual, although all thrusters serve the same function, the propulsive exhaust production behind an RCS thruster varies slightly, depending on the size of the craft.

Starships have primary and auxiliary thrusters. The primary thrusters are powered by a gas-fusion reaction chamber. It uses deuterium fuel from fuel tanks that in turn are fed from the ship's main deuterium tank. Exhaust is delivered through a field trap into the vectored thrust nozzles visible from the outside. Auxiliary thrusters have no tanks or fieldtraps, and are powered by a microfusion chamber. The generated thrust is considerably lower.

Shuttlecraft, escape pods, cargo management units and some probes also use microfusion thrusters. In the Star Trek: Deep Space Nine Technical Manual, the Defiant's lifeboats are said to use impulse microthrusters and microtorpedoes in turn use a miniature fusion thruster for propulsion.

According to Star Trek: Deep Space Nine Technical Manual, the thrusters of Cardassian space stations also use deuterium fuel, fed into a protean-cycle fusion reaction chamber to produce the exhaust to the thrust nozzles. This seems to differ from a starship thruster in the sense that it is designed to create a low thrust. RCS thrusters of a Federation space station are stated to function in a similar way.