A plasma conduit, (sometimes referred to as a power conduit) is a vital part of the warp drive and power grids of many spacefaring cultures.
Cleaning plasma conduits was considered to be a menial task, and sometimes delegated as a disciplinary measure. (ENT: "Singularity", "Dead Stop"; VOY: "Q2")
Warp plasma conduit
A warp plasma conduit directs high energy electro-plasma known as warp plasma or drive plasma from the warp core through the ship to the plasma injectors in the nacelle tube. (TNG: "Phantasms"; ENT: "The Forgotten")
The copper tubing suggested by Lieutenant Barclay to replace the Phoenix's damaged conduit.
In 2063, the time-displaced crew of the USS Enterprise -E assisted Zefram Cochrane with making repairs to his warp ship. Lieutenant Barclay found a length of copper tubing, and suggested that it be used to replace the damaged warp plasma conduit. Commander La Forge approved, but noted that it would have to be reinforced with a nanopolymer. (Star Trek: First Contact)
EPS conduit
An EPS conduit takes small amounts of plasma from the warp core or the impulse engines and redirects it throughout the ship for use in powering other systems, such as weapons and deflectors.
The EPS mains of the Template:ShipClass USS Enterprise-D were located on deck 13, close to cargo bay 4. (TNG: "Schisms")
Specific references
The plasma conduit on a Bajoran raider piloted by Kira Nerys and Jadzia Dax suffered damage in battle, forcing them to eject the associated plasma tank. (DS9: "The Siege")
An unshielded warp plasma conduit can interfere with combadges. (DS9: "For the Uniform")
A Bajoran transport carrying Kai Winn Adami and Vedek Bareil Antos to Deep Space 9 in 2371 had a molecular fracture in one of its plasma conduits. The conduit's collapse destroyed the entire relay system. (DS9: "Life Support")
In early 2371, Joseph Carey and B'Elanna Torres had an argument over realigning the USS Voyager's lateral plasma conduit. This action would have resulted in an overload. (VOY: "Parallax")
In 2372, Tom Paris, affected by hyper-evolution, used a phaser on Voyager's port plasma conduit and knocked out power throughout the ship. (VOY: "Threshold")
Lon Suder tried to use an EPS conduit to dispose of the body of Crewman Darwin after he murdered him, but he damaged the conduit while putting the body inside and the remains were only severely burned instead. (VOY: "Meld")
The warp plasma conduit was one of the areas where a Founder planted a device that gave it access to all of the systems of the USS Defiant later that year. (DS9: "The Adversary")
A blown plasma conduit was one of several reasons proposed by Kira Nerys for an explosion witnessed by herself and Miles O'Brien. (DS9: "Sons of Mogh")