In Wrath of Khan, during the first strike, we see various emergency doors closing on in engineering. One of these appears to bisect part of the warp core. Is this merely an oversight of the production crew?
The Vertical Chamber (the centre of which is located in Main Engineering) provides power for the impulse engines and ship systems. The Horizontal Chamber, which starts in Main Engineering and extends backwards through the ship, provides power for the warp engines. Both chambers are linked, but can operate independently for a time, hence why an emergency door can bisect this feature to prevent a radiation leak from the vertical core stopping them going to warp or a radiation leak from the horizontal core stopping them using impulse and/or losing power for torpedoes and shields.
Located in the center of the room, and extending for many levels both above and below the deck, is the vertical linear intermix chamber. This complex, radically new design in intermix technology provides operational power for the impulse drive system and furnishes enough additional energy to power all other shipboard systems. Both matter and antimatter for the chamber are contained in a series of magnetic bottles, which are housed in pods at the base of the intermix shaft. These pods may be ejected from the ship in case of extreme emergency via two large blow-away panels in the outer hull.
Extending aftward from the vertical shaft is a horizontal chamber which draws its matter/antimatter fuel from the same source. This shaft provides source energy for the warp field nacelles and phaser banks. The linear configuration has proven to be consistently cooler, cleaner, and more efficient than any other system in use today.