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Transmat (short for transmission of matter or matter transmitter) was a common technological form of instantaneous transport. It was a subset of methodologies described as teleportation.
Forms
Transmats existed in two forms. Commonly, both types seemed designed to move no more than three people at a time, suggesting either a built-in safety feature or simply a hard limit of the technology. (DW: The Daleks' Master Plan, The Ark in Space, Silence in the Library / Forest of the Dead)
Close-Ended transmats
This form of transmat required a transmission/reception station at either end of the journey. The traveller entered the station where their molecular structure was scanned and stored for transmission, at which point their body was disintegrated into its component atoms (DW: The Mutants onwards). They typically functioned at interplantary distances, but ones powerful enough to cross the gulf between stars at trans-luminal speeds existed (NA: Love and War).
While some systems transfered this physical component to the reception station, the complexity involved meant that in most cases only the structural data recorded prior to disintegration was transmitted, with a new physical form being constructed from a matter source at the other end (BNA: Down). It seemed likely that the transmat employed on the game station, intended to give the impression of the transmatted person being killed, was an example of this simple version of the technology (DW: Bad Wolf).
Open-Ended transmats
This represented a significant advancement in transmat technology, as it entailed the ability to remotely scan and manipulate the molecular structure of objects. It was typically the product of a higher species.
An open ended transmat may acquire the object to be transferred at either end of the process. It's possible that an open-ended transmat beam was actually a form of wormhole projection, warping space-time to allow the scanning and disassembly/reassembly to take place without having to expend the energy that would be required to make a breach through which an object could physically pass, but it is also possible dimensions like hyperspace were used for transmatting objects over vast distances. It is possible that the Transmat engines used by the pirate planet of Zanak used an open ended hyperspace conduit to travel through space. Romana did mention that Zanak "dropped out of the space dimension" in order to scavenge and mine planets. This implied that other dimensions were often used in transmat technology.
Open-ended transmats could complete transfer trans-luminal speeds. Human examples have spanned interstellar distances in a matter of a few days or even hours (DW: The Daleks' Master Plan), while a Dalek transmat beam moved its victim across the distance between Earth and the edge of its solar system in mere moments (DW: Bad Wolf).
Other variants utilised a travel capsule that might have enhanced the capacity of the system's matter conversion through providing additional computing power in addition to providing protection should the location being transmatted to was hazardous. (DW: Mawdryn Undead)
Durability
The technology involved in transmat technology demonstrates the capacity for robustness. A Sontaran version of the technology, though disrupted by the Doctor's sonic screwdriver, proved easily repairable. Similarly the deployment of the T-Mat system was at least partially predicated on the ease of repairing the systems. (DW: The Sontaran Stratagem)
Some 40,000 years later, the refugees of the Nerva Beacon were able to utilise a transmat to repopulate the Earth after being freed from suspended animation. Admittedly benefiting from vast technological and scientific advances, they were still able to use receiver stations that, despite spending thousands of years unattended on a planet scoured clean by solar flares, remained largely functional with the only noticable defect being a drifting of the reintegration point (DW: The Ark in Space).
Weaknesses
Naturally, the greatest vulnerability of transmat technology rests in the fact that it is reliant upon the beam being successfully transmitted from the point of disintegration to that of reintegration. Signal degradation would prove catastrophic or even fatal. Certain advanced species — such as Time Lords — however possess the knowledge and technical ability to intercept and even redirect transmat beams to new destinations apparently greatly distant from those actually intended. (DW: Genesis of the Daleks)
It is generally inferred that anyone's first journey on a transmat is particularly uncomfortable, often resulting in vomiting or headaches. (DWM: Endgame)
Other references
The Eleventh Doctor thought that Brian Williams sneaked aboard his TARDIS via a transmat. Rory Williams soon revealed to the Doctor that Brian was his father, Brian having been with Rory and Amy Pond when the TARDIS materialised around them. (DW: Dinosaurs on a Spaceship)