Star Trek: Federation Power Generation

Written: 1998.08.01
Last Revised: 1999.02.17

Federation warp core
The warp core of a Federation starship (currently off-line). Plasma conduits can be seen leading to the warp nacelles

Matter/Antimatter Reactors

Fuel Supply

A GCS stores 3000 m³ of antideuterium (TM pg. 68). Many Federation cultists assume that since deuterium is stored at 13.8K, the antideuterium is also stored at 13.8K. However, deuterium can be safely stored in physical double-hulled tanks, while antideuterium must be stored, transported, and processed entirely in magnetic confinement fields (TM pg. 58, pg. 67). Since antideuterium atoms are electrically neutral, magnetic-confinement storage would be extremely difficult. At extreme low temperatures (<0.002K), the ionic shells of hydrogen atoms collapse, and the inter-atomic spacing of solid hydrogen can be calculated based on its atomic radius rather than its ionic radius. This means that super-cooled anti-deuterium could theoretically be stored at densities as high as 5600 kg/m³.
However, if it were feasible to cool their anti-deuterium supply to this sort of extreme low temperature, one would have to ask why they cannot do this with their deuterium supply, which is clearly stated in the TM to be stored in slush form. Cryogenic super-cooling is difficult at best, particularly when dealing with antimatter. There are three possible modes of heat energy removal: conduction, convection, and radiation. Antimatter can only be cooled through one of those three methods, because the other two methods require direct physical contact with coolant- obviously not wise when dealing with antimatter. Even adiabatic demagnetization of paramagnetic crystals (the 20th century method of super-cooling liquids) is merely a technique for improving the effectiveness of convection heat energy removal, rather than a truly new method. Furthermore, the TM states the following:
"Antimatter, from the time of its creation, could neither be contained by nor touch any matter. Numerous schemes were proposed to contain antihydrogen by magnetic fields. This continues to be the accepted method. Appreciable amounts of antihydrogen, in the form of liquid, or better yet, slush, posed significant risks should any portion of the magnetic containment fail. Within the last fifty years, reliable superconducting field sustainers and other measures have afforded a greater degree of safety aboard operational Starfleet vessels." pg. 67
"Slush deuterium is created by standard electro-centrifugal fractioning of a variety of materials, including seawater, outer planet satellite snows and ices, and cometary nuclei, and chilling down the fractionated liquid. Each will result in different proportions of deuterium and tailings, but can be handled by the same Starfleet hardware. Deuterium tanker craft are far more numerous than their antimatter counterparts, and can provide emergency reactants on a few days' notice." pg. 69
Clearly, from the first quote we can determine that they store it in liquid or slush form. If it were being stored in solid metallic form at <0.002K, they would list "solid" or "metallic" as a possible state. Furthermore, if their starships carried far more antideuterium than deuterium (as suggested by some Federation cultists), then there would be no reason for their deuterium tanker fleet to be far larger than their antimatter tanker fleet as described in the second quote. Therefore, the storage density of antideuterium aboard a Starfleet vessel is less than or equal to 160 kg/m³, which is the density of solid (but not metallic) deuterium. At this density, the ship's 3000 m³ storage tanks should hold roughly 480 tons of anti-deuterium.
It is confusing why they would use magnetic field confinement instead of gravimetric confinement, when (as an advanced space-faring civilization with artificial gravity capability) they obviously have the technology to confine antimatter with gravity rather than electromagnetism. Deuterium responds very weakly to magnetic fields unless it is super-cooled to metallic state, and it clearly is not, based on the above quotes. However, it is possible that the TM's description is oversimplified, and overlooks extra techniques they are using to facilitate the storage of slush deuterium, such as forcefields, inertial damping (to make it easier to move the antimatter), or gravimetric suspension. At the very least, it is likely that they suspend their artificial-gravity net in the immediate vicinity of the storage tanks so that the volume of slush needs only an occasional "nudge" to hold it in place.

Power Output

The theoretical energy density of the matter/antimatter reaction is 9E16 J/kg, so an upper limit for their energy yield is roughly 8.6E22 joules (roughly 900 TW average, over three years). This is more than eighty times as large as the 1E21 joule energy yield estimated for the total annihilation of the ship's entire fuel supply in its primary self-destruct sequence (TM pg. 141). The self-destruct sequence occurs in the warp core; the ship simply dumps its entire matter/antimatter storage into its warp core at once, so the limited yield of the self-destruct sequence may suggest poor efficiency for the warp core, perhaps as low as 1.3% (although Federation cultists are loathe to give up their ridiculous and unscientific 100% efficiency assumptions). It is possible that the efficiency of the self-destruct is so low precisely because so much fuel is being dumped into the warp core at once, but this means that we can establish that the range of efficiency is somewhere above 1.3% and somewhere below 100%.
The warp "power" consumption chart in the TM is useless for determining net power generation for two reasons:
  1. It uses megajoules as a unit of power. This is totally incorrect; megajoules are a unit of energy, not power. Without knowing why they used megajoules as units (particularly in a fact-checked document as opposed to a stray spoken word), we cannot determine what time factor should be applied (naturally, Federation cultists assume that the time factor is 1/s in the absence of evidence). This may simply be incompetence; they might have meant "megawatts" but their scientific knowledge is so poor that they used "megajoules" instead; of course, this kind of incompetence casts doubt on all of their figures (spoken or written), but that should not be surprising from such a primitive society.
  2. The chart measures gross consumption rather than net output. Since warp nacelles have an output (spatial distortions) which cannot be measured in terms of watts, it is impossible to measure their output. The warp chart must therefore be measuring the gross fuel consumption and converting it into joules by using the 9E16 J/kg factor. This would explain why the chart defines power usage instead of power output. This information is basically a fuel-efficiency chart rather than a power output chart. For various reasons, the amount of energy that is actually available to onboard ship systems will be much lower.
Nevertheless, if we insist upon using the chart and assuming that it refers to megawatts rather than megajoules, then the power consumption at warp 9.6 would be roughly 3E18 watts. The TM states that they can maintain this speed for only 12 hours, so this indicates that their total energy capacity is somewhere in the area of 1.3E23 joules. This equates to roughly 1440 tons of matter/antimatter, or 720 tons of antimatter. This is higher than the 480 tons derived from the storage tank capacity and density above, but we must remember that the reaction-site temperature is 2E12 K according to the TM, which should be more than enough to achieve nuclear fusion in the drive plasma. This will obviously increase the power output of the reaction to beyond what it would be from matter/antimatter annihilation alone.
Therefore, the peak power output of a GCS is probably in the range of 1E19 to 1E20 watts, and its average power output is roughly 900TW. Important: these figures are based on the energy released at the reaction site inside the warp core, not the point of actual usage. The point where the power output is measured is critical to understanding the wide range of power outputs given by Federation personnel, as we shall see later. These figures would be consistent with Data's 1.3E19 watt quantification from "True Q", and they are also consistent with Geordi Laforge's "terawatt-range" statement from "Masterpiece Society" and Riker's <1TW statement from "Dauphin". Does this seem paradoxical? It should, but it can be explained by noting the context in which those statements were taken, and the specific location in the reaction/conversion/usage stage where they were most likely quantifying their power output (for more details, see the Conflict Resolution).

Federation Cultist Objections

Many Federation cultists prefer to ignore scientific issues and the TM in favour of unqualified scraps of dialogue from Federation crewmembers, but this attitude generally stems from a combination of scientific ignorance and an absolute refusal to concede the possibility that Federation crewmembers can ever make mistakes. Amazingly, they universally maintain this faith in Federation crewmember infallibility in spite of the long string of serious scientific and technical mistakes made by Federation crewmembers over the years:
This is only a small sampling of the serious technical and scientific mistakes made by high-ranking Federation bridge officers, yet Federation cultists continue to insist that any vague dialogue from these characters be treated as more reliable than science and technical analysis of established phenomena! Even Federation technical literature is prone to embarassing scientific errors- the Star Trek Encyclopedia describes neutrinos as "massless particles" when in fact they are known to have mass, and their velocity was established to be <c long before the publication of this Encyclopedia!

Starship Fusion Reactors

The TM makes numerous statements about its fusion reactor fuel supply:

"The fuel supplies for the IPS are contained within the primary deuterium tank (PDT) in the Battle Section and a set of thirty-two auxiliary cryo tanks in the Saucer Module. While the PDT, which also feeds the WPS, is normally loaded with slush deuterium at a temperature of 13.8K, the cryo reactants stored within the Saucer Module tanks are in liquid form. In the event that slush deuterium must be transferred from the main tank, it is passed through a set of heaters to raise the temperature sufficiently to allow proper fuel flow with minimal turbulence and vibration."

A GCS stores 62,500 m³ of deuterium, which is stored at 13.8K, in liquid form (TM pg. 69). The average deuterium density should therefore be roughly 160 kg/m³, for a total mass of 10,000 metric tons of deuterium. This represents the fusion reactor fuel supply which the Federation expects to be necessary for a three-year mission period. However, this figure is based on an assumption of 160 kg/m³ density for the ship's entire fuel supply. The average density is somewhat lower. On pg. 75 of the TM, it states:

"The interval volume of each auxiliary tank is 113 cubic metres and each is capable of storing a total of 9.3 metric tonnes of liquid deuterium."

This quote seems to suggest that the density of liquid deuterium in the Saucer Module storage tanks is a mere 82 kg/m³, which is roughly half the density of liquid deuterium. In fact, this is the density of liquid hydrogen, not liquid deuterium. We can only postulate that these tanks cannot be filled to capacity, and that roughly half of their internal volume is actually low-pressure deuterium vapour. It is possible that structural limitations keep them from filling their tanks to full capacity, or perhaps there are other extenuating factors involving safety concerns. In any case, it would appear that the total fuel capacity of a GCS is less than or equal to 10,000 tons.

A typical isotopic hydrogen fusion reaction yields roughly 20 MeV to 30 MeV of energy, depending on the type of reaction. However, the "coulomb barrier" for this type of  fusion is roughly 200 keV, which means that deuterons must have ~200 keV of kinetic energy to overcome mutual magnetic repulsion and come into contact. Also, two neutrinos are generally produced in each cycle, and this costs roughly 500 keV of energy. Therefore, the theoretical upper limit for net energy production from the fusion of two deuterium atoms is 26 MeV. There are roughly 3E26 deuterium atoms in a kilogram, so this works out to roughly 6.2E14 J/kg. This is a highly unrealistic estimate however, since it assumes that all of the atoms will be grouped into pairs that are headed directly for one another!

In real life, temperatures and pressure vastly in excess of the theoretical minimum are necessary to induce fusion. Even when those temperatures and pressures are present, only a small percentage of the deuterium atoms will actually react. Even in the core of a G-class star, less than 1 in 40,000 deuteron-deuteron encounters will result in fusion. In fact, the extremely low probability of deuteron-deuteron encounters regulates the rate of reaction and is the sole reason that stars exist for as long as they do, rather than exploding. Compounding the problem is the fact that their impulse drive hurls a substantial portion of its fuel into space as propellant, still in hydrogen plasma state (as seen in ST6). Obviously, this means that a very large proportion of the impulse engine's fuel does not react, as postulated above. What does this mean? It means that we cannot make a reasonable determination of fusion reactor output simply by looking at their fuel supply.

So how do we determine the power output of a GCS fusion reactor? There are a few possibilities:

  1. Some Federation cultists attempt to use the instantaneous power figures from the TM to generate unrealistically high power estimates for starship fusion reactors, because it states that the peak instantaneous power during each pellet detonation is 1E11 MW. However, they are ignoring the DS9 TM as well as the distinction between instantaneous and average power. The instantaneous power only describes the peak power during the microsecond that their laser fusion initiators strike each pellet. This information is useless without knowing the number of pellets launched into the reactor per unit time, because the power curve in a pellet-type fusion reactor will be at zero most of the time, and spike to a peak during each pellet reaction. The height of this peak in no way defines the average power output, although it could be used to generate an extremely high upper limit. This upper limit will not be very useful, because of the extreme swings in power output experienced by a pellet-type reactor.

  2. The DS9 TM states that the total power output of DS9's fusion reactors is 790 TW, therefore we can estimate that the fusion reactors of a GCS are much less powerful than 790 TW. Otherwise, it would be difficult to explain how DS9 easily held off entire fleets of starships in Way of the Warrior and A Call to Arms. Those starships had access to fusion power from their impulse drives, as well as warp power (warp cores can produce shared power for ship's systems even when at sublight speeds). It would therefore seem reasonable to suggest that a typical starship's fusion reactor is much less powerful than 790 TW.

  3. According to the warp power chart on page 55 of the TNG TM, the power requirement for achieving warp 1 is approximately 2E4 "megajoules/cochrane", dropping to 2E2 "megajoules/cochrane" just after achieving warp 1 (the energy requirement for crossing the threshold is much higher than the energy requirement once the ship has entered warp). Furthermore, we know that warp 1 is precisely 1 cochrane. If we use the almost universal Federation cultist assumption that the units of megajoules are actually an error, and should be megawatts, then this means that the power requirement for achieving warp 1 is approximately 20 GW, and the power requirement for maintaining warp 1 is approximately 200 MW. 20 GW is therefore the upper limit for GCS fusion reactor output, since a GCS fusion reactor is not powerful enough to achieve warp speed. This is the reason that starships are limited to impulse speeds when their warp cores have either run out of antimatter fuel, become damaged, or been ejected for safety reasons.

Although the inability of an impulse drive to propel a starship to warp speeds is generally accepted, some Federation cultists would undoubtedly object to the logic used to derive the 20GW figure above. Therefore, they will undoubtedly require the usual repetitive evidence before they accept the figure:

"The M/ARA is the principal power-generating system because of the 1E6 greater energy output of the matter/antimatter reaction over that of standard fusion, as found in the impulse propulsion system" pg. 57
"The multimode sustainer engine is not a true warp engine due to its small physical size, one twelfth the minimum matter/antimatter (M/A) reaction chamber size." pg. 129

It is quite clear that a warp core is required to achieve warp speeds. Even Zefram Cochrane's original warpship, the Phoenix, had a warp core. Therefore, since we know that starship fusion reactors cannot generate enough power to achieve warp speeds, they must be limited to 20GW or less. This makes sense, since an entire fleet of starships was unable to overwhelm DS9 even though DS9 is powered by a 790TW fusion reactor group and the starships were using both their fusion reactors and warp cores to supply power.

Space Station Power Generation

 The DS9 TM clearly described the power output of DS9, which is one of the largest and most prominent space stations in the Federation:

"the reaction chamber group is the heart of the generator, potentially capable of producing 790 terawatts of power with all six chambers running."

Since DS9 was able to hold its own against entire fleets of enemy starships in Way of the Warrior and A Call to Arms, we can conclude that its power is at least average for a Federation space station.

Some Federation cultists question why DS9 does not use matter/antimatter reactors, but this is a ludicrous question. On pg. 67, the TM states: "Antimatter is first generated at major Starfleet fueling facilities by combined solar-fusion charge reversal devices ... there is a net energy loss of 24% using this process". In the discussion of its onboard antimatter generation system, it goes on to state: "the law of conservation of energy dictates that the power required for this process will exceed the usable energy ultimately derived from the resulting antimatter fuel" on pg. 72.

In other words, for every kilogram of antimatter stored on a Federation starship, at least 1.8E17 joules of energy were generated in fusion reactors, somewhere in Federation space, to produce it. Another way of putting this is that at least half of the Federation's total power-generation capacity, including both starships and starbases, must be fusion-based. Otherwise, they would not be producing enough antimatter to meet demand.

Therefore, all Federation starbases probably use fusion for their power source. Matter/antimatter is a net-loss system since each kilogram of antimatter will cost at least 1.8E17 joules to produce, and will generate less than 1.8E17 joules when it is annihilated with an equal amount of matter. Fusion is a net-gain system since fusion fuels can be harvested from natural sources. Therefore, the requirements of starship antimatter consumption dictate that the Federation must use net-gain power sources such as fusion, in their starbases and refueling installations.

When we contrast the 790TW of a large Federation space station with the 1E33 watts generated by the Death Star's hypermatter reactor, we can see that it would take more than forty years for one billion DS9 space stations to generate the energy that the Death Star generates in one second! Obviously, the Federation lags so far behind us in power generation technology that there is little point even bothering to perform direct comparisons like this one- the disparity is too large.

Conclusion

Star Trek Federation power generation technology is extremely limited. None of their battlestations are mobile, their starship power generation systems are extremely inefficient, and even the most optimistic quantifications of their power generation systems indicate that their power output is less than 1% of a Star Destroyer's power output. Even a heavily-armed space station like DS9 is limited to terawatt-range power generation, based on deuterium fusion. Starships are limited to mere gigawatt-range power output! They have been unable to produce planetary shields or move planets as we have, and their crewmembers appear to have very poor scientific knowledge (based on their repeated mistakes).


Acknowledgements



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