Ta-180m: How much in a stutterwarp drive?

Introduction

Tantalum is the "magic ingredient" in stutterwarp drives. It's availability and politics fundamentally shaped the (GDW) 2300AD universe.

The idea that the stutterwarp used the Ta-180m isotope was mine, not GDW's. GDW simply picked a rare element whose distribution of known mineral reserves looked like it would give a good universe. I noticed that Ta-180m's transition to Ta-180 would fit the effect of a drive breach exactly. Thus I proposed that the stutterwarp used Ta-180m. This proposal predated Colin Dunn getting the 2320AD gig, and hence joining the 2300 communities. It was incorporated in Mongoose 2k3 without attribution to the original source (me). As the "original inventor," I believe I can comment on it. Colin has even noted (in 2010) that it was fanon (i.e. mine).

The question is, how much Ta-180m would a drive need? It must fit both the observed effects of a drive breach, and the production of starships.

Tantalum-180m Quantities

Ta-180m is spin trapped. The nucleus is spinning on its axis fast enough that the nucleus is not spherical, but prolate (i.e. rugby ball shaped). The nucleus can flip between prolate and oblate (i.e. the axis of rotation), but it is not both simultaneously, unless excited into a very high energy state where it flips so fast between the two states that it has some existence as the intermediate sphere (K mixing). This sphere can (and does) decay into the ground state, releasing the energy (and spin) as a burst of X and gamma rays. The m spin state is 74 to 77 keV above ground, and K mixing occurs 2.74 MeV above the m state. These equate to ca. 10 times its mass in TNT (9.65) and ca. 350 times its mass in energy terms.

The gravimetric charge is probably stored in the Ta-180m by increasing the energy of the nucleus. As they get charged, they flip more and more frequently. The actual quantum states will obey a Boltzmann distribution, and so the possibility of some of the Ta-180m reaching 2.74 MeV occurs well below all of the Ta-180m being charged (see appendix).

The effect of an uncharged or charged drive breaching is described in a task in the GDW boxed set:

A total failure, i.e. the destruction of the drive, results in an EP = 5 explosion. This would be the result of the Ta-180m relaxing, and it would take ca. 50 grams of Ta-180m to release that energy, assuming 100% efficiency and that all the tantalum went up. In reality, without a charge, no chain reaction would occur, and this is just a small fraction of the tantalum going up. No chain reaction would occur as no high energy gamma is released to pump surrounding atoms. Thus the 50 g is a floor. It would have taken isotopic separation of ca. 500 kg of tantalum to produce 50 g of the star drive grade.

From the other side, there were a few hundred thousand tons of tantalum on Earth. 300,000 tons would give ca. 36 tons of stardrive Ta-180m. The number of stutterwarps built in Human history upto 2300AD is maybe 10,000 (3,300 starships in 2300AD, plus missiles, losses etc.) Much of this tantalum came from offworld, probably a majority of it. If, say 84% of the tantalum came from offworld, then an average drive has ca. 50 kg of Ta-180m in it. Call this the ceiling.

In all likelihood, a typical drive might contain, say, 0.1% of the drive mass as Ta-180m. This would be an intermediate value that would fit the amounts available to give the canonical numbers of ships. A Kennedy class light cruiser would have 85 kg of Ta-180m, which needed ca. 700 tons of tantalum isotopically separated to supply it. Known reserves on Earth would be enough for ca. 400 Kennedys without missiles, although each load of missiles would consume ca. 1,200 tons of tantalum.*

Currently, without using it for stardrives, tantalum metal is $250/kg. 700 tons would be 175 million dollars (i.e. MLv21.9 using GDW livres**), and represent much of the Earth's annual production. Notably, this is less than the cost of the stutterwarp drive.

Core Breach Effects

What about the breach of a charged drive. The energy of saturated Ta-180m is ca. 350 times it's mass in TNT (1.46 MJ of gamma per g Ta-180m). It's likely that it is impossible to reach 100% charge, as the amount of charge will be in a distribution. The description of shutting down a drive says that the charge concentrates on the still active parts of a drive, and when a part saturates it breaches.

We should note that the description has implications for space combat. If a ship has a charged drive, and battle damage causes it to be offlined, then the drive will breach, with all that implies.

Using Grays (Gy) as our radiation measure, 1 Gy = 1 joule of absorbed radiation per kg body-mass. The LD50 (the dose at which 50% of people will die of acute radiation poisoning) is 3 Gy, or 210 j of gamma for a 70 kg person. Humans absorb about 50% of the applied gamma, and was 420 j of gamma applied would be LD50. If there is no shielding etc. when a human would be exposed to this from 1 g of saturated Ta-180m 20-30 m from the reactor.

100 Gy, which would kill in minutes, equates to about 14,000 j applied (i.e. more energy than a .50 cal bullet). For 1 g of saturated Ta-180m, this is ca. 1% of the theoretical emitted energy. You'd need to be 2-3 m from the drive to receive that from 1 g of Ta-180m, assuming no shielding. This would likely place you inside the drive.

With the frequencies involved, about 3 mm of lead attenuates 50% of the gamma, or 1 cm of steel. Assuming a casing of 2 cm of steel or so, only 25% of the gamma would escape the drive.

The drive is not likely to be fully saturated. In fact, it is likely to be only around 1-10% of saturated.

If we set the "instant kill" radius at 20-30 m (100x), shielding at 25%, and the amount of Ta-180m crossing the activation energy at 1%, the total Ta-180m in the drive is now 40 kg. Ergo, with these simple assumptions, I am in the same range as above.

Depleted Tantalum

After isotopic separation the depleted Ta-181 is chemically still tantalum, and is an extremely useful and expensive metal used in capacitors etc. Indeed, I can remember someone (Ben Levy, I believe) pointing out that this might create a glut of Ta-181, or "depleted tantalum." It could well be that depleted tantalum jewelry becomes a thing for example. The unscrupulous might try and pass off depleted tantalum as genuine etc. There's a game hook for you.

Mongoose 2300AD and Tantalum

As I have noted previously, Colin, the Mongoose 2k3 author, has tried to remove the tantalum limits of 2300AD. The tantalum issue is one of the core conceits of 2300AD. By removing it, the universe doesn't make sense, but it allows the Libertines to exist (see here for similar on the Mongoose forum in 2013). I understand his reasoning, but it is flawed.

In the 1st Mong edition, Colin got the element wrong, and stated it was Ta-180 (1st Mong 2k3, pgs 3 and 265, itself a word for word reprint of 2320AD pg 309). This has a half-life of 8 hours. The incorporation of Ta-180m proper occurs after a 2014 facebook thread in which I corrected the matter. However, he took his queues from me and wrote in the 1st edition (pg. 265):

Tantalum is a very rare element and the isotope Ta-180 even more so. The Ta-180 isotope is the only one that can be used in a stardrive. It has only a limited availability and although the quantities used in the construction of a stardrive are relatively small, it is still a managed resource. This limited availability ensures that only a limited number of ships can be built per year. A tantalum-180 find of any size is enough to make its discoverers very wealthy.

However, in the few years afterwards he switched to a far more neoliberal economic model. In fact one far more libertarian than the most extreme Chicago school economists. There is a lot of this as the Mong 2k3 run continues, it lurches far to the economic right.

In the 2nd edition (AEH, pg 3), Colin states:

The limiting factor in the construction of new vessels is the rarity of an isotope of tantalum. This isotope, Ta-180m, is one of the rarest in the universe. Fortunately, a starship drive only requires a few grams.

This is demonstrably incorrect. It exists only to try and remove the tantalum limits. Whilst he is free to change how he plays his game (which, of course, alters the Mongoose universe), he can't change the prime canon.

Also, a few grams would not be dangerous if it breached. Thus this interpretation fails both the criteria it needs to fulfill.

Conclusions

Within the core universe, tantalum limits starship production. Following various factors, the amount of highly enriched Ta-180m in a stutterwarp is about 1/1,000th of the mass of the drive. This allows for an approximately correct number of starships, and for the effect of a drive breach to scale correctly.

The alternative idea, that there are grams instead of kg of Ta-180m, doesn't address either the starship numbers, or the effects of a drive breach.

Notes

 * This is completely in keeping with canon. See the 2nd edition Director's Guide, pg 78.

** Note: GDW and 2320AD (and derivatives) livres are not the same. The value of a GDW Livre is 3 US dollars ca. 1986. The 2320/Mongoose livre is pegged to the Traveller Imperial Credit at 1:1, and hence is the value of one ca. 1977 USD. The conversion is 1 GDW livre = 5 2320/Mongoose livres. For converting modern USD to GDW livres, divide by 8.

Appendix: The Boltzmann Distribution

Boltzmann distributions look something like this:

As the general energy goes up, the distribution shifts right. At a certain point, a small portion of the distribution is beyond the activation energy for a reaction. This chart is actually gas particle velocity at increasing temperatures reskinned, but the underlying concept is the same. It does mean that only a tiny fraction of the distribution reacts.