Reality check: energy source for power armour

Question

TLDR: Radioisotope thermoelectric generator (RTG) with polonium($\ce{^{210}Po}$) instead of plutonium($\ce{^{238}Pu}$) cooled by liquid lithium is a superior power source for any power armour. More detailed conclusion is at end.

Setting

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Humanity has conquered the Solar system but has a long way to go before becoming an interstellar species. The Jovian moons, Mars, annd the asteroid belt are colonised, but Titan is not.

Technology levels are similar to Expanse, but without the protomolecule and with a bit more constrained interplanetary transportation.

Gravitational wells of the planets are still serious obstacles. I tried to design the warfare so that it favours small-scale operations that are best done with dedicated military units to exploit speed and mobility.

Naturally, such a state of affairs nudges technological development into focusing as much military might into a single person as possible, thus the power armour.

EDIT: As this tech is quite expensive, power armour is not used by standard infantry, but rather by shock troops to reach dedicated objectives. These include, but not limited to: initial assault from orbit, breach crews for spaceship and station boarding, sabotage. One might say, that toxic nature of the fuel and coolant forbids massive adaptation of this technology even if somebody is rich enough to afford it.

Power armour

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The picture above by ukitakumuki is the best depiction of what I understand as a power armour that I could find on the internet.

However, there is a well-known problem that is faced by any power armour design. The source of power. This tiny backpack in the image above can't hope to supply enough energy without some sort of Clarke magic $^1$ that derails the whole setting.

Power source

TLDR: Accumulators, fuel cells and modern RTGs are unsuitable.

I invite you to ignore the backpack design above and imagine how this thing can actually be powered.

Let's get some rough numbers for a baseline. There is no power armour in real life, but there are exoskeletons and accumulators.

From this article it is possible to infer that the energy consumption of an exoskeleton is in kilowatts.

Power armour is, conceptually, an exoskeleton that carries defense plates, power supply, computers, and weapons. Computers are not particularly power hungry, defense plats and weapons could also eat no energy. So, in a basic setup, one needs to power nothing, but an exoskeleton.

$$ W_{exo} \approx 5 kW $$

Li-ion accumulators

TLDR: Power armour needs half a ton of accumulators for a 24-hour mission. Too much.

From another article it is possible to extract some accumulator data for electric cars. Namely specific energy($W_{se}$) and specific power ($W_{sp}$) and volume-specific power($W_{vsp}$.

$$ W_{se} = 155 \frac{Wh}{kg} $$ $$ W_{sp} = 0.71 \frac{kW}{kg} $$ $$ W_{vsp} = 2.52 \frac{kW}{L} $$

With today's technologies, the power supply should be at least $m = \frac{W_{exo}}{W_{sp}} = \frac{5}{0.71} = 7 kg$, not so bad. But this is just to ensure a continuous function. For the deployment time of $t_h = 24$ hours the mass of accumulators should be about $m = \frac{W_{exo} \cdot t_h}{W_{se}} = 774 kg$.

Ouch, this is definitely too much.

Hydrogen fuel cells

TLDR: Power armour needs over 500L of modern hydrogen fuel for a 24-hour hour mission. Moreover, compressed hydrogen itself is a bad idea for a combat situation.

Following a very informative report it is possible to infer stats for a modern system of hydrogen fuel cells.

$$ m_{cell} = 43 kg $$

$$ W_{sp} = 2.9 \frac{kW}{kg} $$ $$ W_{svp} = 3.37 \frac{kW}{L} $$

The fuel cell could be fuelled. The tricky part is to choose how much hydrogen is compressed and how much to store. Because the more it is compressed, the more energy-dense the fuel is. However, if compressed, it explodes upon mechanical impact. Not a good quality for a part of power armour.

Modern energy density of $\ce{H_2}$ fuel is around $4.5 \frac{kWh}{kg}$, and $225 \frac{Wh}{L}$, which is similar to $205 \frac{Wh}{L}$ of electric car accumulators. At this pressure the hydrogen mass-to-volume ratio is $0.05 \frac{kg_{H_2}}{L}$.

So, let's see how much mass and volume one should take for a $t_h = 24$-hour mission.

$$ m = 43 + \frac{5 kW \cdot 24 t_h}{4.5 kW} = 43_{cell\ mass} + 26.6_{fuel\ mass} = 69.6 kg $$

Now, the fuel volume:

$$ V = \frac{26.6}{0.05} = 533 L $$

Here is a 500-litre tank for reference.

One can compress hydrogen further and even liquify it. But then, cooling and/or safe storage are of critical importance. One well-aimed projectile and the whole thing explodes and then sets ablaze if oxygen is present. Furthermore, this is unlikely to significantly change with improved technologies as hydrogen is fundamentally hard to handle and the fuel efficiency is already relatively high(about 40%-60%).

Thus, I say the fuel cell is out.

RTGs, my beloved

TLDR: Too little power

Today radioisotope thermoelectric generators are used in space, there are many variants, but I will use MMRTG as a reference point.

Almost all of them use plutonium as it has several very important features that are very handy in space missions.

• Has long half-life: 87.7 years
• Undergoes almost exclusively $\alpha$-decay

The stats for MMRTG with $^{238}Pu$ are as follows:

$$ m = 45kg $$

$$ W = 0.125 kW $$

$$ W_{sp} = 0.0028 \frac{kW}{kg} $$

$$ W_{vsp} = 0.022 \frac{kW}{L} $$

This is quite low and can't power any kind of power armour.

Speculation about RTGs

TLDR: Polonium provides plenty of energy for a considerable amount of time and can be manufactured from stable components on site. However, it needs to be cooled to ensure RTG does not melt. Water is not sufficient, lithium is a better alternative. Lastly, its radiotoxic qualities are manageable as alpha radiation is detectable and extraterrestrial environments are naturally resilient to contamination.

First, let's examine another good, modulo extreme toxicity, candidate material for RTG fuel: polonium, more precisely $^{210}Po$. It also undergoes almost exclusively $\alpha$-decay, but unlike plutonium, its half-life is only 138 days$^2$. All polonium below is assumed to be of this isotope unless specified otherwise.

The short half-life is quite good actually, the power output from it is much higher than from plutonium. The downside is that one can't store it and needs to produce it on-site from stable bismuth via neutron bombardment. For a reasonably timed mission, it is more than enough. However, if the mission is expected to be longer than a month and supplies are scarce, then no luck.

The MMRTG itself has quite moderate weight and size as one can see in the picture above. The tricky part with polonium is to cool it down as it obviously emits much more thermal power compared to plutonium.

There are existing designs for polonium RTG, but they are old and for space. It seems like they do not reflect the extent of power harvesting that is possible with polonium fuel as they are limited by their field of application.

Energy output

TLDR: Polonium energy output is not only enough for exoskeleton baseline, but permits wet mass over 2 tons while preserving ability to run.

Thus, for speculation, let's just scale existing MMRTG to polonium based on the power-to-volume ratio.

The thermal power density of polonium is $140 \frac{kW}{kg}$ instead of $0.54 \frac{kW}{kg}$ for plutonium. Accounting for density, the scale factor for specific energy outputs is as follows: $$ scale = \frac{W_{Po\ thermal} \cdot \rho_{Po}}{W_{Pu\ thermal} \cdot \rho_{Pu}} = 120 $$

And the stats themselves:

$$ W_{sp} = 0.33 \frac{kW}{kg} $$

$$ W_{vsp} = 2.64 \frac{kW}{L} $$

These numbers approach those of accumulator but with no drawback of limited capacity. The decay continues without stopping and the degradation of the power supply won't bother the wearer for weeks.

And for the whole thing $W_{Po} = 125 W * 120_{scale} = 15 kW$. Seems perfect for $W_{exo}$.

To put these numbers into perspective let's see what are mass limitations for this thing to run. The power output of running humans is provided by table here, as one can see it is a good estimate to have $W_{running} = 5 \frac{W}{kg}$. Assuming modern electrical motor efficiency of $\alpha = 0.75$ the wet mass of the soldier is as follows.

$$ m_{wet} = \alpha \frac{W_{Po}}{W_{running}} = 2.25 \text{ tons} $$

This is a lot of room for equipment.

Production

TLDR: Polonium production could be done in the field from stable materials on demand.

An interesting paper explores a very efficient way to produce polonium, as found by @Vesper. It suggests a self-sustaining reaction in bismuth beryllium acetate. There are few details in the paper regarding this substance, so I assume it is a mixture of bismuth acetate $\ce{C6H9BiO6}$ with beryllium acetate $\ce{C4H6BeO4}$ in some undisclosed proportion. These are stable compounds that are very transportable.

Magic happens when polonium is added to the mixture. The process goes as follows.

1. Polonium decays and emits high energy(5.4 MeV) $\alpha$-particle. This turns polonium into lead.
2. High energy $\alpha$-particle interacts with $\ce{Be}$ and get turned into neutron, producing stable $^{12}_6\ce{C}$ carbon. $\alpha$ -particles and resulting neutrons also interact with light elements(thus acetate) to create even more neutrons and fine-tune existing ones to suitable energies(read the paper for details).
3. Resulting neutrons interact with $\ce{Bi}$ creating its unstable isotope that shortly decays into precious $\ce{Po}$

The paper claims that not only it is possible to effectively produce polonium in this way, but also quite easy to extract. Far easier than from a molten metal mixture of reactor coolant.

The paper lacks details on the values for their theoretical model that were determined by the experiment. Still, judging by their graphs, it is safe to assume that a considerable portion of bismuth was turned into polonium after 50 hours of reaction time.

Let's approximate some yields. Molar masses are $\mu_{Bi\ acetate} = 386.11 \frac{g}{mol}$, $\mu_{Be\ acetate} = 127.1 \frac{g}{mol}$ . Densities are unavailable, so I will assume something like $\rho = 1.75 \frac{kg}{L}$ following calcium acetate and other similar metal compounds.

So, assuming $V = 100 L$ container of the 50/50 mixture w.r.t molar masses is a standard supply pack, the following mass of bismuth acetate is present.

$$ m_{BiA_3} = \frac{V \cdot \rho}{1 + \frac{\mu_{BiA_3}}{\mu_{BeA_2}}} = 43 kg $$

Then bismuth acetate substance amount is $\frac{43 \cdot 10^3}{389.11} = 112 \text{ mol}$, with single bismuth per molecule the with molar mass of bismuth being $\mu_{Bi} = 209 \frac{g}{mol}$ overall bismuth mass is as follows.

$$ m_{Bi} = 112 \text{mol} \cdot \mu_{Bi} = 23.5 \text{ kg} $$

As polonium is produced the mass slightly changes, but it should be less than a percent due to the single nucleon difference.

If plutonium is replaced by polonium in MMRTG with volume preservation, its mass would be 2.4 kg per RTG. Overall, this means that from a single 100L container, after a little more than two days of waiting, one can produce polonium to fuel $\frac{23.5}{2.4} = 9.8$ fresh RTGs.

This is, of course, assuming all bismuth is turned into polonium, and it is quite reasonable to assume high efficiency, but even if this container turns only half bismuth into polonium it is enough to refill a full squad of five power armour wearers. Moreover, they themselves can trigger the production by just unloading their depleted RTGs into the supplied container.

No need to transport hot pieces of equipment fuming with lithium as the fuel can be made right before deployment. One can't stop existing ones, but these can be recycled or safely stored.

Thus, I call success on production possibilities.

Cooling

Disclamer: The cooling is actually the most problematic part. There are few mistakes in the section below, but the results are mostly correct. I hit character limit, so for corrections, more armour depictions, $\ce{LiH}$ coolant, and more nuanced calculations, please, go here.

TLDR: Water is not efficient enough as a coolant, lithium is almost ten times more effective.

It is easy to have radiation shielding for alpha decay, but it is much harder to deal with heat.

The thermal power of polonium is two orders of magnitude stronger than that of plutonium. With a 6.25% efficiency of MMRTG, if one would use water to remove heat by evaporation, the water would need to dissipate about $120_{scale} * 2\ kW_{Pu\ thermal} = 240kW$ of continuous heat.

Good thermoelectric elements are themselves thermal insulators. With advanced material science, it is not a long stretch to assume that it is possible to thermally isolate a human wearer from the power source. This does not solve the task of preventing an RTG from melting but allows the use of more exotic coolants that can operate at higher temperatures.

Suggestions for cooling materials are welcome by the way.

Water

Accounting for evaporation energy of the water $E_{\ce{H2O}} = 40 \frac{kJ}{mol}$ and its molar mass $18 \frac{g}{mol}$. It turns out that the water loss would be about $\frac{240 \cdot 18}{40} = 108 \frac{g}{s}$ means that for a 24-hour mission, one would need to take 400 kg of water. Too much.

Lithium

Turns out lithium is almost ten times more effective per kilogram. Evaporation energy $E_{\ce{Li}} = 136 \frac{kJ}{mol}$ with a molar mass of $6.9 \frac{g}{mol}$ its loss is going to be only $\frac{240 \cdot 6.9}{136} = 12 \frac{g}{s}$ with demand for a 24-hour mission being "only" 43 kg with a volume of 81 liters.

The boiling point of lithium is 1330 °C. There is a handy paper about lithium evaporation which allows inferring that, near the boiling point, lithium evaporates with speed in grams per second from each square centimeter. Precise value is hard to recover and, honestly, is excessive. The result is that for successful cooling lithium evaporation could be sufficient.

Polonium salting

Unfortunately, the boiling point of polonium is only 962 °C. Nobody wants to handle boiling polonium, this is ridiculous. Polonium fissions into lead and this process naturally increases boiling point, but the process is slow. I found very little information about polonium compounds, for example, density values are nowhere to be found.

There is one polonium compound with thulium $TmPo$. It is reported to have a melting point of 2200 °C. My speculation is that it is possible to "salt" polonium with it to increase boiling point in a similar manner we salt water. This is purely my speculation and I have nothing to support it in terms of papers or articles.

Compensating burst movements

One way to reduce coolant needs is to reduce heat emission, but it reduces the electric power. However, for any device, including power armour, peak and average loads exist. This means that it is impossible to effectively use all available $W_0=15$ kW without storing some of it. For calculations below the fully loaded configuration, which uses all $W_0$ while running, is assumed.

Walking and running, naturally, use different amounts of power. As specified above, running is about $W_{running} = 5 \frac{W}{kg}$, while here it is reported that $W_{walking} \approx 2.5 \frac{W}{kg}$ for $2 \frac{m}{s}$. It could be immediately inferred that walking uses half of $W_0$ in a fully loaded configuration.

We cut the polonium RTG by $0 \lt a \lt 1$ in size and energy output. This reduces power output and coolant consumption.

It is reasonable to assume that power armour with depleted accumulators should permit walking. Thus, $a \gt \frac{W_{walking}}{W_{running}} = 0.5$.

To ensure that the burst power is still $15$ kW the following equation must hold.

$$ W_{sp}^{acc} = 0.71 \frac{kW}{kg} $$

$$ W_0 = a \cdot W_0 + m_{acc}\cdot W_{sp}^{acc} \iff m_{acc} = 21.2 \cdot (1 - a) \text{ kg} \implies m_{acc} < 10.6 \text{ kg} $$

The maximum burst time in seconds is $t_b = \frac{m_{acc} \cdot W_{se}^{acc}}{(1 - a) \cdot W_0} = \frac{2 \cdot 10.6 \cdot 55.8 \frac{kJ}{kg}}{15 kW } = 78.9 \text{ s}\approx 1.3 \text{ min}$, with the same recharge time, while idle.

So, It seems like accumulators are just not worth it to compensate for burst movements. Some power can be stored for an occasional consumption spike by equipment, but running is just too power-hungry.

The above assumed that accumulators are occupying extra space that is produced by downsizing an RTG. Potentially, nothing forbids to just take more to reduce lithium consumption. This is not effective volume-wise though.

Radiotoxicity of polonium

Disclaimer: I must confess that I do not have much expertise in biology or medicine, thus I welcome any suggestions on how to improve the analysis below.

TLDR: Decontamination by itself happens after less than six year. There are way to effectively detect and combat polonium spread even today. Extraterrestrial habitats are naturally tolerant to radioactivity.

First, let's investigate how deadly polonium is.

The first thing to mention is that polonium is almost exclusively an alpha emitter and does not pose a danger outside of living tissues. Exceptions for humans are eyes and, I assume, mucous membranes.

Practically this means that it is enough to have breathing gear and some skin protection to avoid exposure. Power armour application domain lies well beyond Earth, so it is natural to assume that space suit is a norm.

Extreme radiotoxicity establishes itself when polonium is ingested, inhaled, or absorbed otherwise. There is a promising antidote, but it is best to avoid situations where one needs it.

Lethal doses are small, but upper limit for safe dose is more interesting and it is as small as 6.8 pico grams.

The immediate conclusion here is that it is impossible to have a polonium-based power source that surely contaminates the area in case of a leak. After the battle took place it is safe to assume that some of the fallen wore power armour and their RTGs are surely raptured.

Below I am going to explore why I think that this conclusion is premature.

Natural decontamination due to decay

Polonium decays into lead, so let's see after what time lead poisoning would be more probable than polonium poisoning.

Upper limits on safe lead levels in blood are $10 \frac{\mu g}{100g}$. Blood density is 1060 $\frac{kg}{m^3}$ with average adult having $5L = 5 \cdot 10^{-3} m^3$, meaning that $m_{blood} = 5 \cdot 1.06 = 5.3$ kg. Then the upper mass of lead in blood is $m_{Pb}^{\text{safe}} = 5.3 \mu g = 5.3 \cdot 10^{-9}$ kg. The safe does of polonium meanwhile is $m_{Po}^{\text{safe}} 6.8 \cdot 10^{-15}$ kg. Relation between lead and polonium is thus $\frac{6.8}{5.3} \cdot 10^{-6} = 1.28 \cdot 10^{-6}$.

Radioactive decay is exponential and respects the following equation.

$$ N(t) = N_0 \cdot 2 ^{- \frac{t}{t_{1/2}}} $$

The molar mass of lead produced from polonium is exactly $206 \frac{g}{mol}$, while polonium isotope has $210 \frac{g}{mol}$. This is close enough to disregard.

$$ 1.28 \cdot 10^{-6} = 2 ^{- \frac{t}{t_{1/2}}} \iff t = 13.56 \cdot t_{1/2} = 1876 \text{ days} = \text{5 years, 3 months and 1 week} $$

Which is not even that long. However, it is long enough to consider decontamination.

Active decontamination

There is an interesting article about one famous polonium contamination cleanup in 2006 in the UK.

The obvious solution is to dismantle contaminated objects, dig a waste pit, and dispose of everything there. However, for solid surfaces, other two methods were used.

1. Decontamination agents
2. Source sealing

The first method refers to chemical agents that extract polonium from hard-to-reach places to be removed with the agent later. They could be quite advanced and as the power armour wearer returns from deployment it is reasonable to assume that decontamination could be up to a full submerge of the thing into a vat with the agent.

The second method uses the fact that alpha particles are easily stopped by matter. For example, a new coat of paint. Solid surfaces benefit mostly from this method.

Lastly, the most compelling reason why I think that polonium radiation is not a critical hazard is detection. One can detect its presence in dust, liquid, and gas as It emits alpha particles. It is very easy to find it if you know what you are looking for as, usually, alpha particles travel a few centimeters in the air.

Environmental specifics

All the points until now apply universally, but this power armour lives in a setting that includes space exploration. I am actually quite positive that these suits are forbidden to use on Earth's surface and whoever uses them could face nuclear retaliation.

Even if they are used though, five years is not that long. However, there are other environments in the solar system. Please, bear with me through some setting details and skip until the conclusion at the bottom if you are not interested.

Mars

Mars is colonized locally, all humans live in seven enormous cities ranging from 70M population at Argyre Planitia to 127M population at Noctis Labyrinth.

They are pressurized and their interior water and air are carefully monitored and recycled. They mine and process their own ores and ices to be mostly self-sufficient and, honestly, I designed the power armour to precisely allow their assault.

The power for the cities comes from ITER-style fusion reactors and this by itself makes polonium unlikely to pose a significant challenge. Neutron irradiation of reactor materials is an ever-present hazard and their safe storage is of critical importance. Accidental contamination of water, food, or air must be detected as soon as possible to stop the spread in the early stages.

Furthermore, vast distances between cities are not traversable. The only means of conflict for them are ICBMs and orbital assaults. Each city has nuclear capabilities and that implies fissile reactors which facilitate radioactive leak monitoring and means of decontamination.

Asteroids, stations and spaceships

Space is quite radioactive. Thus radiation level monitoring is vital and it is improbable for polonium particles with their alpha emission to be undetected past the airlock. There is initially no air to stop them there.

The space stations themselves are very cleanable and if a battle took place there, decontamination might be as easy as a new coat of paint.

After all, if boarding took place, it is unlikely that much of the vessel is still pressurized.

Galilean moons

Io is a powerhouse of the Jovian system: geothermal power and available elements fuel asteroid forges and shipyards on Europa, promote food growth on Ganymede, and feed research efforts on Callisto. However, it is worth remembering that Io is a radioactive hell. If one can survive that, polonium is also manageable.

Closing thoughts on radiotoxicity

Overall, radioactive contamination could be a great hazard and should not be underestimated. Especially if it reaches food production or water sources. However, I believe that space colonisation is not possible without robust methods of radiation management and that implies contamination tolerance of extraterrestrial habitats.

Sure, spilled polonium is a very deadly substance, but it is possible to isolate it and decontaminate. There is no biosphere in space where it could propagate until it fully decays. I also like because it highlights the price of waging a war in space

Conclusion

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There are several candidates for practical fuel sources for power armour.

• Accumulators

If no additional power source exists within power armour then with a consumption of 5kW the wearer would need more than half a ton worth of accumulators for a 24-hour mission.

• Hydrogen fuel cells

The fuel cell itself is all right, but the hydrogen needs to be pressurised to store energy efficiently. This is undesired, as pressurised gas could explode the wearer if damaged. Furthermore, if a 24-hour mission is assumed, then over 500 liters of modern hydrogen fuel is needed. One can compress them further, but this increases the structural vulnerability of the armour.

• Modern RTGs

Not enough power generation

• Polonium RTG with lithium coolant

Energy output is comparable with accumulators but with no capacity constraints. The only issue is the low efficiency of heat-to-electricity conversion. This requires very effective cooling system. Water is too ineffective, so lithium is chosen. For the 24-hour mission armour needs to evaporate 43kg of lithium. Polonium radiotoxicity hazard is limited due to natural resilience of extraterrestrial habitats to radioactive contamination.

Furthermore, if one looks at potential improvements for the above technologies, certain asymmetry could be noticed.

• Accumulators could always be assumed to improve. To be fair, this whole thing could be avoided by just handwaving in their direction, but what's fun in that? For example, Li-air with its demonstrated $W_{se} = 1.7 \frac{kWh}{kg}$ specific energy.
• Fuel cells are good, but their efficiency is already quite high. Around 40% it seems, the fuel could be different though, but that's a whole other story.
• Modern RTGs are inefficient. With a thermal-to-electrical efficiency of around 6%, they are roadblocked by thermoelectrical elements. Materials with low thermal and high electric conductivities are hard to make with today's technology. Thus, with better material science it is possible to increase their performance dramatically. This will reduce their coolant needs, and make them more compact due to reduced fuel demands.

Overall, it seems like a polonium RTG option is the way for power armour.

The question

Could it work in a hard sci-fi setting or does this sound ridiculous and I am too far into the rabbit hole to notice?

Edit: The answers I aim for are about validity of the logic and technical assumptions above. For example, if there is some technical limitation for lithium evaporation that I have missed, or that polonium boils regardless of the salting used, or that logistics for breach crew with this tech is impossible. The best answer is the one that shows the biggest hole in the power armour design.

Also, I would really appreciate any feedback regarding the whole napkin math I did.

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$^1$: Any sufficiently advanced technology is indistinguishable from magic.

$^2$: There is $^{208}Po$ which has half-life of 2 years. It might be a better candidate for fuel instead of $^{210}Po$. However, so little information is available about it, that I just gave up.

Note: It is possible to make the thermal power adjustable, with altered heat source design.

Answer 1

The whole scheme appears to be based on a misunderstanding of how RTGs work: they do not convert heat into electricity. They are heat engines, they produce power output from a temperature difference. The maximum possible efficiency is determined by the ratio of the temperature difference to the hot-side temperature.

The cold shoe temperature for a MMRTG used on a Mars rover is around 400 K, the hot shoe temperature around 800 K. Lithium only evaporates at any significant rate near its boiling point of 1603 K. If the RTG cold side is cooled by lithium evaporation in an open-cycle cooling system, to achieve the same maximum efficiency the hot side would have to be around 3200 K. To achieve the same power output for the same converter mass, you would also need to have thermoelectric materials that not only equal the performance of the MMRTG, but are made from the very limited range of materials that are still solid under these conditions.

A polonium MMRTG wouldn't just replace the plutonium with an equal mass of polonium, it would replace it with a far lesser quantity of polonium with similar thermal output, leading to similar hot and cold shoe temperatures, and a similar electrical output. This would reduce the overall mass by a few percent, but any huge increases in power density must come from improved thermoelectric junctions. Technological advances could increase the hot-side temperature somewhat, but the cold side needs to stay as cold as possible to keep the Carnot efficiency up, probably not even above the melting point of lithium.

The obvious solution here is to use a fission reactor as a heat source instead. Reactors can vary their output and be shut down, drastically reducing the need for coolant in an open-cycle cooling system. The shielding requirements are problematic, but far less so than the complications of trying to use a polonium RTG with the same peak power output.

Answer 2

Apart from the practical problems Vesper points out (can't turn it off, difficulty of resupply, vaporised lithium is a distinctive signature) there's a very serious political problem.

Breaking open a Po-210 RTG creates deadly pollution. A microgram is more than a fatal dose for an adult human. Worse, the pollution spreads by itself. The high-energy alpha decay of Po-210 means the resulting Pb-206 nucleus recoils violently. If it is near the surface of a piece of polonium, that's enough to tear it and a few other atoms free and send them floating as a tiny polonium particle in the atmosphere.

Anywhere that Po-210 powered machines have been damaged will be uninhabitable for decades, and the borders of the area will expand with time. Sending Po-210-powered battlesuits into enemy territory is actually a nuclear attack, and ICBMs are a reasonable response.

Answer 3

RTGs are bad for this system

The primary issue with RTGs, especially this powerful as you depict (240 kW of heat), is that they cannot be stopped once created, regardless of whether their power is being consumed or not, because the underlying elements' half-life does not depend on external influence (while might be accelerated, it cannot decelerate). This will cause various issues for the army that would be using these as their power source:

• First, RTGs are a constant heat source which is unable to be supppressed; heat detectors on Titan would spoil your advancing army way before it'll have a change to engage its target, even if that army consists of a single trooper in a power armor suit. While this is tolerated in the exact heat of battle, you should not expose your movements before contact, thus you want to use less power on the march. And with RTGs you cannot do that.

• Second, supplying your advancing regiments with extra polonium would be a serious hassle. EDIT: You have provided a means of creating polonium-210 on site; however the process of polonium creation via Pb-Bi coolant and/or Bi neutron bombardment is highly inefficient; while it's still being produced somehow, the displayed supply ratio on Wiki is mere 8 g/month (see Production), which is inadequate for your use - a single suit of power armor with a 5-kW RTG of your construction requires no less than 2400/2/(138/30) = 260.8 grams of extra Po-210 per month. The linked report proposed some means to increase Po-210 production by including beryllium as a (α,n) neutron producer, however it doesn't provide exact figures on how fast could it be when scaled to industry levels. The displayed figures suggest at least double speed per sample, which would really help. Also the Wiki article displays only the Russia->US supply of polonium though, which means the exact production rate is bigger; also RTGs' electric efficiency might be increased from your mentioned 2% to at least 4% of Beta-M RTG series (they were producing 10 W of electric power over 250 W of heat at build time), or up to proposed 22% with ASRG that uses Stirling engines used as power converters instead of direct thermoelectric elements, thus the difference between supply and demand could be largely closed with assumptions of better processes for either thermoelectric power converters or polonium production by your facilities; still this aspect remains a problem to be solved somehow. Maybe one specifically designed reactor could support several power armors with polonium, still it would require a facility to recharge those RTGs in the field, so far any such facilities are way away from being available in the thick of warfare.

• Third, even if your army did win a local battle, they would need some rest - and KAPOW, RTGs cannot rest, they still smoke vaporized lithium out of their power armors - quite unhealthy for your own troops. There are some means of mitigation for this particular issue, namely, the "home" facility might contain better cooling systems for RTGs, dissipating heat in less expensive manner, for example, using techniques like "reverse-geothermal" AKA transferring excess heat to crust - best used on Europa with its ice-covered surface; or maybe the offending party sent more soldiers than power armors, thus a power armor never really rests, but instead the crew is replaced and the armor goes away for another mission.

• Polonium itself is highly toxic (mostly due to alpha activity). Your cooling systems should be EXTREMELY reliable to not get your own troops suffer from acute radiation sickness, which is nearly impossible to achieve in the field. Even more concern goes about technicians whose job is to repair damaged power armors - unless your armors are kind of "one shot", as in, if it's damaged, it's abandoned altogether, but this approach makes intrusion missions very costly, and no army would want overly expensive missions, be it here on Earth or in space. Also normal cooling systems for that power armor might not be that demanding on coolant, given that energy conversion capability could be improved significantly, so maybe even old steam cooling or even a sort of passive cooling would satisfy; yet the constant heat generation should be accounted for.

Reactors are your friends

The aforementioned ASRG might not be highly scalable upwards, but overall using other means of energy conversion would still help with more powerful sources. As a potential engine, the Kilopower reactor already fits your bill with a decent margin, with the proposed electric power of 10 kW, thermal power of mere 43 kW (five times less than your RTG!), passive radiation cooling designed for space (and some environment-based cooling could be used if the battlefield has an atmosphere) and weight of 1500 kg, leaving 800 kg for power armor mechanisms and another 2500 kg for maintaining power to mass ratio required by your expected armor design. If this reactor could be slightly scaled upwards, while maintaining its ability to self-regulate against supercriticality (which Kilopower design does have), it should be a lot easier to maintain in longer missions while also not requiring external fragile facilities for handling of dangerous materials. Not to mention that this reactor is designed for several years of sustained power, compared to your proposed 4 months for polonium-based RTG.

In the near future it might be possible to convert a heavier fuel-based reactor such as BN reactor family into lower-power designs, or adapt existing small modular reactors for lower electric power, heat and weight to make them suitable for war machines (Gundam-style robots, if you wish, or conventional hexapods, tanks and whatnot), making them a lot more efficient solution for powering assault missions than RTGs.

Po-210 RTGs were proposed and discarded already

The idea itself is quite decent, but was rejected in favor of Pu-238 RTGs for long space missions, and is about to be replaced with Kilopower-like fission reactors for more power-demanding shorter-term missions such as Opportunity; see Wiki page "Applications" setting for some details. Our society's primary issues are inability of producing enough of the isotope to employ it for large scale devices, and overall extreme toxicity and chemical reactivity of the metal itself. In your setting the latter issue is somewhat mitigated by initial inhospitability of those places where Po-210 RTGs are expected to be used, but the first issue remains, and technological advances in reactor building allowed cheaper and more reliable (perhaps even cleaner) power sources to be employed instead of them.

Answer 4

You asked about Polonium feasability, but did some analysis of alternatives that you then rejected. Here is a possible choice that you did not consider but, at the level of detail I've gone into, seems more feasible. I have discussed cooling only briefly at the end, but note that as efficiencies are in the 60-80% range, cooling requirements will be substantially lower.(60% efficiency requires half the cooling of 20% efficiency and 80% efficiency requires one quarter the cooling).
Accordingly, any cooling solutions which you consider acceptable for Polonium will be even more accptable here. Usefully, while water cooling is less mass effective that Lithium, the lower rate needed may make it viable and so contamination becomes very substantially less important. So ...

Hydrocarbons MAY meet your need.
The highest energy content hydrocarbon contains 55 Mj/kg = 15.25 kWh/kg. Hydrogen is about 40 kWh/kg but has the containment issues that you mentioned.

Natural gas = Methane.
Image from here

Methane fuel cells can exceed 60% efficiency This page enthusiastically claims " ... methane fuel cells excel in this regard. These electrochemical devices offer an exceptional efficiency rate, consistently surpassing 60%, ... "

This paper* suggests best case potential efficiencies of 80%+. This may require waste heat recovery to etract te extra 20%+. Stirling cycle machines operating at the high temperatures of Methan fuel cells operate at in excess of 50% efficient. If the fuel cell acieves 60% efficiency a Striling machine will add an extra 20%+. A Stirling converter has the advantage of increasing efficiency as the cold sink temperature is reduced. Space applications may allow extra power output per fuel used. [* paper can be read online on researchgate or downloaded. I am often uncertain about the legitimacy of this source.]

Image from above paper.

With suitably developed Science you can safely assume that you can achieve the upper end of this range. If you assume 66% efficiency you achieve 10 kWh/kg, and at 80% = 12 kWh/kg. For 24 hours at a mean 5 kW that requires fuel alone of 10 - 12 kg. To that you must add fuel cell mass, tankage, Stirling converter (if used) and related plumbing.

A very large caveat is that Oxygen is required at a 4:1 Methan:Oxygen ratio.
In an Oxygen atmosphere this can be atmosphere sourced.
In space or other non Oxygen environment add 40 or 50 kG of O2 per 24 hours :-( .

I'm an engineer. I feel that the 5 kW power level is lilely to be substantially higher than required in a non duress situation. This needs more detail and close study as it tens towards being a make-or-break factor.

Overall it's "not light" but appears competitive with alternatives.

Four Solid Oxide Fuel Cells comparisons.
Comparison of the exergy efficiency of four power generation systems from methane using fuel cells They note

• ... Generally, the CH4-SOFC and CH4-SOFC-CLC processes which directly use CH4 as the fuel of cells have higher exergy efficiency. MC-SOFC-DCFC reaches an overall exergy efficiency of 71.4%, ...

One (probably) needs to assue that what may require large supporting mass and volume can be substantially miniaturised by the time that power armour time happens.

Added:

Cooling:

You suggest water cooling of a Polonium RTG with 6.25% efficiency would require say 400 kg of water per 24 hours, whereas Lithium cooling would only require about 40 kg of Lithium for 24 hours of cooling. A hydrocarbon based fuel cell system operating at say 70% efficiency would require about 30% of the coolant of a Polonium system.
(6.25% efficiency = 93.75% heat. 75% efficiency = 25% heat.
93.75/25 = 3.75 times less cooling or ~= 27%).

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Answer 5

Batteries and wireless transmission

You're asking for RTG's, though I want to give a frame challenge. The first energy source you mention are batteries. Batteries in their current form are unsuitable. They are simoly too bulky. They could still offer a solution however. With wireless transmission, as well as integration into structure itself as support or armour.

Of course it isn't recommended to put anything holding energy against oneself. That being said, it is also important how easily the energy can be released. Any material used for a suit holds enough power to level a small town in a nuclear explosion. It is simply stable enough to use without worry. This is why we can look at new innovations that can be a solution. If we can use the batteries as part of the suit itself, and not an add on, it can solve the weight problem. Let's look at some options first.

Solid state batteries

Some ceramic electrolytes are very robust, with a high density. Density should only applied where you need it for protection. This safes weight compared to ceramic plates or other that do not carry energy. It would still be recommended to have some protection between the user and the battery, so any ignition of the battery is relatively harmless. With further compartmentalising the batteries if should be relatively harmless if a battery is destroyed. These batteries can go up to 350Wh per kilogram. Keep in mind that this is a very young field, which can mean great improvements in the future. https://en.m.wikipedia.org/wiki/Solid-state_battery

Carbon Fiber Structural Batteries

Carbon fiber batteries can be directly implemented into structural components. This again saves weight. Unfortunately these batteries do not carry as much charge. Around 30Wh per kg. Even so they can be an interesting addition to the suit. https://research.chalmers.se/en/publication/542818

Graphene enhanced batteries

Graphene can enhance certain batteries. It has been able to improve some lithium-sulfur batteries to have an energy density of 500Wh per kg. This allows further reduction of weight.

https://academic.oup.com/ce/article/8/3/194/7664581

These three options show both that there are alternative solutions, as well as that the field is still young and making big strides.

Microwave Power Transmission (MPT)

You want a 24h operational capacity without charging. We can see that in our current setting we don't even do this. Busses, cars, phones or watches are charged regularly. This is regardless of electric or gas vehicles. We just don't carry the power for a full service at all times. That begs the question, why would you carry all power at all times? If you can continuously or periodically charge the suit, they can easily reach many more times the projected charge of a battery.

Of course you run into problems. A charging port isn't there at all times. So we need to charge on the go. We can do something like one person having a larger suit that carries a larger reactor for charging. Much like some people in squads have had non combative roles, like soldiers with radio's in the past. They join the squad for charging and do not engage in combat unless absolutely required. However, I would try to cut out this liability and use it only in specific scenarios. I would go for MPT.

MPT is a microwave, created just like in the microwave at home. With dishes you can focus the wave into a narrow beam. This can be picked up by an antenna, allowing it to generate electricity. This isn't very efficient, though in lab conditions they could get a 95% efficiently. In the field a 50% would be generous. It doesn't matter that much though. You can receive kilowatts of power through the air. With a station close by providing the power, and improved localisation of each suit you could charge them while in the field. That means you can severely reduce the amount of energy they need to carry. It dies not work well through buildings though. However, it can be expected that wireless charging of a base that is yours is a given. Any base or ship you would want to capture will have an objective to capture the power station, allowing for recharging inside.

A view how it would work

Your soldiers drop from orbit. Depending on the scenario MPT is used to charge from orbit or via a station taken with them. For the more complex missions they'll employ one or a few soldiers with charging capabilities, like a larger, well constructed RTG on their back. Alternatively a charging station without MPT. Their armour is meant to deflect most fire. Anything that does penetrate a battery can lead to a large flame, the remains of the smouldering battery removed at the first opportunity. Though power is certainly an objective for both parties, with hours of operation it isn't the highest priority.

Conclusion

We do not need to carry all energy at all times. It is better to take a hybrid approach. Use creative ways to pack more energy in a suit, as well as allowing for charging in the field. Wireless where possible, with larger energy carriers where needed.

Answer 6

Your calculations are missing several practical considerations, in my opinion.

Practicability

For one, those RTG's would need to be cooled constantly, not only on a mission. They would need to be cooled standing still. They would need to be cooled while being delivered to the frontline. And if a soldier dies, his RTG needs to be recovered and hooked up to cooling before the lithium runs out, or it will melt and rupture. (See John's answer about that.)

And here's the snag: You are talking about boarding actions. In space. That means the RTG's would need to be cooled in vacuum. That adds a whole layer of complexity to the cooling system, because you can't just have the vents open to the outside, because your boiling point of lithium (and, thus, its cooling capacity) would drop sharply...

And the process of producing Po-210 in the amounts required, and seperating it (red hot and unbelievably toxic) from the other involved materials (which are extremely radioactive in their own right) is a hellish procedure. You could probably get better results if you're doing the neutron bombardment in a fusion reactor (due to the much higher neutron flux), but you'd still be toying with all kinds of extreme radiation hazards. This sounds like a Warhammer 40k setting...

Calculations

Your calculation of energy requirements for power armor is very much overly optimistic. You are taking the energy required by a human to walk, something the human body is supremely optimized for (thanks, evolution), and scale that to your power armor. For one, thanks to the square-cube law, power requirements don't scale like that. We are talking armor, which means weight in a wholly different order of magnitude. And we're talking moving that weight around in a very suboptimal way: Since there's a squishy human inside, the actuators cannot make use of an endoskeleton, which will reduce effectiveness significantly. And we're not just talking about walking. A power armor would be expected to run, jump, run high-powered sensor arrays, defend against such with jammers, and possibly power weaponry as well. If all your armor can do is walk and perhaps run, why bother with making yourself a bigger, more cumbersome target?

(For comparison, the Sarcos Guardian XO exoskeleton -- a unit with a very short list of capabilities -- runs at 3kW of power consumption, and couldn't even lift the weight of a soldier, let alone a soldier in armor.)

Military Strategy

So you are near objects of interest, and you're in a battle (i.e., being shot at). At this point it is irrelevant whether you win or lose the battle, because your "object of interest" is now contaminated for a couple of years in the most ridiculously overkill way imaginable (see @John's answer) unless you were able to overpower your enemy so totally that none of your units got hit (and then, why bother with power armor if you're so superior to your enemy?).

So far, you merly handwaved away the contamination as "easily detectable" while implying that it would be easily decontaminated (which it wouldn't). You also failed to specify who the enemy is that would allow you to limit the fighting to areas you really don't care about getting contaminated this way.

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Could it be done, if you're hell-bent on the idea? Perhaps. Could it be explained in a way that would actually make sense in a hard sci-fi setting (i.e., being more efficient than other types of energy, or other weapon systems altogether)? Probably not.

Answer 7

How about wifi cables? Aka drones with fueltanks or battery packs? They follow the power armour, delivering consumables and either returning empty or to be used as a battledrone?

There are drone-deliveries in the ukraine war today, large drone swarms are probed for by nearly all militaries. Automated docking and loading mechanisms exist. A drone can deliver a - en.wikipedia.org/wiki/Baba_Yaga_(aircraft) can transport 15 kg of fuel or ammunition. So a swarm of delivery ants can keep up a constant delivery - or they can be turned into a ammunition stream, going down on the enemy.

They can deliver energy ahead of time and come down hard on the enemy or other supply line drones .

Drones dont have to fly necessarily the whole way. They can land and crawl the rest of the way- or just land and wait- making it the suit owners job to come to the supplies.

Answer 8

You got it wrong by forcussing on RTGs and Po-210.

Well, RTGs (as commonly understood) are still the solution: you want a (small-ish) box that generates heat based on nuclear fission.

When you get technical and nitpicky about definitions though, you need a reactor (which boosts fission using neutron moderators) instead of purely relying on passive, innate decay. I am still talking about the simplest possible setup of just having your fuel encased permanently without much granular control. Just with a neutron moderator present.

Why? Because then you can turn it on when you need it while enjoying somewhat long-ish shelf lifes of the fuel and the ability to store it without massive cooling setups.

You'd still be sending basically dirty bombs into enemy territory so if there's anything even vaguely resembling our current day Geneva Conventions you're absolutely violating them and the presence of these troops is literal nuclear blackmail: "Don't (really) fight them or we poison the entire place for centuries!".

With my approach however this would somewhat be lessened compared to Po-210 RTGs. By boosting the fission (aka drastically lowering the effective half-life) you also increase the output-per-(unit of)-fuel in the desired timeframe, meaning that you need far less dangerous, radioactive material (while increasing the options of fuel available).

Yes, keeping the chain-reaction under control (aka walking the fine line between very low output and activating a nuke) would still be a challenge, but for a civilisation that can engineer and manufacture mass-production-ready power armor suits, it's just something that'll take the engineering team a year and not an insurmounteable issue as there's nothing inherently disallowing it in physics. Small nukes are sub-25kg and smaller than a scuba-diver airtank(and that was engineered with 1950s technology) so getting the fuel critical is absolutely possible in the given weight and space restrictions.

You don't need (moveable) control rods or anything of the sort since that fine-tuned output control is an optional nicety, just a well-designed moderating vessel (that likely has to change over the duration of active use but there are many solutions to achieve that without complex machinery).

Having your core be practically molten down from the start also gives some huge physical advantages: The higher the difference in heat, the more effective cooling is. So if you engineer the most critical parts to simply contain 2000 C molten uranium, you can get away with far simpler cooling setups (and - depending on how you extract the useful energy - more efficient setups / higher initial voltages etc)

Tl:dr: RTG (with low-decay fuel) + neutron moderator boosting output = shelf stable until activation. With the combination of fuel and moderator being the activation. The result is the elimination of most of the logistical impossibilities.

Answer 9

Solid-state batteries could be the answer if they can be used also as part of the armour.

Solid state batteries are made from ceramics and ceramics are used as an outer layer of many armours. It is feasible that some invented in the future ceramics could provide a reasonable layer of protection and be a good energy storage. It might even work as a kind of Electric armour The batteries would not be the only protective element but they would be important. You would need to fudge your numbers a bit but this could work. Twice the energy density, assume that some time is spent on a lower activity, more efficient motors and you could get to 200kg of batteries, more than a reasonable number.

An alternative are old boring hydrocarbons. A gas turbine burying gasoline would provide you with enough energy.

Answer 10

The mass you cite for RTGs does NOT include the significant mass of the required shielding to protect not just the user of the power armour but all those in the pretty wide vicinity from the emitted radiation!

The end result of not adding such shielding (which could well amount to several hundred kilos) would not be pretty, severe radiation sickness for anyone within several meters of the device for more than a few minutes, a slow and lingering, very painful death.

And adding the necessary shielding would not just increase the mass of the device to beyond practical limits, but also the size/bulk. You'd end up having to haul the RTG behind you on a cart, with a thick cable connecting it to the suit to provide power.

See tales of the many radiation related accidents caused by neglected Soviet RTGs used in remote areas of the USSR to power radio stations, lighthouses, and things like that.

The reason they're so useful in spacecraft is that shielding can be very limited, basically you mount the RTG on a telescopic arm with a Cadmium or Lead plate between it and the main body of the space probe and you're good as there is nothing to get harmed by the radiation from any other direction (but installation and transport to the launch site become tricky, obviously, usually this is then done in shielded vehicles and rooms, by remote control, for example, if the people handling it are sane, the Soviets building those RTGs weren't, many had next to no shielding at all and had to be serviced by people with very little protection, many of whom ended up with radiation related health problems).