1) DF doesn't add up like that at low concentrations. Then it comes down to selectivity of the material. Sodium and cesium have similar chemical characteristics, but CsTreat is very efficient in selecting Cs over Na.
2) Material you are using as filter becomes radioactive waste. You want to keep the volume at minimum.
3) With CsTreat you already reach radioactive Cs levels below measurable limit. There is no reason to try to remove more Cs from that water :)
Honest question. Is is being CsTreated since eight years, why we do have radioactive Caesium still accumulating in the coast?
> 2) Material you are using as filter becomes radioactive waste. You want to keep the volume at minimum.
This is very reasonable, but storing sand for 50 years somewhere is technically feasible and maybe even cheaper than storing water. You can put the sand in concrete and obtain a solid block. Then put the package in some kind of coating and bury it in a safe vault. Water instead has the bad habit to leak, run away, and enter in the life chain when bad weather, monsoon or accidents happen. A huge concrete block is also less vulnerable to terrorism than a water tank. Is not so easy to steal a jar of it, for example. Even if you could make a hole in the coating, the product will not just flow out.
>Is is being CsTreated since eight years, why we do have radioactive Caesium still accumulating in the coast?
As far as I know, this is because about 10 PBq of Cs-137 was released during the accident and the released material is transferred by ocean currents. CsTreat is being used for purification of the water, which is pumped into and out the containment to keep core remnants cool. Nowadays the releases are very limited if any.
>This is very reasonable, but storing sand for 50 years somewhere is technically feasible...
You're right. Also CsTreat is solid, rock/sand-like material. It can be stored as mixed into concrete and disposed as low/intermediate-level radioactive waste.
Now you probably want to ask: Why there is huge amounts of radioactive water stored at the plant site? Because of tritium, which is chemically equal to hydrogen and is very expensive to separate from water. Under normal operating licenses of NPPs, you could release such water into environment, but at Fukushima standards are nowadays peculiar.
In fact the fission[1] part in such small scale is hard. Curiosity and other probes using thermonuclear batteries harness alpha decay[2], which is relatively easy as it happens whether or not you want it to happen, but creates also much less power. In that case the hard part is to obtain material with appropriate half-life and other properties. Perhaps best material for this is Pu-238, which is far more expensive to create than weapons grade plutonium.
I don't think "thermonuclear" is the right term for the batteries in probes. Wikipedia says "thermoelectric"[1], as the electricity is generated directly by thermocouples.
"Thermonuclear" usually refers to the sorts of fusion reactions found in stars and modern nuclear warheads.
Sorry I wasn't using the strict term of fission[1].
This reactor says it uses U-235 which would be full fission similar to the US SNAP-10A[2] or Russian BES-5 RTG[3]
So yes the fission part is more complicated than a P-238 alpha decay RTG. Perhaps I mischaracterized the R&D complexity on the reactor portion, although it has been done before.
When writing the answer, I didn't even consider, that those reactors need to be fast reactors. In retrospect it is obvious, but makes controlling the power even harder.
I still remember Kaisa telling in primary school, that Euclid's proof of infinite number of prime numbers is often considered as the most beautiful proof in mathematics.
We were both in a very small school in the countryside and when I was on 5th and she on 6th grade, we had wonderful teacher, Harri Ketamo (Google him and you'll end up wondering, what on earth he was doing in that school). Harri was especially interested in teaching mathematics. As there was only about ten pupils in the class, he had possibility to teach more advanced pupils further covering among other things programming and prime numbers.
I don't remember if it was in school or after school, when we had with Kaisa a debate over whether or not there was infinite number of prime numbers. The next day or so she presented, that it has been proven and here it is. Back in those days I didn't get it completely, but she was already there.
I think infinities also have use in the real world. Take the insolubility of the quintic. You can reword this as saying that none of the infinitely many candidate solutions for quintics work. Its real world utility is straightforward: there's no point to continue looking for a solution.
Maybe the biggest drawback for tritium is the decay energy of 0.02 MeV compared to 5 MeV of Pu238. On longer missions also half-life may create problems (12 years / 70 years).
That's a good point. Of course if you can produce tritium cheap enough it might be feasible to just start each mission with a grossly over-powered nuclear battery.
Nuclear waste is waste because it doesn't contain enough fissile nuclides (i.e. nuclides, which could produce heat in fission). It has almost nothing to do with radioactivity or decay power. Radioactivity just makes it harder to manage.
But you have it right: The decay power density of nuclear waste is quite soon not enough for such a probe.
