On the topic of building a calutron, let's design a calutron to separate lithium into its isotopes. Let's make it like the original, ions travel 180
degrees before hitting the collector cup.
The cyclotron formula:
E = q^2 B^2 r^2 / (2m)
Energy (E): let's assume the ion source is a simple ion gun, no fancy accelerator stages. The largest transformer I have is 75kV 5ma and I doubt many
people can beat that, so I will assume the energy of both Li-6 and Li-7 is 75keV.
Charge (q): the charge of Li+ ions is 1 elementary charge
Magnetic field (B): iron cores saturate at 1.6 T so I will assume that will be our field, although it is highly ambitious to actually achieve this
field strength
Radius (r): that is what we are solving for
Mass (m): Li-6 is 6 amu, Li-7 is 7 amu
If we plug in all the numbers and solve for radius, we get:
Li-6, 60.4 mm
Li-7, 65.2 mm
Therefore the magnetic poles will have to be a minimum of 130.4 mm (5 inches) in diameter.
Now let's take a look at a real magnet, like a Varian V-3400 NMR magnet. It is 9 inches in diameter and "The magnet weighs 1780 pounds, it requires 40
volts at 168 amps, 7Kilowatts, to produce the maximum field of 1.2 Tesla." Recalculating the above values with 1.2 tesla gives 80.5 mm and 86.9 mm for
Li-6 and -7 respectively. The diameter of the ion arc is 6.842 inches which will fit nicely into a 9" magnet.
The targets for Li-6 and Li-7 will have to be 2x(86.9 - 80.5) = 12.8 mm apart. That means the spot size of the beam also has to be 12.8 mm or less in
order not to overlap (though some overlap is expected anyway). Sounds generous but that means the ion beam half-angle should be no greater than 1.34
degrees, so simple optics and tuning will be required.
Now suppose a lithium calutron was built, how long would it take to process a gram (144 mmol) of lithium? That's 8.672×10^22 atoms which is 13.89 kC
of charge. At 5mA it will take 32 days 3 hours 40 minutes, assuming 100% efficiency. In reality, it will be more like 1 year to process 1 gram of
natural lithium metal. More current will speed things up, but even the transformer I used for this example is already massive.
In 32 days it will cost $20.16 in electricity to run the transformer (5mA * 75 kV * 32 days * [7 cents per kilowatt hour]), $376.32 for the
electromagnet, and possibly a similar amount for the vacuum pumps. If it did end up taking an entire year it would cost $230 and $4292 for the two.
If you just want to prove a point, making 1 mg should be enough and will be much cheaper.
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